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Lesson 1: Volume of Cylinders

• • Volume of Cylinders – Page No. 402
  • Volume of Cylinders – Page No. 403
  • Volume of Cylinders – Page No. 404

Lesson 2: Volume of Cones

• • Volume of Cones – Page No. 408
  • Volume of Cones – Page No. 409
  • Volume of Cones – Page No. 410

Lesson 3: Volume of Spheres

• • Volume of Spheres – Page No. 414
  • Volume of Spheres – Page No. 415
  • Volume of Spheres – Page No. 416

Model Quiz :

• • Model Quiz – Page No. 417

Review :

• • Mixed Review – Page No. 418

Guided Practice – Volume of Cylinders – Page No. 402

Question 1.
Vocabulary Describe the bases of a cylinder.
Type below:
____________

Answer:
The ends of a cylinder are the bases of the cylinder of the two flat surfaces.

Question 2.
Figure 1 shows a view from above of inch cubes on the bottom of a cylinder. Figure 2 shows the highest stack of cubes that will fit inside the cylinder. Estimate the volume of the cylinder. Explain your reasoning.

________ in³

Answer:

427in³

Explanation:
Number of inch cubes that fit in the base of the cylinder = 61
Number of inch cubes that fit in the length of the cylinder = 7
The volume of cylinder = base area x height
V= 61 x 7
V = 427 cubic units.
Volume of each cube = 1 in³
Volume of cylinder = 427in³

Lesson 13.1 Volume of Cylinders Practice and Problem Solving a/b Question 3.
Find the volume of the cylinder to the nearest tenth. Use 3.14 for π.

The volume of the cylinder is approximately _____ m³.
________ m³

Answer:
The volume of the cylinder is approximately 1695.6 m³.
1695.6m³

Explanation:
V = πr²h
V = π . 6² . 15
V = 3.14 × 36 × 15
V = 1695.6m³

Question 4.
A Japanese odaiko is a very large drum that is made by hollowing out a section of a tree trunk. A museum in Takayama City has three odaikos of similar size carved from a single tree trunk. The largest measures about 2.7 meters in both diameter and length, and weighs about 4.5 metric tons. Using the volume formula for a cylinder, approximate the volume of the drum to the nearest tenth.
The radius of the drum is about _____ m.
The volume of the drum is about _____ m³.
The radius of the drum is about ___________ m
The volume of the drum is about ___________ m³

Answer:
The radius of the drum is about 1.35 m.
The volume of the drum is about 15.5 m³.

Explanation:
Diameter of base of drum = 2.7 m
The radius of the base of the drum = 2.7/2
R = 1.35 m
The volume of cylinder = πr²h
Height (h) = 2.7 m
Radius (R) = 1.35 m
Volume = 3.14 × (1.35) × 2.7
V = 15.4511 m³
V = 15.5 m³

ESSENTIAL QUESTION CHECK-IN

Question 5.
How do you find the volume of a cylinder? Describe which measurements of a cylinder you need to know.
Type below:
____________

Answer:
The volume of the cylinder is = πr²h

Explanation:
We need to find the radius of the base, r, and the height of the cylinder, h.
The volume of the cylinder is = πr²h

13.1 Independent Practice – Volume of Cylinders – Page No. 403

Find the volume of each figure. Round your answers to the nearest tenth if necessary. Use 3.14 for π.

Question 6.

_________ cm³

Answer:
569.9 cm³

Explanation:
Radius of base = 11 cm
Height of cylinder = 1.5 cm
The volume of the cylinder = πr²h
V = 3.14 × (11)² × 1.5
V = 569.91
V = 569.9 cm³

Question 7.

_________ in³

Answer:
1205.8 in³

Explanation:
Radius of base = 4 in
Height of cylinder = 24 in
The volume of cylinder = πr²h
V = 3.14 × (4)² × 24
V = 1205.76
V = 1205.8 in³

8th Grade Review for Volume of Cylinders, Cones, and Spheres Answer Key Question 8.

_________ m³

Answer:
1256 m³

Explanation:
Radius of base = 5 m
Height of cylinder = 16 m
The volume of the cylinder = πr²h
V = 3.14 × (5)² × 16
V = 1256
V = 1256 m³

Question 9.

_________ in³

Answer:
942 in³

Explanation:
Diameter of base = 10 in
Radius of base = 5 in
Height of cylinder = 12 in
The volume of the cylinder = πr²h
V = 3.14 × (5)² × 12
V = 942 in³

Question 10.
A cylinder has a radius of 4 centimeters and a height of 40 centimeters.
_________ cm³

Answer:
2009.6 cm³

Explanation:
Radius of base = 4 cm
Height of cylinder = 40 cm
The volume of cylinder = πr²h
V = 3.14 × (4)² × 40
V = 2009.6 cm³

Question 11.
A cylinder has a radius of 8 meters and a height of 4 meters.
_________ m³

Answer:
803.8 m³

Explanation:
The radius of base = 8 m
Height of cylinder = 4 m
The volume of the cylinder = πr²h
V = 3.14 × (8)² × 4
V = 803.84 m³
V = 803.8 m³

Round your answer to the nearest tenth, if necessary. Use 3.14 for π.

Question 12.
The cylindrical Giant Ocean Tank at the New England Aquarium in Boston is 24 feet deep and has a radius of 18.8 feet. Find the volume of the tank.
_________ ft³

Answer:
26635.2 ft³

Explanation:
The base radius of the tank = 18.8 ft
Depth of the tank in the ocean = 24 ft
The volume of the cylinder = πr²h
V = 3.14 × (18.8)² × 24
V = 3.14 × 354.44 × 24
V = 26635.2384 ft³
V = 26635.2 ft³

Question 13.
A standard-size bass drum has a diameter of 22 inches and is 18 inches deep. Find the volume of this drum.
_________ in³

Answer:
6838.9 in³

Explanation:
The base diameter of the drum = 22 in
Base radius of the drum = 22/2 = 11 in
Depth of the bass drum = 18 in
The volume of the bass drum = πr²h
V = 3.14 × (11)² × 18
V = 3.14 × 121 × 18
V = 6838.92 in³
V = 6838.9 in³

Question 14.
Grain is stored in cylindrical structures called silos. Find the volume of a silo with a diameter of 11.1 feet and a height of 20 feet.
_________ ft³

Answer:
1934.4 ft³

Explanation:
Base diameter of silo = 11.1 ft
Base radius of the silo = 11.1/2 = 5.55 ft
Depth of the silo = 20 ft
Volume of the silo = πr²h
V = 3.14 × (5.55)² × 18
V = 3.14 × 30.8025 × 18
V = 1934.397 ft³
V = 1934.4 ft³

Question 15.
The Frank Erwin Center, or “The Drum,” at the University of Texas in Austin can be approximated by a cylinder that is 120 meters in diameter and 30 meters in height. Find its volume.
_________ m³

Answer:
339120 m³

Explanation:
Base diameter of the drum = 120 m
Base radius of the drum = 120/2 = 60 m
Height of the drum = 30 m
Volume of the drum = πr²h
V = 3.14 × (60)² × 30
V = 3.14 × 3600 × 30
V = 339120 m³

Volume of Cylinders – Page No. 404

Question 16.
A barrel of crude oil contains about 5.61 cubic feet of oil. How many barrels of oil are contained in 1 mile (5280 feet) of a pipeline that has an inside diameter of 6 inches and is completely filled with oil? How much is “1 mile” of oil in this pipeline worth at a price of $100 per barrel?
__________ barrels
$ __________

Answer:
184.7 barrels
$18470

Explanation:
Volume of barrel = 5.61 cubic feet
Length of the pipe = 1 mile = 5280 feet
Diameter of the pipe = 6 inches = 0.5 feet
Radius of the pipe = 6/2 inches = 3 inches = 0.25 feet
Volume of oil in the pipe = πr²h = 3.14 × (0.25)² × 5280 = 1036.2 cubic feet
Number of barrels in the pipe = 1036.2/5.61 = 184.7 barrels
Cost of one barrel = $100
Cost of 184.7 barrels =184.7 × $100 = $18470

Question 17.
A pan for baking French bread is shaped like half a cylinder. It is 12 inches long and 3.5 inches in diameter. What is the volume of uncooked dough that would fill this pan?

_________ in³

Answer:
57.697 in³

Explanation:
The length of the pan = 12 in
The diameter of the pan = 3.5 in
Radius = 3.5/2 = 1.75 in
The volume of uncooked dough = Half the volume of the full cylinder of the above dimensions.
= (πr²h)/2 = (3.14 × (1.75)² × 12)/2 = 115.395/2 = 57.697 in³

FOCUS ON HIGHER ORDER THINKING

Question 18.
Explain the Error A student said the volume of a cylinder with a 3-inch diameter is two times the volume of a cylinder with the same height and a 1.5-inch radius. What is the error?
Type below:
_______________

Answer:
The volume of the cylinder of 3 in is four times the volume of the new cylinder of radius 1.5 in

Explanation:
The volume of a cylinder is directly proportional to the square of the radius of the cylinder. The volume does not depend on the radius linearly.
Volume = πr²h
V1 = π(3)²h
V2 = π(1.5)²h
V1/V2 = (π(3)²h)/(π(1.5)²h)
V1/V2 = 4
V1 = 4V2

Volume of Cylinders and Cones Mini Quiz Answer Key Question 19.
Communicate Mathematical Ideas Explain how you can find the height of a cylinder if you know the diameter and the volume. Include an example with your explanation.
Type below:
_______________

Answer:
Let the diameter be D.
Radius r = D/2
Volume = πr²h
Volume = π(D/2)²h
V = π((D)²/4)h
h = 4V/π(D)²
To find the height of a cylinder with diameter D = 2 m
Let the volume be 10 m³
h = 4V/π(D)²
h = (4 × 10)/(3.14 × 2²)
h = 3.18 m³

Question 20.
Analyze Relationships Cylinder A has a radius of 6 centimeters. Cylinder B has the same height and a radius half as long as cylinder A. What fraction of the volume of cylinder A is the volume of cylinder B? Explain.
Fraction: \(\frac{□}{□}\)

Answer:
\(\frac{VA}{4}\)

Explanation:
rA = 6 cm
rB = half of the radius of cylinder A = 3 cm
hA = hB
VA = πrA²h
VB = πrB²h
VA/VB = (πrA²h)/(πrB²h)
VA/VB = 6²/3² = 36/9 = 4
Thus VB = VA/4

Guided Practice – Volume of Cones – Page No. 408

Question 1.
The area of the base of a cylinder is 45 square inches and its height is 10 inches. A cone has the same area for its base and the same height. What is the volume of the cone?

The volume of the cone is _____ in³.
_________ in³

Answer:
150 in³

Explanation:
In the question, the area of the base of the cylinder, B = 45 in²
Height of the cylinder, h = 10 inch
Volume of the cylinder, V cylinder = B × h = 45 × 10 = 450 inch³
Volume of the cone, V Cone = 1/3 V cylinder
=1/3(450 inch) = 150 inch³
So, the volume of the cone is
Vcone = 150 in³

Volume of Cylinders and Cones Mini Quiz Answer Key Question 2.
A cone and a cylinder have congruent heights and bases. The volume of the cone is 18 m³. What is the volume of the cylinder? Explain.
_________ m³

Answer:
54 m³

Explanation:
The volume of the cone is 18 m³.
Vcone = 1/3 Vcylinder
Vcylinder = 3Vcone
Vcylinder = 3.18
Vcylinder = 54 m³

Find the volume of each cone. Round your answer to the nearest tenth if necessary. Use 3.14 for π.

Question 3.

_________ ft³

Answer:
65.94 ft³

Explanation:
the diameter of the cone is 6ft.
so, the radius of the cone is 3ft.
the height of the cone is 7ft.
the volume of the cone = 1/3 × πr²h = 1/3 × 3.14 × 3² × 7 = 65.94 ft³

Question 4.

_________ in³

Answer:
113982in³

Explanation:
The radius is 33inch and the height is 100 inch
Volume of the cone = 1/3 × πr²h = 1/3 × π(33)²100 = 113982in³

Question 5.
Gretchen made a paper cone to hold a gift for a friend. The paper cone was 15 inches high and had a radius of 3 inches. Find the volume of the paper cone to the nearest tenth. Use 3.14 for π.
_________ in³

Answer:
141.3in³

Explanation:
the radius of the cone is 3inch and the height of the cone is 15inch.
Volume of the cone = 1/3 × πr²h = 1/3 × π(3)² × 15 = 141.3in³

Question 6.
A cone-shaped building is commonly used to store sand. What would be the volume of a cone-shaped building with a diameter of 50 meters and a height of 20 meters? Round your answer to the nearest tenth. Use 3.14 for π.
_________ m³

Answer:
13083.33 m³

Explanation:
The diameter of the cone is 50 meters. So, the radius of the cone is 25 meters. The height of the cone is 20 meters.
Volume of the cone = 1/3 × πr²h = 1/3 × π(25)² × 20 = 13083.33 m³

ESSENTIAL QUESTION CHECK-IN

Question 7.
How do you find the volume of a cone?
Type below:
____________

Answer:
V cone = 1/3 V cylinder
V cone = 1/3 πr²h

13.2 Independent Practice – Volume of Cones – Page No. 409

Find the volume of each cone. Round your answers to the nearest tenth if necessary. Use 3.14 for π.

Question 8.

_________ mm³

Answer:
410.3 mm³

Explanation:
Radius r = 7 mm
height = 8 mm
Volume of cone = 1/3 πr²h
Volume = 1/3(3.14)(7)²(8)
Volume = 410.29 mm³
Volume = 410.3 mm³

Question 9.

_________ in³

Answer:
25.1 in³

Explanation:
Radius r = 2 in
Height = 6 in
Volume of cone = 1/3 πr²h
Volume = 1/3(3.14)(2)²(6)
Volume = 25.12 in³
Volume = 25.1 in³

Lesson 2 Extra Practice Volume of Cones Answers Key Question 10.
A cone has a diameter of 6 centimeters and a height of 11.5 centimeters.
_________ cm³

Answer:
108.3 cm³

Explanation:
Diameter of base = 6 cm
Radius = 6/2 cm = 3 cm
Height = 11.5 cm
Volume of cone = 1/3 πr²h
Volume = 1/3(3.14)(3)² (11.5)
Volume = 108.33 cm³
Volume = 108.3 cm³

Question 11.
A cone has a radius of 3 meters and a height of 10 meters.
_________ m³

Answer:
94.2 m³

Explanation:
Radius r = 3 m
Height = 10 m
Volume of cone = 1/3 πr²h
Volume = 1/3(3.14)(3)²(10)
Volume = 94.2 m³

Round your answers to the nearest tenth if necessary. Use 3.14 for π.

Question 12.
Antonio is making mini waffle cones. Each waffle cone is 3 inches high and has a radius of \(\frac{3}{4}\) inch. What is the volume of a waffle cone?
_________ in³

Answer:
1.8 in³

Explanation:
Radius = 3/4 in
Radius r = 0.75 in
Height = 3 in
Volume of each waffle cone = 1/3 πr²h
Volume = 1/3 (3.14) (0.75)² (3)
Volume = 1.76625 in³
Volume = 1.8 in³

Question 13.
A snack bar sells popcorn in cone-shaped containers. One container has a diameter of 8 inches and a height of 10 inches. How many cubic inches of popcorn does the container hold?
_________ in³

Answer:
167.5 in³

Explanation:
Diameter of base = 8 in
Radius = 8/2 in = 4 in
Height = 10 in
Volume of cone = 1/3 πr²h
Volume = 1/3 (3.14) (4)² (10)
Volume = 167.466 in³
Volume = 167.5 in³

Question 14.
A volcanic cone has a diameter of 300 meters and a height of 150 meters. What is the volume of the cone?
_________ m³

Answer:
3534291.7 m³

Explanation:
Diameter of base = 300 m
Radius = 300/2 m = 150 m
Height = 150 m
Volume of cone = 1/3 πr²h
Volume = 1/3 (3.14) (150)² (150)
Volume = 3534291.735 m³
Volume = 3534291.7 m³

The volume of Cones Answers Key Question 15.
Multistep Orange traffic cones come in a variety of sizes. Approximate the volume, in cubic inches, of a traffic cone that has a height of 2 feet and a diameter of 10 inches. Use 3.14 for π.
_________ in³

Answer:
628 in³

Explanation:
The radius of the cone is Diameter/2 = 10/2 = 5
The height of the cone is 2 ft = 2 . 12 = 24 in
Vcone = 1/3 πr²h
Vcone = 1/3 (3.14) (5)² (24)
Vcone = 628 in³

Find the missing measure for each cone. Round your answers to the nearest tenth if necessary. Use 3.14 for π.

Question 16.
radius = _______
height = 6 in.
volume = 100.48 in3
_________ in.

Answer:
radius = 4 in.
4 in.

Explanation:
Let radius be R.
Height = 6 in
Volume = 100.4 in
Volume of cone = 1/3 πr²h
√(3v/hπ) = R
√((3 × 100.48)/(18.84)) = R
√(301.44/18.84) = R
R = √(16)
R = 4 in

Question 17.
diameter = 6 cm
height = _______
volume = 56.52 cm³
_______ cm

Answer:
height = 6 cm
h = 6 cm

Explanation:
Let height be h
Diameter = 6 cm
Radius = 6/2 = 3 cm
Volume = 56.52 cm
Volume of cone = 1/3 πr²h
(3V/r²h) = h
(3 × 56.52)/(3² × 3.14) = h
169.56/28.26 = h
h = 6 cm

Question 18.
The diameter of a cone-shaped container is 4 inches, and its height is 6 inches. How much greater is the volume of a cylinder-shaped container with the same diameter and height? Round your answer to the nearest hundredth. Use 3.14 for π.
Type below:
____________

Answer:
The volume of the cylinder is 50.24 in³ greater than the volume of the cone.

Explanation:
The diameter of a cone, d = 4 inch
radius of a cone, r = d/2 = 4/2 = 2 inches
height of a cone, h = 6 inches.
So, the volume of a cone, V cone = 1/3 πr²h
= 1/3 (3.14) (2)² (6)
= 25.12 in³
And the volume of a cylinder with the same diameter and height,
V cylinder = πr²h = (3.14) (2)² (6) = 75.36 in³
The volume of the cylinder is 50.24 in³ greater than the volume of the cone.

FOCUS ON HIGHER ORDER THINKING – Volume of Cones – Page No. 410

Question 19.
Alex wants to know the volume of sand in an hourglass. When all the sand is in the bottom, he stands a ruler up beside the hourglass and estimates the height of the cone of sand.
a. What else does he need to measure to find the volume of sand?
____________

Answer:
To find the volume of the sand, he needs to measure the radius of the base of the hourglass.

Question 19.
b. Make a Conjecture If the volume of sand is increasing at a constant rate, is the height increasing at a constant rate? Explain.
____________

Answer:
The volume of the cone is linearly proportional to the height of the cone. Therefore, if the volume is increasing at a constant rate, the height is also increasing at a constant rate.

Question 20.
Problem Solving The diameter of a cone is x cm, the height is 18 cm, and the volume is 301.44 cm³. What is x? Use 3.14 for π.
________ cm

Answer:
8 cm

Explanation:
V cone = 1/3 πr²h
301.44 = 1/3 . 3.14 . r² . 18
r² = 904.32/56.52
r² = 16
r = 4 cm
The diameter of the circle is twice its radius, therefore
x = 2 . r
x = 2 . 4
x = 8 cm

Question 21.
Analyze Relationships A cone has a radius of 1 foot and a height of 2 feet. How many cones of liquid would it take to fill a cylinder with a diameter of 2 feet and a height of 2 feet? Explain.
________ cones

Answer:
3 cones

Explanation:
The diameter of the base of the cylinder is 2 feet, which means that its radius is 1 foot. Its height is 2 feet. The volume of this cylinder is
V cylinder = πr²h
V cylinder = (3.14) (1)² (2)
V cylinder = 6.28
The radius of the cone is 1 foot and the height of the cone is 2 feet. The volume of the cone is:
V cone = 1/3 πr²h
V cone = 1/3 (3.14) (1)² (2)
V cone = 1/3 × 6.28
V cone = 1/3 . V cylinder
V cone = 2.09
It would take 3 cones of liquid to fill the cylinder.

Question 22.
Critique Reasoning Herb knows that the volume of a cone is one third that of a cylinder with the same base and height. He reasons that a cone with the same height as a given cylinder but 3 times the radius should therefore have the same volume as the cylinder, since \(\frac{1}{3}\) ⋅ 3 = 1. Is Herb correct? Explain.
____________

Answer:
The volume of the given cylinder is V cylinder = πr²h
The volume of the cone with the same height h as a given cylinder but 3 times the radius r is
V cone = 1/3 π(3r)²h
V cone = 3 πr²h
V cone = 3 V cylinder
As we can see, Herb is not correct. The volume of the cone is not equal to the volume of the cylinder. But it is three times the volume of the cylinder.

Guided Practice – Volume of Spheres – Page No. 414

Question 1.
Vocabulary A sphere is a three-dimensional figure with all points _____ from the center.
Type below:
____________

Answer:
A sphere is a three-dimensional figure with all points at equal distances from the center.

Lesson 13.2 Volume of Cones Practice and Problem Solving a/b Answers Question 2.
Vocabulary The _____ is the distance from the center of a sphere to a point on the sphere.
Type below:
____________

Answer:
radius

Explanation:
The radius is the distance from the center f the sphere to a point on the sphere

Find the volume of each sphere. Round your answers to the nearest tenth if necessary. Use 3.14 for π.

Question 3.

_______ in³

Answer:
4.12 in³

Explanation:
V = 4/3πr³
V = 4/3 (3.14) (1)³
V = 4.12 in³

Question 4.

_______ cm³

Answer:
4186.7 cm³

Explanation:
Diameter = 20 cm
Radius r = 20/2 = 10 cm
Volume of sphere = 4/3πr³
Volume = 4/3 (3.14) (10)³
Volume = 4186.66 cm³
Volume = 4186.7 cm³

Question 5.
A sphere has a radius of 1.5 feet.
_______ ft³

Answer:
14.1 ft³

Explanation:
Radius r = 1.5 ft
The volume of the sphere = 4/3πr³
Volume = 4/3 (3.14) (1.5)³
Volume = 14.13 ft³
Volume = 14.1 ft³

Question 6.
A sphere has a diameter of 2 yards.
_______ yd³

Answer:
4.2 yd³

Explanation:
Diameter = 2 yards
Radius r = 2/2 yards
Radius r = 1 yd
Volume of sphere = 4/3πr³
Volume = 4/3 (3.14) (1)³
Volume = 4.1866 yd³
Volume = 4.2 yd³

Question 7.
A baseball has a diameter of 2.9 inches. Find the volume of the baseball. Round your answer to the nearest tenth if necessary. Use 3.14 for π.
_______ in³

Answer:
12.8 in³

Explanation:
Diameter of baseball = 2.9 in
Radius r = 2.9/2 in
Radius of baseball = 1.45 in
The volume of the sphere = 4/3πr³
Volume = 4/3 (3.14) (1.45)³
Volume = 12.763 in³
Volume = 12.8 in³

Lesson 13.3 Volume of Spheres Practice and Problem Solving a/b Question 8.
A basketball has a radius of 4.7 inches. What is its volume to the nearest cubic inch? Use 3.14 for π.
_______ in³

Answer:
1304 in³

Explanation:
Radius of baseball = 4.7 in
The volume of the sphere = 4/3πr³
Volume = 4/3 (3.14) (4.7)³
Volume = 1304.0168 in³
Volume = 1304 in³

Question 9.
A company is deciding whether to package a ball in a cubic box or a cylindrical box. In either case, the ball will touch the bottom, top, and sides.

a. What portion of the space inside the cylindrical box is empty? Explain.
Type below:
_______________

Answer:
The volume of the cylinder is V cylinder = πr²h
Since the ball touches the bottom, top, and sides, then the height of the cylinder will be equal to 2r.
V cylinder = πr²(2r) = 2πr³
On the other hand, the volume of the sphere is
V sphere = 4/3 πr³
The volume of the empty space inside the cylindrical box is found by subtracting the volume of the sphere from the volume of the cylinder
V cylinder – V sphere = 2πr³ – 4/3 πr³
= (2 – 4/3)πr³
= 2/3πr³

Question 9.
b. Find an expression for the volume of the cubic box.
Type below:
_______________

Answer:
The volume of a cube with side a is V cube = a³
Since the ball touches the bottom, top, and sides, then the side of the cube will be equal to 2r.
V cube = (2r)³
V cube = 8r³

Question 9.
c. About what portion of the space inside the cubic box is empty? Explain
Type below:
_______________

Answer:
The volume of the empty space inside the cubical box is found by subtracting the volume of the sphere from the volume of the cube:
V cube – V sphere = 8r³ – 4/3 πr³
= (8 – 4/3π)r³
= (8 – 4.2)r³
= 3.8r³

ESSENTIAL QUESTION CHECK-IN

Question 10.
Explain the steps you use to find the volume of a sphere.
Type below:
_______________

Answer:
Step 1: The radius of the sphere is found out.
Step 2: The volume of the sphere is 4/3 πr³; where R is the radius.
Step 3: Put the value of radius in the equation of volume.
Step 4: Calculate the volume.

13.3 Independent Practice – Volume of Spheres – Page No. 415

Find the volume of each sphere. Round your answers to the nearest tenth if necessary. Use 3.14 for π.

Question 11.
radius of 3.1 meters
_______ m³

Answer:
124.7 m³

Explanation:
The volume of the sphere with a radius of 3.1 meter is 4/3 πr³
V = 4/3 . (3.14) . (3.1)³
V = 124.7 m³

Question 12.
diameter of 18 inches
_______ in³

Answer:
3052.1 in³

Explanation:
The diameter of the sphere is 18 inches, which means that its radius is 9 inches. The volume of the sphere is
V = 4/3 πr³
V = 4/3 . (3.14) . (9)³
V = 3052.08 in³
V = 3052.1 in³

Volume of Cylinders Cones and Spheres Iready Answers Question 13.
r = 6 in.
_______ in³

Answer:
904.3 in³

Explanation:
The volume of the sphere with a radius of 6 inches is
V = 4/3 πr³
V = 4/3 (3.14) (6)³
V = 904.32
V = 904.3 in³

Question 14.
d = 36 m
_______ m³

Answer:
24416.6 m³

Explanation:
d = 36 m
radius r = 36/2 = 18 m
Volume = 4/3 πr³
= 4/3 (3.14) (18)³
= 24416.64
Volume = 24416.6 m³

Question 15.

_______ cm³

Answer:
5572.5 cm³

Explanation:
The volume of the sphere with a radius of 11 centimeters is
V = 4/3 πr³
V = 4/3 (3.14) (11)³
V = 5572.5 cm³

Question 16.

_______ ft³

Answer:
8.2 feet³

Explanation:
The diameter of the sphere is 2.5 feet, which means that its radius is 1.25 feet. The volume of the sphere is
V = 4/3 πr³
V = 4/3 . (3.14) . (1.25)³
V = 8.2 feet³

The eggs of birds and other animals come in many different shapes and sizes. Eggs often have a shape that is nearly spherical. When this is true, you can use the formula for a sphere to find their volume.

Question 17.
The green turtle lays eggs that are approximately spherical with an average diameter of 4.5 centimeters. Each turtle lays an average of 113 eggs at one time. Find the total volume of these eggs, to the nearest cubic centimeter.
_______ cm³

Answer:
5389 cm³

Explanation:
The diameter of an egg (sphere) is 4.5 centimeters, which means that its radius is 2.25 centimeters. The volume of a single egg is
V = 4/3 πr³
V = 4/3 (3.14) (2.25)³
V = 47.68875 cm³
Therefore, the total volume of 113 eggs is
113 . V = 113(47.68875)
= 5388.82875
= 5389 cm³

Question 18.
Hummingbirds lay eggs that are nearly spherical and about 1 centimeter in diameter. Find the volume of an egg. Round your answer to the nearest tenth.
_______ cm³

Answer:
0.5 cm³

Explanation:
The diameter of an egg (sphere) is 1 centimeter, which means that its radius is 0.5 centimeters. The volume of a single egg is
V = 4/3 πr³
V = 4/3 (3.14) (0.5)³
V = 0.5 cm³

Question 19.
Fossilized spherical eggs of dinosaurs called titanosaurid sauropods were found in Patagonia. These eggs were 15 centimeters in diameter. Find the volume of an egg. Round your answer to the nearest tenth.
_______ cm³

Answer:
1766.25 cm³

Explanation:
Diameter of an egg = 15 cm
Its radius = 15/2 = 7.5 cm
Volume = 4/3 πr³
V = 4/3 (3.14) (7.5)³
V = 1766.25 cm³

Volume and Surface Area of Spheres Question 20.
Persevere in Problem Solving An ostrich egg has about the same volume as a sphere with a diameter of 5 inches. If the eggshell is about \(\frac{1}{12}\) inch thick, find the volume of just the shell, not including the interior of the egg. Round your answer to the nearest tenth.
_______ in³

Answer:
6.8 in³

Explanation:
Diameter including the eggshell
= 5 + (2 . 1/2)
= (5 + 1/6) in
= 5.166 in
Radius including eggshell = 5.166/2 = 2.5833 in
Volume = 4/3 πr³
Volume = 4/3 (3.14) (2.5833)³
=72.176 in³
Volume with shell = 72.2 in³
Radius excluding shell = 5/2 = 2.5 in
Volume = 4/3 (3.14) (2.5)³
= 65.416 in³
Volume (without shell) = 65.4 in³
Volume of shell = Total volume – Inner Volume
= 72.2 – 65.4
= 6.8 in³

Question 21.
Multistep Write the steps you would use to find a formula for the volume of the figure at right. Then write the formula.

Type below:
_____________

Answer:
5/3πr³

Explanation:
The radius of the hemisphere = r
The radius of cylinder = r
Height of cylinder = r
Step 1: Find the formula for the volume of a hemisphere
The volume of hemisphere = 4/3 π/2 r³
= 2/3πr³
Step 2: Find the formula for the volume of a cylinder
The volume of the cylinder = πr²h
=πr³
Step 3: Add both the volume expressions:
Total volume = 2/3πr³ + πr³
= 5/3πr³

Volume of Spheres – Page No. 416

Question 22.
Critical Thinking Explain what happens to the volume of a sphere if you double the radius.
Type below:
_____________

Answer:
Let Radius = r
Volume V1 = 4/3πr³
Radius = 2r
Volume V2 = 4/3π(2r)³
= 8 . 4/3πr³
= 8 V1
= 8(initial volume)
By doubling the radius of the sphere we make the volume 8 times the initial value.

Question 23.
Multistep A cylindrical can of tennis balls holds a stack of three balls so that they touch the can at the top, bottom, and sides. The radius of each ball is 1.25 inches. Find the volume inside the can that is not taken up by the three tennis balls.

_______ in³

Answer:
12.3 in³

Explanation:
Radius of the ball = 1.25 inch
Height of the cylinder = (2 × 1.25) × 3
= (2.5) × 3
= 7.5 in
radius of base of cylinder = 1.25 in.
Volume of cylinder = πr²h
= (3.14) (1.25)² (7.5)
= 36.7968
= 36.8 in³
Volume of a ball (all three) = 3 × 4/3πr³
= 4 (3.14) (1.25)³
= 24.53125 in³
= 24.5 in³
Volume of empty space = Volume of cylinder – Volume of ball
= 36.8 – 24.5 = 12.3 in³

FOCUS ON HIGHER ORDER THINKING

Question 24.
Critique Reasoning A sphere has a radius of 4 inches, and a cube-shaped box has an edge length of 7.5 inches. J.D. says the box has a greater volume, so the sphere will fit in the box. Is he correct? Explain.
_____________

Answer:
The volume of sphere = 4/3πr³
= 4/3 (3.14) (4)³
= 267.9466
= 268
The volume of cube = (7.5)³
= 421.875
=421.9
The volume of cube > Volume of a sphere
But the base of the cube has an area of (7.5 × 7.5) = 56.25 while the cross-action area of the sphere.
πr² = (3.14) (4)² = 50.24
The cross-section area of the cube is less than that of a sphere. thus J.D. is wrong and the ball (sphere) will not fit in the cube.

Question 25.
Critical Thinking Which would hold the most water: a bowl in the shape of a hemisphere with radius r, a cylindrical glass with radius r and height r, or a cone-shaped drinking cup with radius r and height r? Explain.
_____________

Answer:
The volume of a sphere with radius r is
V sphere = 4/3πr³
Therefore, the volume of a hemisphere is
V hemisphere = V sphere/2
V hemisphere = 2/3πr³
The volume of a cylinder with radius r and height r is
V cylinder = πr²h
V cylinder = πr³
The volume of a cone with radius r and height r is
V cone = 1/3πr²h
V cone = 1/3πr³
V cone < V hemisphere < V cylinder
Therefore, the cylindrical glass with radius r and height r will hold the most water.

8th Grade Review for Volume of Cylinders, Cones, and Spheres Answer Key Question 26.
Analyze Relationships Hari has models of a sphere, a cylinder, and a cone. The sphere’s diameter and the cylinder’s height are the same, 2r. The cylinder has radius r. The cone has diameter 2r and height 2r. Compare the volumes of the cone and the sphere to the volume of the cylinder.
Type below:
_____________

Answer:
Radius of sphere = 2r/2 = r
Volume of sphere = 4/3πr³
The radius of cylinder = r
Height of cylinder = 2r
volume of cylinder = πr²(2r)
V cylinder = 2πr³
Radius of cone = 2r/2 = r
Height of cone = 2r
Volume of cone = 1/3 πr²(2r)
V cone = 2/3πr³
Volume of cylinder > Volume of sphere > Volume of cone
2πr³ > 4/3πr³ > 2/3πr³

Question 27.
A spherical helium balloon that is 8 feet in diameter can lift about 17 pounds. What does the diameter of a balloon need to be to lift a person who weighs 136 pounds? Explain.
_______ feet

Answer:
Diameter of ballon = 8 ft
Weight it could lift = 17 pound
Volume = 4/3 π(8/2)³
= 4³(4π/3)
4³/x(4π/3) = 17/36
1/x = 1/8 × 3/4π × 1/48
x = 4π/3 . 4³ . 2³
x = 4/3. π . 8³
The volume of ballon which can lift 136 pounds is equal to 4/3. π . 8³
The radius of that ballon = 8ft
Diameter = 8 . 2 = 16 ft

Ready to Go On ? – Model Quiz – Page No. 417

13.1 Volume of Cylinders

Find the volume of each cylinder. Round your answers to the nearest tenth if necessary. Use 3.14 for π.

Question 1.

_______ ft³

Answer:
904.8 ft³

Explanation:
Radius of base = 6 ft
Height of cylinder = 8 ft
The volume of cylinder = πr²h
Volume = (3.14) (6)² (8)
Volume = 904.77 ft³
Volume = 904.8 ft³

Volume of Cylinders, Cones, and Spheres Iready Answers Question 2.
A can of juice has a radius of 4 inches and a height of 7 inches. What is the volume of the can?
_______ in³

Answer:
351.7 in³

Explanation:
Radius if cylindrical can = 4 in
Height of cylindrical can = 7 in
The volume of cylinder = πr²h
Volume = (3.14) (4)² (7)
Volume = 351.68 in³
Volume = 351.7 in³

13.2 Volume of Cones

Find the volume of each cone. Round your answers to the nearest tenth if necessary. Use 3.14 for π.

Question 3.

_______ cm³

Answer:
565.2 cm³

Explanation:
Radius of base of cone = 6 cm
Height of cone = 15 cm
Volume of cone = 1/3πr²h
Volume = 1/3 (3.14) (4)² (7)
Volume = 565.2 cm³

Question 4.

_______ in³

Answer:
3014.4 in³

Explanation:
The radius of the base of cone = 12 in
Height of cone = 20 in
The volume of cone = 1/3πr²h
Volume = 1/3 (3.14) (12)² (20)
Volume = 3014.4 in³

13.3 Volume of Spheres

Find the volume of each sphere. Round your answers to the nearest tenth if necessary. Use 3.14 for π.

Question 5.

_______ in³

Answer:
113 in³

Explanation:
Radius of sphere = 3 ft
Volume of sphere = 4/3πr³
Volume = 4/3 (3.14) (3)³
Volume = 113.04 ft³
Volume = 113 in³

Volume of Cylinders Cones and Spheres Iready Quiz Answers Question 6.

_______ cm³

Answer:
1149.8 cm³

Explanation:
Diameter = 13 cm
Radius = 13/2 cm = 6.5 cm
Volume of sphere = 4/3πr³
Volume = 4/3 (3.14) (6.5)³
Volume = 1149.7633 cm³
Volume = 1149.8 cm³

ESSENTIAL QUESTION

Question 7.
What measurements do you need to know to find the volume of a cylinder? a cone? a sphere?
Type below:
___________

Answer:
Sphere: To find the volume of the sphere, the radius is to be measured.
Cylinder: To measure the volume of the cylinder, we need to find out the base radius of the base of the cylinder along with the height of the cylinder.
Cone: To calculate the volume of the cone, we need to calculate the base radius of the base of the cone along with the height of the cone.

Explanation:
The volume of sphere = 4/3 πr³
Sphere: For finding the volume of the sphere, the radius is to be measured
The volume of Cylinder = πr²h
Cylinder: To calculate the volume of the cylinder, we need to find out the base radius of the base of the cylinder along with the height of the cylinder
The volume of Cone = 1/3 πr²h
Cone: To calculate the volume of the cone, we need to measure the base radius of the base of the cone along with the height of the cone

Selected Response – Mixed Review – Page No. 418

Question 1.
The bed of a pickup truck measures 4 feet by 8 feet. To the nearest inch, what is the length of the longest thin metal bar that will lie flat in the bed?
Options:
a. 11 ft 3 in.
b. 10 ft 0 in.
c. 8 ft 11 in.
d. 8 ft 9 in.

Answer:
d. 8 ft 9 in.

Explanation:
The length of the longest thin metal bar that will lie flat in the bed’s equal to the length of the bed’s hypotenuse. Let a = 4 and b = 8. Using the Pythagorean Theorem
a² + b² = c²
4² + 8² = c²
16 + 64 = c²
80 = c²
Rounding the length of the hypotenuse to the nearest tenth of a foot
c = 8.9 ft
Therefore, the length of the longest thin metal bar that will lie flat in the bed is 8 ft. 9 in.

Question 2.
Using 3.14 for π, what is the volume of the cylinder below to the nearest tenth?

Options:
a. 102 cubic yards
b. 347.6 cubic yards
c. 1,091.6 cubic yards
d. 4,366.4 cubic yards

Answer:
c. 1,091.6 cubic yards

Explanation:
Diameter of the base of the cylinder = 11.4 yd
Radius = 11.4/2 yd = 5.7 yd
Height = 10.7 ys
Volume of cylinder = πr²h
Volume = (3.14) (5.7)² (10.7)
Volume = 1091.599 yd³
Volume = 1091.6 yd³

Question 3.
Rhett made mini waffle cones for a birthday party. Each waffle cone was 3.5 inches high and had a radius of 0.8 inches. What is the volume of each cone to the nearest hundredth?
Options:
a. 1.70 cubic inches
b. 2.24 cubic inches
c. 2.34 cubic inches
d. 8.79 cubic inches

Answer:
c. 2.34 cubic inches

Explanation:
Height of each waffle cone = 3.5 in
Radius of base = 0.8 in
Volume of cone = 1/3 πr²h
Volume = 1/3 (3.14) (0.8)² (3.5)
Volume = 2.344533 in³
Volume = 2.34 in³

Question 4.
What is the volume of a cone that has a height of 17 meters and a base with a radius of 6 meters? Use 3.14 for π and round to the nearest tenth.
Options:
a. 204 cubic meters
b. 640.6 cubic meters
c. 2,562.2 cubic meters
d. 10,249 cubic meters

Answer:
b. 640.6 cubic meters

Explanation:
Height of the cone = 17 m
Radius of base = 6 m
Volume of cone = 1/3 πr²h
Volume = 1/3 (3.14) (6)² (17)
Volume = 640.56 m³
Volume = 640.6 m³

Lesson 13.3 Volume of Spheres Question 5.
Using 3.14 for π, what is the volume of the sphere to the nearest tenth?

Options:
a. 4,180 cubic centimeters
b. 5,572.5 cubic centimeters
c. 33,434.7 cubic centimeters
d. 44,579.6 cubic centimeters

Answer:
b. 5,572.5 cubic centimeters

Explanation:
Diameter of the base of the sphere = 22 cm
Radius = 22/2 yd = 11 cm
Volume of sphere = 4/3 πr³
Volume = 4/3 (3.14) (11)³
Volume = 5572.4533 cm³
Volume = 5572.5 cm³

Mini-Task

Question 6.
A diagram of a deodorant container is shown. It is made up of a cylinder and half of a sphere.

Use 3.14 for π and round answers to the nearest tenth.
a. What is the volume of the half sphere?
_______ cm³

Answer:
8.574 cm³

Explanation:
The radius of the cylinder as well as the hemisphere = 1.6 cm
Height = 6.2 cm
the volume of the hemisphere = 2/3 πr³
the volume of the hemisphere = 2/3 (3.14) (1.6)³
the volume of the hemisphere = 8.574 cm³

Question 6.
b. What is the volume of the cylinder?
_______ cm³

Answer:
49.838 cm³

Explanation:
The volume of cylinder = πr²h
= (3.14) (1.6)² (6.2)
= 49.838 cm³

Question 6.
c. What is the volume of the whole figure?
_______ cm³

Answer:
58.4 cm³

Explanation:
Total volume = Volume of cylinder + volume of a hemisphere
Total volume = 8.574 cm³ + 49.838 cm³
Total volume = 58.4 cm³

Conclusion:

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Students who are willing to practice more number of questions can Download Go Math Grade 4 Answer Key Homework Practice FL Chapter 10 Two-Dimensional Figures pdf. Here we provide the solutions for each and every question with pictures in an easy manner. With the help of Go Math Grade 4 Homework Practice FL Chapter 10 Answer Key, you can complete your homework in time.

Go Math Grade 4 Answer Key Homework Practice FL Chapter 10 Two-Dimensional Figures

The topics of Two-Dimensional Figures consist of Lines, Rays and Angles, Classify Triangles, Parallel Lines and Perpendicular Lines, Classify Quadrilaterals, Line Symmetry, and so on. All you have to do is to click on the below links and kickstart your preparation.

Lesson: 1 – Lines, Rays, and Angles

• Common Core – Two-Dimensional Figures – Page No. 189
• Common Core – Two-Dimensional Figures – Page No. 190

Lesson: 2 – Classify Triangles

• Common Core – Two-Dimensional Figures – Page No. 191
• Common Core – Two-Dimensional Figures – Page No. 192

Lesson: 3 – Parallel Lines and Perpendicular Lines

• Common Core – Two-Dimensional Figures – Page No. 193
• Common Core – Two-Dimensional Figures – Page No. 194

Lesson: 4 – Classify Quadrilaterals

• Common Core – Two-Dimensional Figures – Page No. 195
• Common Core – Two-Dimensional Figures – Page No. 196

Lesson: 5 – Line Symmetry

• Common Core – Two-Dimensional Figures – Page No. 197
• Common Core – Two-Dimensional Figures – Page No. 198

Lesson: 6 – Find and Draw Lines of Symmetry

• Common Core – Two-Dimensional Figures – Page No. 199
• Common Core – Two-Dimensional Figures – Page No. 200

Lesson: 7 – Problem Solving Shape Patterns

• Common Core – Two-Dimensional Figures – Page No. 201
• Common Core – Two-Dimensional Figures – Page No. 202

Chapter 10 – Extra Practice

• Common Core – Two-Dimensional Figures – Page No. 203
• Common Core – Two-Dimensional Figures – Page No. 204

Common Core – Two-Dimensional Figures – Page No. 189

Lines, Rays, and Angles

Draw and label an example of the figure.

Question 1.
obtuse ∠ABC

Think: An obtuse angle is greater than a right angle. The middle letter, B, names the vertex of the angle.
________

Answer:

Explanation:
An obtuse angle is greater than a right angle. The middle letter, B, names the vertex of the angle.

Question 2.
\(\overrightarrow{G H}\)

Answer:

Explanation:
GH is a ray that has one endpoint and continues without an end in one direction.

Question 3.
acute ∠JKL
________

Answer:

Explanation:
Angle JKL is an acute angle that is less than a right angle.

Question 4.
\(\overline{B C}\)

Answer:

Explanation:
BC is a line that continues without an end in both directions.

Use the figure for 5–8.

Question 5.
Name a line segment.

Answer:
line segment EF

Explanation:
EF line is a straight path of points that continues without an end in both directions.

Question 6.
Name a right angle.
∠ _____

Answer:
∠EJF

Explanation:
EJF is a right angle that forms a square corner.

Question 7.
Name an obtuse angle.
obtuse ∠ _____

Answer:
∠CEJ

Explanation:
CEJ is an obtuse angle that is greater than a right angle.

Problem Solving

Use the figure at the right for 9–11.

Question 9.
Classify ∠AFD
________

Answer:
Obtuse Angle

Explanation:
AFD is an obtuse angle that is greater than a right angle.

Question 10.
Classify ∠CFE.
________

Answer:
Right Angle

Explanation:
∠CFE is a right angle that forms a square corner.

Question 11.
Name two acute angles.
acute ∠ _____ acute ∠ _____

Answer:
∠AFB and ∠DFE

Explanation:
∠AFB and ∠DFE are two acute angles with less than a right angle.

Common Core – Two-Dimensional Figures – Page No. 190

Lesson Check

Question 1.
The hands of a clock show the time 12:25.

Which best describes the angle between the hands of the clock?
Options:
a. acute
b. right
c. obtuse
d. straight

Answer:
c. obtuse

Explanation:
The hands of the time 12:25 are forming greater than a right angle. So, the answer is the Obtuse angle.
Thus the correct answer is option c.

Question 2.
Which of the following name two different figures?
Options:
a. \(\overline{A B} \text { and } \overline{B A}\)
b. \(\overleftrightarrow { AB } \) and \(\overleftrightarrow { BA } \)
c. \(\overrightarrow { AB } \) and \(\overrightarrow { BA } \)
d. ∠ABC and ∠CBA

Answer: \(\overrightarrow { AB } \) and \(\overrightarrow { BA } \)

Explanation:
In \(\overrightarrow { AB } \) A is an end point and B continues without end in one direction.
In \(\overrightarrow { BA } \) B is an end point and A continues without an end in one direction.
Thus the correct answer is option c.

Spiral Review

Question 3.
Jan’s pencil is 8.5 cm long. Ted’s pencil is longer. Which could be the length of Ted’s pencil?
Options:
a. 0.09 cm
b. 0.8 cm
c. 8.4 cm
d. 9.0 cm

Answer:
d. 9.0 cm

Explanation:
9 ones is greater than 8 ones. So, 9.0 cm > 8.5 cm
Thus the correct answer is option d.

Question 4.
Kayla buys a shirt for $8.19. She pays with a $10 bill. How much change should she receive?
Options:
a. $1.81
b. $1.89
c. $2.19
d. $2.81

Answer:
a. $1.81

Explanation:
Kayla buys a shirt for $8.19. She pays with a $10 bill. To find the change she received, $10 – $8.19 = 1.81
Thus the correct answer is option a.

Question 5.
Sasha donated \(\frac{9}{100}\) of her class’s entire can collection for the food drive. Which decimal is equivalent to \(\frac{9}{100}\) ?
Options:
a. 9
b. 0.99
c. 0.9
d. 0.09

Answer:
d. 0.09

Explanation:
\(\frac{9}{100}\) is 9 hundredths. So, the decimal is 0.09.
Thus the correct answer is option d.

Question 6.
Jose jumped 8 \(\frac{1}{3}\) feet. This was 2 \(\frac{2}{3}\) feet farther than Lila jumped. How far did Lila jump?
Options:
a. 5 \(\frac{1}{3}\)
b. 5 \(\frac{2}{3}\)
c. 6 \(\frac{1}{3}\)
d. 11

Answer: 5 \(\frac{2}{3}\)

Explanation:
Jose jumped 8 \(\frac{1}{3}\) feet. This was 2 \(\frac{2}{3}\) feet farther than Lila jumped.
8 \(\frac{1}{3}\) feet – 2 \(\frac{2}{3}\)
= 25/3 – 8/3
= 7/3
= 5 \(\frac{2}{3}\)
Thus the correct answer is option b.

Common Core – Two-Dimensional Figures – Page No. 191

Classify Triangles

Classify each triangle. Write acute, right, or obtuse.

Question 1.

Think: Angles A and C are both acute.
Angle B is obtuse.

Answer:
Obtuse triangle;
Angle A and Angle C are both acute.
Angle B is obtuse.

Explanation:
From triangle, ABC, Angle A, and Angle C are both acute with less than a right angle. Angle B is an obtuse angle that is greater than a right angle.

Question 2.

________

Answer:
Right Triangle; Triangle DEF;
∠D and ∠F are acute angles.
∠E is Right angle

Explanation:
∠D and ∠F are acute angles with less than a right angle. ∠E is the Right angle that forms a square corner. A triangle that has one right angle is called a right triangle.

Question 3.

________

Answer:
Acute triangle;
Angle G, Angle J, and Angle H are acute angles.

Explanation:
From triangle GJH, Angle G, Angle J, and Angle H are acute angles with less than a right angle. A triangle with three acute angles called an acute triangle. So, the given triangle is an acute triangle.

Question 4.

________

Answer:
Obtuse triangle;
Angle L and Angle N are both acute.
Angle M is obtuse.

Explanation:
From triangle LMN, Angle L and Angle N are both acute with less than a right angle. Angle M is an obtuse angle that is greater than a right angle. A triangle with an obtuse angle is called an obtuse triangle.

Problem Solving

Question 5.
Use figure ABCD below. Draw a line segment from point B to point D. Name and classify the triangles formed.

Two _______ triangles
△ _______
△ _______

Answer:

Two Acute triangles.
△ ABD
△ BCD

Explanation:
If we draw a line segment from point B to point D, then there are two traingles formed with less than right angles. They are △ ABD and △ BCD.

Question 6.
Use figure ABCD below. Draw a line segment from point A to point C. Name and classify the triangles formed.

Two _______ triangles
△ _______
△ _______

Answer:

Two Acute triangles.
△ ABC
△ ADC

Explanation:
If we draw a line segment from point A to point C, then there are two triangles formed with less than right angles. They are △ ABC and △ ADC.

Common Core – Two-Dimensional Figures – Page No. 192

Lesson Check

Question 1.
Stephen drew this triangle. How many obtuse angles does the triangle have?

Options:
a. 0
b. 1
c. 2
d. 3

Answer: a. 0

Explanation:
The given image has three acute angles. So, there are 0 obtuse angles.
Thus the correct answer is option a.

Question 2.
Joan was asked to draw a right triangle. How many right angles are in a right triangle?
Options:
a. 0
b. 1
c. 2
d. 3

Answer:
b. 1

Explanation:
A right triangle has only one right angle.
Thus the correct answer is option b.

Spiral Review

Question 3.
Oliver drew the figure below to show light traveling from the sun to Earth. Name the figure he drew.

Options:
a. segment SE
b. ray SE
c. line SE
d. ray ES

Answer:
b. ray SE

Explanation:
SE is a ray that has one endpoint and continues without an end in one direction.
Thus the correct answer is option b.

Question 4.
Armon added \(\frac{1}{10}\) and \(\frac{8}{100}\). Which is the correct sum?
Options:
a. \(\frac{18}{10}\)
b. \(\frac{9}{10}\)
c. \(\frac{9}{100}\)
d. \(\frac{18}{100}\)

Answer: d. \(\frac{18}{100}\)

Explanation:
\(\frac{10}{100}\) + \(\frac{8}{100}\) = \(\frac{18}{100}\)
Thus the correct answer is option d.

Question 5.
Sam counted out loud by 6s. Jorge counted out loud by 8s. What are the first three numbers both students said?
Options:
a. 8, 16, 24
b. 14, 28, 42
c. 24, 48, 72
d. 48, 96, 144

Answer:
c. 24, 48, 72

Explanation:
Sam counted out loud by 6s = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72.
Jorge counted out loud by 8s = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80.
Both students said the first three numbers are 24, 48, 72.
Thus the correct answer is option c.

Question 6.
A basketball team averaged 105 points per game. How many points did the team score in 6 games?
Options:
a. 605 points
b. 630 points
c. 900 points
d. 6,030 points

Answer:
b. 630 points

Explanation:
A basketball team averaged 105 points per game.
They score in 6 games = 6 x 105 = 630 points.
Thus the correct answer is option b.

Common Core – Two-Dimensional Figures – Page No. 193

Parallel Lines and Perpendicular Lines

Use the figure for 1–3.

Question 1.
Name a pair of lines that appear to be perpendicular.
Think: Perpendicular lines form right angles.
\(\overleftrightarrow { AB } \) and \(\overleftrightarrow { EF } \) appear to form right angles.
\(\overleftrightarrow { AB } \) and \(\overleftrightarrow { EF } \)

Answer:
\(\overleftrightarrow { AB } \) and \(\overleftrightarrow { EF } \)

Explanation:
Perpendicular lines form right angles.
\(\overleftrightarrow { AB } \) and \(\overleftrightarrow { EF } \) appear to form right angles.
\(\overleftrightarrow { AB } \) and \(\overleftrightarrow { EF } \)

Question 2.
Name a pair of lines that appear to be parallel.
____ and ____

Answer:
\(\overleftrightarrow { AB } \) and \(\overleftrightarrow { CD } \)

Explanation:
Parallel lines never interest each other. \(\overleftrightarrow { AB } \) and \(\overleftrightarrow { CD } \) are parallel lines.

Question 3.
Name another pair of lines that appear to be perpendicular.
____ and ____

Answer:
\(\overleftrightarrow { CD } \) and \(\overleftrightarrow { EF } \)

Explanation:
Perpendicular lines form right angles.
\(\overleftrightarrow { CD } \) and \(\overleftrightarrow { EF } \) appear to form right angles.
\(\overleftrightarrow { CD } \) and \(\overleftrightarrow { EF } \)

Draw and label the figure described.

Question 4.
\(\overleftrightarrow { MN } \) and \(\overleftrightarrow { PQ } \) intersecting at point R

Answer:

Explanation:
MN and PQ are two lines and interesting at point R.

Question 5.
\(\overleftrightarrow { WX } \) || \(\overleftrightarrow { YZ } \)

Answer:

Explanation:
WX and YZ are parallel lines and they never intersect with each other.

Question 6.
\(\overleftrightarrow { FH } \) ⊥ \(\overleftrightarrow { JK } \)

Answer:

Explanation:
FH and JK are two lines and intersecting each other to form four right angles.

Problem Solving

Use the street map for 7–8.

Question 7.
Name two streets that intersect but do not appear to be perpendicular.
Type below:
_______

Answer:
Maple and Oak or Oak and Birch

Explanation:
Maple and Oak or Oak and Birch; They are intersecting with each other and not perpendicular.

Question 8.
Name two streets that appear to be parallel to each other.
Type below:
_______

Answer:
Maple and Birch

Explanation:
Maple and Birch are streets and not intersect with each other. They appear to be parallel to each other.

Common Core – Two-Dimensional Figures – Page No. 194

Lesson Check

Question 1.
Which capital letter appears to have perpendicular line segments?
Options:
a. N
b. O
c. T
d. V

Answer:
c. T

Explanation:
T has two lines and interesting to form four right angles.

Question 2.
In the figure, which pair of line segments appear to be parallel?

Options:
a. \(\overline{F G} \text { and } \overline{G H}\)
b. \(\overline{F J} \text { and } \overline{G H}\)
c. \(\overline{F G} \text { and } \overline{J H}\)
d. \(\overline{J H} \text { and } \overline{F J}\)

Answer:
c. \(\overline{F G} \text { and } \overline{J H}\)

Explanation:
\(\overline{F G} \text { and } \overline{J H}\) are parallel lines that never intersect

Spiral Review

Question 3.
Nolan drew a right triangle. How many acute angles did he draw?
Options:
a. 0
b. 1
c. 2
d. 3

Answer:
c. 2

Explanation:
A triangle with one right angle will have two acute angles.

Question 4.
Mike drank more than half the juice in his glass. What fraction of the juice could Mike have drunk?
Options:
a. \(\frac{1}{3}\)
b. \(\frac{2}{5}\)
c. \(\frac{3}{6}\)
d. \(\frac{5}{8}\)

Answer:
d. \(\frac{5}{8}\)

Explanation:
Mike drank more than half the juice in his glass. He drunk \(\frac{5}{8}\) of the juice.

Question 5.
A school principal ordered 1,000 pencils. He gave an equal number to each of 7 teachers until he had given out as many as possible. How many pencils were left?
Options:
a. 2
b. 4
c. 6
d. 142

Answer:
c. 6

Explanation:
A school principal ordered 1,000 pencils. He gave an equal number to each of the 7 teachers until he had given out as many as possible. He shared 142 pencils for each of the 7 teachers. So, 142 × 7 = 994. The remaining pencils are 6.

Question 6.
A carton of juice contains 64 ounces. Ms. Wilson bought 6 cartons of juice. How many ounces of juice did she buy?
Options:
a. 364 ounces
b. 370 ounces
c. 384 ounces
d. 402 ounces

Answer:
c. 384 ounces

Explanation:
A carton of juice contains 64 ounces. Ms. Wilson bought 6 cartons of juice. 64 X 6 = 384 ounces juice she can buy.

Common Core – Two-Dimensional Figures – Page No. 195

Classify Quadrilaterals

Classify each figure as many ways as possible. Write quadrilateral, trapezoid, parallelogram, rhombus, rectangle, or square.

Question 1.

Type below:
________
Answer:
Quadrilateral, Parallelogram, and rhombus.

Explanation:
2 pairs of parallel sides
4 sides of equal length
0 right angles
Quadrilateral, Parallelogram, and rhombus.

Question 2.

Type below:
________

Answer:
Quadrilateral, Parallelogram, Rectangle

Explanation:
2 pairs of parallel sides
2 pairs of sides of equal length
4 right angles
Quadrilateral, Parallelogram, Rectangle

Question 3.

Type below:
________

Answer:

Explanation:
1 pair of parallel sides
2 sides of equal length
0 right angles
Quadrilateral, Trapezoid

Question 4.

Type below:
________

Answer:
Quadrilateral

Explanation:
0 pair of parallel sides
0 sides of equal length
0 right angles
Quadrilateral

Question 5.

Type below:
________

Answer:
Quadrilateral, Parallelogram, and rhombus

Explanation:
2 pairs of parallel sides
4 sides of equal length
0 right angles
Quadrilateral, Parallelogram, and rhombus

Question 6.

Type below:
________

Answer:

Explanation:
1 pair of parallel sides
0 sides of equal length
2 right angles
Quadrilateral, Trapezoid

Question 7.

Type below:
________

Answer:

Explanation:
2 pairs of parallel sides
2 pairs of sides of equal length
0 right angles
Quadrilateral, Parallelogram

Problem Solving

Question 8.
Alan drew a polygon with four sides and four angles. All four sides are equal. None of the angles are right angles. What figure did Alan draw?
________

Answer:
Quadrilateral or rhombus

Explanation:
Alan drew a polygon with four sides and four angles. All four sides are equal. None of the angles are right angles. Alan drew Quadrilateral or rhombus

Question 9.
Teresa drew a quadrilateral with 2 pairs of parallel sides and 4 right angles. What quadrilateral could she have drawn?
________

Answer:
square or rectangle

Explanation:
2 pairs of parallel sides and 4 right angles. she could draw a square or rectangle.

Common Core – Two-Dimensional Figures – Page No. 196

Lesson Check

Question 1.
Joey is asked to name a quadrilateral that is also a rhombus. What should be his answer?
Options:
a. square
b. rectangle
c. parallelogram
d. trapezoid

Answer:
a. square

Explanation:
The quadrilateral square is also called a rhombus. Both square and rhombus have 2 pairs of parallel sides and 4 sides of equal length.
Thus the correct answer is option a.

Question 2.
Which quadrilateral has exactly one pair of parallel sides?
Options:
a. square
b. rhombus
c. parallelogram
d. trapezoid

Answer:
d. trapezoid

Explanation:
A trapezoid has exactly one pair of parallel sides.
Thus the correct answer is option d.

Spiral Review

Question 3.
Terrence has 24 eggs to divide into equal groups. What are all the possible numbers of eggs that Terence could put in each group?
Options:
a. 1, 2, 3, 4
b. 2, 4, 6, 8, 12
c. 1, 2, 3, 4, 6, 8, 12, 24
d. 24, 48, 72, 96

Answer:
c. 1, 2, 3, 4, 6, 8, 12, 24

Explanation:
Terrence has 24 eggs to divide into equal groups. Terence could put in each group in 1, 2, 3, 4, 6, 8, 12, 24 ways.
Thus the correct answer is option c.

Question 4.
In a line of students, Jenna is number 8. The teacher says that a rule for a number pattern is add 4. The first student in line says the first term, 7. What number
should Jenna say?
Options:
a. 31
b. 35
c. 39
d. 43

Answer:
b. 35

Explanation:
In a line of students, Jenna is number 8. The teacher says that a rule for a number pattern is to add 4. The first student in line says the first term, 7.
7 + 4 = 11
11 + 4 = 15
15 + 4 = 19
19 + 4 = 23
23 + 4 = 27
27 + 4 = 31
31 + 4 = 35.
Jenna says 35.
Thus the correct answer is option b.

Question 5.
Lou eats \(\frac{6}{8}\) of a pizza. What fraction of the pizza is left over?
Options:
a. \(\frac{1}{8}\)
b. \(\frac{1}{4}\)
c. \(\frac{1}{2}\)
d. \(\frac{3}{4}\)

Answer:
b. 1/4
Explanation:
Lou eats 6/8 of a pizza. So, 6 parts of the pizza are finished and the remaining 2 parts of the pizza have remained. So, the left over pizza is 2/8 = 1/4.
Thus the correct answer is option b.

Question 6.
Which capital letter appears to have parallel lines?
Options:
a. D
b. L
c. N
d. T

Answer:
c. N

Explanation:
N has two parallel lines and never intersect each other.
Thus the correct answer is option c.

Common Core – Two-Dimensional Figures – Page No. 197

Line Symmetry

Tell if the dashed line appears to be a line of symmetry. Write yes or no.

Question 1.

yes

Answer:
Yes

Explanation:
The line of symmetry divides a shape into two parts that are the same size and shape.

Question 2.

____

Answer:
No

Explanation:
The line of symmetry divides a shape into two parts that are not of the same size and shape.

Question 3.

____

Answer:
Yes

Explanation:
The line of symmetry divides a shape into two parts that are the same size and shape.

Question 4.

____

Answer:
No

Explanation:
The line of symmetry divides a shape into two parts that are not of the same size and shape.

Question 5.

____

Answer:
No

Explanation:
The line of symmetry divides a shape into two parts that are not of the same size and shape.

Question 6.

____

Answer:
Yes

Explanation:
The line of symmetry divides a shape into two parts that are the same size and shape.

Question 7.

____

Answer:
No

Explanation:
The line of symmetry divides a shape into two parts that are not of the same size and shape.

Question 8.

____

Answer:
Yes

Explanation:
The line of symmetry divides a shape into two parts that are the same size and shape.

Complete the design by reflecting over the line of symmetry.

Question 9.

Answer:

Question 10.

Answer:

Problem Solving

Question 11.
Kara uses the pattern below to make paper dolls. The dashed line represents a line of symmetry. A complete doll includes the reflection of the pattern over the line of symmetry. Complete the design to show what one of Kara’s paper dolls looks like.

Answer:

Common Core – Two-Dimensional Figures – Page No. 198

Lesson Check

Question 1.
Which best describes the line of symmetry in the letter D?

Options:
a. horizontal
b. vertical
c. diagonal
d. half turn

Answer:
a. horizontal

Explanation:
The horizontal line of symmetry in the letter D can exactly separate two parts equally.

Question 2.
Which shape has a correctly drawn line of symmetry?
Options:
a.
b.
c.
d.

Answer:
b.

Spiral Review

Question 3.
The class has 360 unit cubes in a bag. Johnnie divides the unit cubes equally among 8 groups. How many unit cubes will each group get?
Options:
a. 40
b. 44
c. 45
d. 48

Answer:
c. 45

Explanation:
The class has 360 unit cubes in a bag. Johnnie divides the unit cubes equally among 8 groups. 360/8= 45.

Question 4.
There are 5,280 feet in one mile. How many feet are there in 6 miles?
Options:
a. 30,680
b. 31,260
c. 31,608
d. 31,680

Answer:
d. 31,680

Explanation:
There are 5,280 feet in one mile. So, for 6 miles = 6 x 5, 280 = 31,680.

Question 5.
Sue has 4 pieces of wood. The lengths of her pieces of wood are \(\frac{1}{3}\) foot, \(\frac{2}{5}\) foot, \(\frac{3}{10}\) foot, and \(\frac{1}{4}\) foot. Which piece of wood is the shortest?
Options:
a. the \(\frac{1}{3}\) foot piece
b. the \(\frac{2}{5}\) foot piece
c. the \(\frac{3}{10}\) foot piece
d. the \(\frac{1}{4}\) foot piece

Answer:
d. the 1/4 foot piece

Explanation:
The lengths of 1/4 foot piece is less compared to other lengths.

Question 6.
Alice has \(\frac{1}{5}\) as many miniature cars as Sylvester has. Sylvester has 35 miniature cars. How many miniature cars does Alice have?
Options:
a. 7
b. 9
c. 40
d. 175

Answer:
a. 7

Explanation:
Alice has 1/5 as many miniature cars as Sylvester has. Sylvester has 35 miniature cars. Alice has 1/5 × 35 = 7 miniature cars.

Common Core – Two-Dimensional Figures – Page No. 199

Find and Draw Lines of Symmetry

Tell whether the shape appears to have zero lines, 1 line, or more than 1 line of symmetry. Write zero, 1, or more than 1.

Question 1.

1

Answer:
more than 1

Explanation:
There is more than 1 line of symmetry that separates two parts equally.

Question 2.

________

Answer:
more than 1

Explanation:
There is more than 1 line of symmetry that separates two parts equally.

Question 3.

________

Answer:
Zero

Explanation:
There are 0 lines of symmetries.

Question 4.

________

Answer:
more than 1

Explanation:

There is more than 1 line of symmetry that separates two parts equally.

Does the design have line symmetry? Write yes or no.
If your answer is yes, draw all lines of symmetry.

Question 5.

____

Answer:
Yes

Question 6.

____

Answer:
Yes

Question 7.

____

Answer:
No

Question 8.

____

Answer:
Yes

Draw a shape for the statement. Draw the line or lines of symmetry.

Question 9.
zero lines of symmetry

Answer:

Question 10.
1 line of symmetry

Answer:

Question 11.
2 lines of symmetry

Answer:

Problem Solving

Use the chart for 12–13.

Question 12.
Which number or numbers appear to have only 1 line of symmetry?
____

Answer:
3

Explanation:
The number 3 has only 1 line of symmetry.

Question 13.
Which number or numbers appear to have 2 lines of symmetry?
____

Answer:
0 and 8

Explanation:
The numbers 0 and 8 appear to have 2 lines of symmetry.

Common Core – Two-Dimensional Figures – Page No. 200

Lesson Check

Question 1.
How many lines of symmetry does this shape appear to have?

Options:
a. 0
b. 2
c. 6
d. 12

Answer:
c. 6

Explanation:

The given shape has 6 lines of symmetry.
Thus the correct answer is option c.

Question 2.
Which of the following shapes appears to have exactly 1 line of symmetry?
Options:
a.
b.
c.
d.

Explanation:

The trapezoid has exactly 1 line of symmetry.
Thus the correct answer is option d.

Spiral Review

Question 3.
Richard practiced each of 3 piano solos for \(\frac{5}{12}\) hour. How long did he practice in all?
Options:
a. \(\frac{2}{3}\) hours
b. 1 \(\frac{1}{4}\) hours
c. 1 \(\frac{1}{3}\) hours
d. 1 \(\frac{5}{12}\) hours

Answer:
b. 1 1/4 hours

Explanation:
Richard practiced each of 3 piano solos for 5/12 hour. 5/12 hour = 1 1/4 hours hours.
Thus the correct answer is option b.

Question 4.
Which of the following decimals is equivalent to three and ten hundredths?
Options:
a. 0.30
b. 0.31
c. 3.01
d. 3.1

Answer:
d. 3.1

Explanation:
three and ten hundredths = 310 hundredths = 3.1
Thus the correct answer is option d.

Question 5.
Lynne used \(\frac{3}{8}\) cup of flour and \(\frac{1}{3}\) cup of sugar in a recipe. Which number below is a common denominator for \(\frac{3}{8}\) and \(\frac{1}{3}\)?
Options:
a. 8
b. 12
c. 16
d. 24

Answer:
d. 24

Explanation:
Lynne used 3/8 cup of flour and 1/3 cup of sugar in a recipe. To find the common denominator for 3/8 and 1/3, multiply 8 X3 and 3 X 8 = 24.
Thus the correct answer is option d.

Question 6.
Kevin draws a figure that has four sides. All sides have the same length. His figure has no right angles. What figure does Kevin draw?
Options:
a. square
b. trapezoid
c. rhombus
d. rectangle

Answer:
c. rhombus

Common Core – Two-Dimensional Figures – Page No. 201

Problem Solving Shape Patterns

Solve each Problem.

Question 1.
Marta is using this pattern to decorate a picture frame. Describe the pattern. Draw what might be the next three figures in the pattern.

Possible answer: the pattern repeats: one trangle followed by two squares.

Answer:

The pattern repeats one triangle followed by two squares.

Question 2.
Describe the pattern. Draw what might be the next three figures in the pattern. How many circles are in the sixth figure in the pattern?

____ circles

Answer:

Add one more column with 1 more circle than in the previous column; 21.

Question 3.
Larry stencils this pattern to make a border at the top of his bedroom walls. Describe the pattern. Draw what might be the missing figure in the pattern.

Answer:

2 triangles placed side to side followed by 2 sets of 2 triangles placed vertex to vertex

Common Core – Two-Dimensional Figures – Page No. 202

Lesson Check

Question 1.
What might be the next three figures in this pattern?

Options:
a.
b.
c.
d.

Answer:
a.

Explanation:
the pattern has odd numbers of up arrows then even number of down arrows. So, the next three figures are

Question 2.
Which might be the missing figure in the following pattern?

Options:
a.
b.
c.
d.

Answer:
a.

Explanation:
From the pattern, the missing image will have a vertical rectangle with the circle and X mark in it.

Spiral Review

Question 3.
Chad has two pieces of wood. One piece is \(\frac{7}{12}\) foot long. The second piece is \(\frac{5}{12}\) foot longer than the first piece. How long is the second piece?
Options:
a. \(\frac{2}{12}\) foot
b. \(\frac{1}{2}\) foot
c. \(\frac{12}{18}\) foot
d. 1 foot

Answer:
d. 1 foot

Explanation:
7/12 + 5/12 = 12/12 = 1 foot.

Question 4.
Olivia finished a race in 40.64 seconds. Patty finished the race in 40.39 seconds. Miguel finished the race in 41.44 seconds. Chad finished the race in 40.46 seconds. Who finished the race in the least time?
Options:
a. Olivia
b. Patty
c. Miguel
d. Chad

Answer:
b. Patty

Explanation:
Patty finished the race in 40.39 seconds that is the least time compared to others.

Question 5.
Justin bought 6 ribbons for an art project. Each ribbon is \(\frac{1}{4}\) yard long. How many yards of ribbon did Justin buy?
Options:
a. \(\frac{2}{3}\) yard
b. 1 \(\frac{1}{4}\) yards
c. 1 \(\frac{1}{2}\) yards
d. 1 \(\frac{3}{4}\) yards

Answer:
c. 1 1/2 yards

Explanation:
Justin bought 6 ribbons for an art project. Each ribbon is 1/4 yard long. So, 6 X 1/4 = 3/2 = 1 1/2 yards.

Question 6.
Kyle and Andrea were asked to make a list of prime numbers.
Kyle: 1, 3, 7, 19, 23
Andrea: 2, 3, 5, 7, 11
Whose list is correct?
Options:
a. Only Kyle’s list
b. Only Andrea’s list
c. Both lists are correct.
d. Neither list is correct.

Answer:
b. Only Andrea’s list

Explanation:
1 is not a prime number. So, the answer is Only Andrea’s list is correct.

Common Core – Two-Dimensional Figures – Page No. 203

Lesson 10.1

Draw and label an example of the figure.

Question 1.
acute ∠MNP
Type below:
_________

Answer:

Question 2.
\(\overline{Q R}\)
Type below:
_________

Question 3.
\(\overrightarrow { TS } \)
Type below:
_________

Lesson 10.2

Classify each triangle. Write acute, right, or obtuse.

Question 4.

_____

Answer: Acute

Explanation:
The above triangle is less than 90º, thus the above figure is an acute angle triangle.

Question 5.

_____

Answer: Obtuse

Explanation:
The above triangle is greater than 90º, thus the above figure is an obtuse angle triangle.

Question 6.

_____

Answer: Right

Explanation:
The above figure has 90º, thus the above figure is an right angle triangle.

Lesson 10.3

Use the street map for 1–2.

Question 7.
Name two streets that appear to be parallel.
_________

Answer: Oak and elm

Explanation:
By seeing the above figure we say that Oak and Elm are two non-intersecting lines. Thus the two streets that appear to be parallel are Oak and Elm.

Question 8.
Name two streets that appear to be perpendicular.
Type below:
_________

Answer: Park and Oak or Park and Elm

Explanation:
Park and Oak, Park and Elm are intersecting lines, thus the two streets that appear to be perpendicular are Park and Oak or Park and Elm.

Lesson 10.4

Classify each figure as many ways as possible. Write quadrilateral, trapezoid, parallelogram, rhombus, rectangle, or square.

Question 9.

Type below:
_________

Answer:
Quadrilateral, Parallelogram, Rectangle

Explanation:
2 pairs of parallel sides
2 pairs of sides of equal length
4 right angles
Quadrilateral, Parallelogram, Rectangle

Question 10.

Type below:
_________

Answer: Quadrilateral, Trapezoid

Explanation:
1 pair of parallel sides
2 sides of equal length
0 right angles
Quadrilateral, Trapezoid

Common Core – Two-Dimensional Figures – Page No. 204

Lesson 10.5

Tell if the dashed line appears to be a line of symmetry.
Write yes or no.

Question 1.

_____

Answer: Yes

Explanation:
The line of symmetry divides a shape into two parts that are the same size and shape.

Question 2.

_____

Answer: Yes

Explanation:
The line of symmetry divides a shape into two parts that are the same size and shape.

Question 3.

_____

Answer: Yes

Explanation:
The line of symmetry divides a shape into two parts that are the same size and shape.

Lesson 10.6

Does the design have line symmetry? Write yes or no.

If your answer is yes, draw all lines of symmetry.

Question 4.

_____

Answer: Yes

Explanation:
The line of symmetry divides a shape into two parts that are not with the same size and shape. The above figure is not symmetrical.

Question 5.

_____

Answer: Yes

The above figure is symmetrical.

Question 6.

_____

Answer: Yes

Explanation: The above figure is symmetrical.

Lesson 10.7

Question 7.
Sonia made a pattern. The first nine shapes are shown below. Describe the pattern. Draw what might be the next three shapes in Sonia’s pattern.

Type below:
_________

Answer: The pattern repeats circle, square, circle.

Question 8.
Leo makes a pattern with triangles. Draw what might be the next figure in the pattern. How can you describe the pattern?

Type below:
_________

Answer: The pattern grows by one triangle each time.

Conclusion:

Refer Go Math Grade 4 Answer Key Homework Practice FL Chapter 10 Two-Dimensional Figures to score the highest marks in the exam. Our aim to provide quick learning with clear-cut explanations for all the students of Grade 4. In addition to this students can also follow Go Math Grade 4 Answer Key Chapter 10 Two-Dimensional Figures to get an idea of the model of questions. All the very best!!!

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Go Math Grade 4 Answer Key Homework Practice FL Chapter 7 Add and Subtract Fractions

Before starting the preparation we suggest the students check out the topics of Go Math Grade 4 Answer Key Homework Practice FL Chapter 7 Add and Subtract Fractions. The solutions are prepared by math experts. So you need not worry about the solutions. We have provided a brief explanation for all the questions.

Lesson: 1 – Add and Subtract Parts of a Whole

• Common Core – Add and Subtract Fractions – Page No. 133
• Common Core – Add and Subtract Fractions – Page No. 134

Lesson: 2 – Write Fractions as Sums

• Common Core – Add and Subtract Fractions – Page No. 135
• Common Core – Add and Subtract Fractions – Page No. 136

Lesson: 3 – Add Fractions Using Models

• Common Core – Add and Subtract Fractions – Page No. 137
• Common Core – Add and Subtract Fractions – Page No. 138

Lesson: 4 – Subtract Fractions Using Models

• Common Core – Add and Subtract Fractions – Page No. 139
• Common Core – Add and Subtract Fractions – Page No. 140

Lesson: 5 – Add and Subtract Fractions

• Common Core – Add and Subtract Fractions – Page No. 141
• Common Core – Add and Subtract Fractions – Page No. 142

Lesson: 6 – Rename Fractions and Mixed Numbers

• Common Core – Add and Subtract Fractions – Page No. 143
• Common Core – Add and Subtract Fractions – Page No. 144

Lesson: 7 – Add and Subtract Mixed Numbers

• Common Core – Add and Subtract Fractions – Page No. 145
• Common Core – Add and Subtract Fractions – Page No. 146

Lesson: 8 – Record Subtraction with

• Common Core – Add and Subtract Fractions – Page No. 147
• Common Core – Add and Subtract Fractions – Page No. 148

Lesson: 9 – Fractions and Properties of Addition

• Common Core – Add and Subtract Fractions – Page No. 149
• Common Core – Add and Subtract Fractions – Page No. 150

Lesson: 10 – Read each problem and solve.

• Common Core – Add and Subtract Fractions – Page No. 151
• Common Core – Add and Subtract Fractions – Page No. 152

Lesson 7.1

• Common Core – Add and Subtract Fractions – Page No. 153
• Common Core – Add and Subtract Fractions – Page No. 154

Common Core – Add and Subtract Fractions – Page No. 133

Add and Subtract Parts of a Whole

Use the model to write an equation.

Question 1.

Explanation:
By seeing the above 3 figures we can say that the fraction of the shaded part of the first circle is 3/8, the fraction of the second figure is 2/8
By adding the 2 fractions we get the fraction of the third circle.
3/8 + 2/8 = 5/8

Question 2.

Type below:
_________

Answer: 4/5 – 3/5 = 1/5

Explanation:
The fraction of the shaded part for the above rectangle is 4/5
The fraction of the box is 3/5
The equation for the above figure is 4/5 – 3/5 = 1/5

Question 3.

Type below:
_________

Answer: 1/4 + 2/4 = 3/4

Explanation:
The name of the fraction for the shaded part of first figure is 1/4
The name of the fraction for the shaded part of second figure is 1/4
The name of the fraction for the shaded part of third figure is 3/4
So, The equation for the above figure is 1/4 + 2/4 = 3/4

Use the model to solve the equation.

Question 4.

\(\frac{2}{6}+\frac{3}{6}\) = \(\frac{□}{□}\)

Answer: \(\frac { 2 }{ 6 } +\frac { 3 }{ 6 } =\frac { 5 }{ 6 } \)

Explanation:
The name of the fraction for the shaded part of first figure is 2/6
The name of the fraction for the shaded part of second figure is 3/6
The name of the fraction for the shaded part of third figure is 5/6
So, The equation for the above figure is \(\frac { 2 }{ 6 } +\frac { 3 }{ 6 } =\frac { 5 }{ 6 } \)

Question 5.

\(\frac{3}{5}-\frac{2}{5}\) = \(\frac{□}{□}\)

Answer: \(\frac { 3 }{ 5 } -\frac { 2 }{ 5 } =\frac { 1 }{ 5 } \)

Explanation:
The name of the fraction for the shaded part of figure is 3/5
The name of the fraction for the shaded part of closed box is 2/5
So, The equation for the above figure is \(\frac { 3 }{ 5 } -\frac { 2 }{ 5 } =\frac { 1 }{ 5 } \)

Problem Solving

Question 6.
Jake ate \(\frac{4}{8}\) of a pizza. Millie ate \(\frac{3}{8}\) of the same pizza. How much of the pizza was eaten by Jake and Millie?
\(\frac{□}{□}\)

Answer: 7/8 of pizza

Explanation:
Given that,
Jake ate \(\frac { 4 }{ 8 } \) of a pizza.
Millie ate \(\frac { 3}{ 8 } \) of the same pizza.
To find how much of the pizza was eaten by Jake and Millie
We have to add both the fractions
\(\frac { 4 }{ 8 } \) + \(\frac { 3 }{ 8 } \) = \(\frac { 7 }{ 8 } \)
Thus the fraction of the pizza eaten by Jake and Millie is \(\frac { 7 }{ 8 } \)

Question 7.
Kate ate \(\frac{1}{4}\) of her orange. Ben ate \(\frac{2}{4}\) of his banana. Did Kate and Ben eat \(\frac{1}{4}+\frac{2}{4}=\frac{3}{4}\) of their fruit?
Explain.
Type below:
__________

Answer: No, one whole refers to orange and the other whole to a banana.

Common Core – Add and Subtract Fractions – Page No. 134

Lesson Check

Question 1.
A whole pie is cut into 8 equal slices. Three of the slices are served. How much of the pie is left?
Options:
a. \(\frac{1}{8}\)
b. \(\frac{3}{8}\)
c. \(\frac{5}{8}\)
d. \(\frac{7}{8}\)

Answer: \(\frac { 5 }{ 8} \)

Explanation:
Given,
A whole pie is cut into 8 equal slices. Three of the slices are served.
The fraction of 8 slices is 8/8.
Out of which 3/8 are served.
8/8 – 3/8 = 5/8
Therefore \(\frac { 5 }{ 8} \) of the pie is left.
Thus the correct answer is option c.

Question 2.
An orange is divided into 6 equal wedges. Jody eats 1 wedge. Then she eats 3 more wedges. How much of the orange did Jody eat?
Options:
a. \(\frac{1}{6}\)
b. \(\frac{4}{6}\)
c. \(\frac{5}{6}\)
d. \(\frac{6}{6}\)

Answer: \(\frac { 4}{ 6 } \)

Explanation:
Given,
An orange is divided into 6 equal wedges.
Jody eats 1 wedge.
Then she eats 3 more wedges.
The fraction of orange that Jody eat is \(\frac { 4}{ 6 } \).
Thus the correct answer is option b.

Spiral Review

Question 3.
Which list of distances is in order from least to greatest?
Options:
a. \(\frac{1}{8} mile, \frac{3}{16} mile, \frac{3}{4} mile\)
b. \(\frac{3}{4} mile, \frac{1}{8} mile, \frac{3}{16} mile\)
c. \(\frac{1}{8} mile, \frac{3}{4} mile, \frac{3}{16} mile\)
d. \(\frac{3}{16} mile, \frac{1}{8} mile, \frac{3}{4} mile\)

Answer: \(\frac { 1 }{ 8 } \) Mile, \(\frac { 3 }{ 16 } \) Mile, \(\frac { 3 }{ 4 } \) Mile

Explantion:
Compare the three fractions 1/8, 3/4 and 3/16
Make the common denominators.
1/8 × 2/2 = 2/16
3/4 × 4/4 = 12/16
The fractions are 2/16, 12/16 and 3/16
The numerator with the highest number will be the greatest.
The fractions from least to greatest is \(\frac { 1 }{ 8 } \) Mile, \(\frac { 3 }{ 16 } \) Mile, \(\frac { 3 }{ 4 } \) Mile.
Thus the correct answer is option d.

Question 4.
Jeremy walked \(\frac{6}{8}\) of the way to school and ran the rest of the way. What fraction, in simplest form, shows the part of the way that Jeremy walked?
Options:
a. \(\frac{1}{4}\)
b. \(\frac{3}{8}\)
c. \(\frac{1}{2}\)
d. \(\frac{3}{4}\)

Answer: \(\frac { 3 }{ 4 } \)

Explanation:
Given,
Jeremy walked 6/8 of the way to school and ran the rest of the way.
The simplest form of 6/8 is 3/8.
The simplest form of part of the way that Jeremy walked is 3/8.
Thus the correct answer is option b.

Question 5.
An elevator starts on the 100th floor of a building. It descends 4 floors every 10 seconds. At what floor will the elevator be 60 seconds after it starts?
Options:
a. 60^th floor
b. 66^th floor
c. 72^nd floor
d. 76^th floor

Answer: 76th floor

Explanation:
Given,
An elevator starts on the 100th floor of a building.
It descends 4 floors every 10 seconds.
4 floors – 10 seconds
? – 60 seconds
60 × 4/10 = 240/10 = 24 floors
100 – 24 = 76th floor
Thus the correct answer is option d.

Question 6.
For a school play, the teacher asked the class to set up chairs in 20 rows with 25 chairs in each row. After setting up all the chairs, they were 5 chairs short. How many chairs did the class set up?
Options:
a. 400
b. 450
c. 495
d. 500

Answer: 495

Explanation:
Given,
For a school play, the teacher asked the class to set up chairs in 20 rows with 25 chairs in each row.
After setting up all the chairs, they were 5 chairs short.
20 × 25 = 500
500 – 5 = 495
Therefore the class set up 495 chairs.
Thus the correct answer is c.

Common Core – Add and Subtract Fractions – Page No. 135

Write Fractions as Sums

Write the fraction as a sum of unit fractions.

Question 1.

Answer: 1/5 + 1/5 + 1/5 + 1/5

Explanation:
The sum of the unit fractions for 4/5 is 1/5 + 1/5 + 1/5 + 1/5.

Question 2.
\(\frac{3}{8}\) =
Type below:
__________

Answer: 1/8 + 1/8 + 1/8

Explanation:
The sum of the unit fractions for 3/8 is 1/8 + 1/8 + 1/8

Question 3.
\(\frac{6}{12}\) =
Type below:
__________

Answer: 1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12

Explanation:
The sum of the unit fractions for 6/12 is 1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12

Question 4.
\(\frac{4}{4}\) =
Type below:
__________

Answer: 1/4 + 1/4 + 1/4 + 1/4

Explanation:
The sum of the unit fractions for 4/4 is 1/4 + 1/4 + 1/4 + 1/4

Write the fraction as a sum of fractions three different ways.

Question 5.
\(\frac{7}{10}\)
Type below:
__________

Answer: 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10

Explanation:
The sum of the unit fractions for 7/10 is 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10

Question 6.
\(\frac{6}{6}\)
Type below:
__________

Answer: 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6

Explanation:
The sum of the unit fractions for 6/6 is 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6

Problem Solving

Question 7.
Miguel’s teacher asks him to color \(\frac{4}{8}\) of his grid. He must use 3 colors: red, blue, and green. There must be more green sections than red sections. How can Miguel color the sections of his grid to follow all the rules?
Type below:
__________

Answer: 1/8 red, 1/8 blue, and 2/8 green

Explanation:
If there are 8 tiles, coloring \(\frac { 4 }{ 8 }\) means coloring 4 tiles. Using those three colors, we could use each 1 time with 1 leftover. Since we must have more green, we would use it twice; this would give us 2 green, 1 red and 1 blue.
Since the grid is not necessarily 8 squares, we must account for this by saying 2/8 green, 1/8 red, and 1/8 blue

Question 8.
Petra is asked to color \(\frac{6}{6}\) of her grid. She must use 3 colors: blue, red, and pink. There must be more blue sections than red sections or pink sections. What are the different ways Petra can color the sections of her grid and follow all the rules?
Type below:
__________

Answer: 3/6 blue, 2/6 red, 1/6 pink

Explanation:
1. 3 blues, 2 red, 1 pink.
2. 3 blues, 2 pink, 1 red.
3. 4 blues, 1 red, 1 pink
The different ways in which Petra can color the sections of her grid and follow the rules are;
1. 3 blues, 2 red, 1 pink.
2. 3 blues, 2 pink, 1 red.
3. 4 blues, 1 red, 1 pink
All these three ways follows the rules that; there must be three colors an also Blue sections are more than red sections or pink sections.

Common Core – Add and Subtract Fractions – Page No. 136

Lesson Check

Question 1.
Jorge wants to write \(\frac{4}{5}\) as a sum of unit fractions. Which of the following should he write?
Options:
a. \(\frac{3}{5}+\frac{1}{5}\)
b. \(\frac{2}{5}+\frac{2}{5}\)
c. \(\frac{1}{5}+\frac{1}{5}+\frac{2}{5}\)
d. \(\frac{1}{5}+\frac{1}{5}+\frac{1}{5}+\frac{1}{5}\)

Answer: \(\frac { 1 }{ 5 } +\frac { 1 }{ 5 } +\frac { 1 }{ 5 } +\frac { 1 }{ 5 } \)

Explanation:
Given,
Jorge wants to write \(\frac { 4 }{ 5 } \) as a sum of unit fractions.
The sum of the unit fraction for \(\frac { 4 }{ 5 } \) is \(\frac { 1 }{ 5 } +\frac { 1 }{ 5 } +\frac { 1 }{ 5 } +\frac { 1 }{ 5 } \)
Thus the correct answer is option d.

Question 2.
Which expression is equivalent to \(\frac{7}{8}\)?
Options:
a. \(\frac{5}{8}+\frac{2}{8}+\frac{1}{8}\)
b. \(\frac{3}{8}+\frac{3}{8}+\frac{1}{8}+\frac{1}{8}\)
c. \(\frac{4}{8}+\frac{2}{8}+\frac{1}{8}\)
d. \(\frac{4}{8}+\frac{2}{8}+\frac{2}{8}\)

Answer: \(\frac { 4 }{ 8 } +\frac { 2 }{ 8 }+\frac { 1 }{ 8 } \)

Explanation:
The fraction equivalent to \(\frac { 7 }{ 8 } \) is \(\frac { 4 }{ 8 } +\frac { 2 }{ 8 }+\frac { 1 }{ 8 } \).
Thus the correct answer is option c.

Spiral Review

Question 3.
An apple is cut into 6 equal slices. Nancy eats 2 of the slices. What fraction of the apple is left?
Options:
a. \(\frac{1}{6}\)
b. \(\frac{2}{6}\)
c. \(\frac{3}{6}\)
d. \(\frac{4}{6}\)

Answer: \(\frac { 4 }{ 6 } \)

Explanation:
Given,
An apple is cut into 6 equal slices. Nancy eats 2 of the slices.
6 – 2 = 4
\(\frac { 6 }{ 6 } \) – \(\frac { 2 }{ 6 } \) = \(\frac { 4 }{ 6 } \)
Thus the correct answer is option d.

Question 4.
Which of the following numbers is a prime number?
Options:
a. 1
b. 11
c. 21
d. 51

Answer: 11

Explanation:
A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers.
11 is a multiple of 1 and itself.
Thus the correct answer is option b.

Question 5.
A teacher has a bag of 100 unit cubes. She gives an equal number of cubes to each of the 7 groups in her class. She gives each group as many cubes as she
can. How many unit cubes are left over?
Options:
a. 1
b. 2
c. 3
d. 6

Answer: 2

Explanation:
Given,
A teacher has a bag of 100 unit cubes. She gives an equal number of cubes to each of the 7 groups in her class.
She gives each group as many cubes as she can.
100 divided by 7 is 14 r 2, so there are 2 leftover.
Thus the correct answer is option b.

Question 6.
Jessie sorted the coins in her bank. She made 7 stacks of 6 dimes and 8 stacks of 5 nickels. She then found 1 dime and 1 nickel. How many dimes and nickels does Jessie have in all?
Options:
a. 84
b. 82
c. 80
d. 28

Answer: 84

Explanation:
Given,
Jessie sorted the coins in her bank. She made 7 stacks of 6 dimes and 8 stacks of 5 nickels.
She then found 1 dime and 1 nickel.
43 dimes and 41 nickles
43 + 41 = 84
Jessie has 84 dimes and nickels in all.
Thus the correct answer is option a.

Common Core – Add and Subtract Fractions – Page No. 137

Add Fractions Using Models

Find the sum. Use fraction strips to help.

Question 1.

Answer: 3/6

Question 2.
\(\frac{4}{10}+\frac{5}{10}\) = \(\frac{□}{□}\)

Answer: 9/10

Question 3.
\(\frac{1}{3}+\frac{2}{3}\) = \(\frac{□}{□}\)

Answer: 3/3

Question 4.
\(\frac{2}{4}+\frac{1}{4}\) = \(\frac{□}{□}\)

Answer: 3/4

Question 5.
\(\frac{2}{12}+\frac{4}{12}\) = \(\frac{□}{□}\)

Answer: 6/12

Question 6.
\(\frac{1}{6}+\frac{2}{6}\) = \(\frac{□}{□}\)

Answer: 3/6

Question 7.
\(\frac{3}{12}+\frac{9}{12}\) = \(\frac{□}{□}\)

Answer: 12/12

Question 8.
\(\frac{3}{8}+\frac{4}{8}\) = \(\frac{□}{□}\)

Answer: 7/8

Question 9.
\(\frac{3}{4}+\frac{1}{4}\) = \(\frac{□}{□}\)

Answer: 4/4

Question 10.
\(\frac{1}{5}+\frac{2}{5}\) = \(\frac{□}{□}\)

Answer: 3/5

Explanation:

Problem Solving

Question 11.
Lola walks \(\frac{4}{10}\) mile to her friend’s house. Then she walks \(\frac{5}{10}\) mile to the store. How far does she walk in all?
\(\frac{□}{□}\) mile

Answer: \(\frac { 9 }{ 10 } \) mile

Explanation:
Given,
Lola walks \(\frac { 4 }{ 10} \) mile to her friend’s house.
Then she walks \(\frac { 5 }{ 10 } \) mile to the store.
\(\frac { 4 }{ 10} \) + \(\frac { 5 }{ 10 } \) = \(\frac { 9 }{ 10 } \)
Therefore she walked \(\frac { 9 }{ 10 } \) mile in all.

Question 12.
Evan eats \(\frac{1}{8}\) of a pan of lasagna and his brother eats \(\frac{2}{8}\) of it. What fraction of the pan of lasagna do they eat in all?
\(\frac{□}{□}\)

Answer: \(\frac { 3 }{ 8 } \) of the pan

Explanation:
Given,
Evan eats \(\frac { 1 }{ 8 } \) of a pan of lasagna and his brother eats \(\frac { 2 }{ 8 } \) of it.
\(\frac { 1 }{ 8 } \) + \(\frac { 2 }{ 8 } \)
= \(\frac { 3 }{ 8 } \)

Question 13.
Jacqueline buys \(\frac{2}{4}\) yard of green ribbon and \(\frac{1}{4}\) yard of pink ribbon. How many yards of ribbon does she buy in all?
\(\frac{□}{□}\) yard

Answer: \(\frac { 3 }{ 4 } \) yard

Explanation:
Given,
Jacqueline buys \(\frac { 2 }{ 4 } \) yard of green ribbon and \(\frac { 1 }{ 4 } \) yard of pink ribbon.
\(\frac { 2 }{ 4 } \) + \(\frac { 1 }{ 4 } \)
= \(\frac { 3 }{ 4 } \)
Thus Jacqueline bought \(\frac { 3 }{ 4 } \) yards of ribbon in all.

Question 14.
Shu mixes \(\frac{2}{3}\) pound of peanuts with \(\frac{1}{3}\) pound of almonds. How many pounds of nuts does Shu mix in all?
\(\frac{□}{□}\) pound

Answer: 3/3 pound

Explanation:
Given,
Shu mixes \(\frac { 2 }{ 3 } \) pound of peanuts with \(\frac { 1 }{ 3 } \) pound of almonds.
\(\frac { 2 }{ 3 } \) + \(\frac { 1 }{ 3 } \)
= \(\frac { 3 }{ 3 } \)
Therefore Shu mix \(\frac { 3 }{ 3 } \) pounds of nuts in all.

Common Core – Add and Subtract Fractions – Page No. 138

Lesson Check

Question 1.
Mary Jane has \(\frac{3}{8}\) of a medium pizza left. Hector has \(\frac{2}{8}\) of another medium pizza left. How much pizza do they have altogether?
Options:
a. \(\frac{1}{8}\)
b. \(\frac{4}{8}\)
c. \(\frac{5}{8}\)
d. \(\frac{6}{8}\)

Answer: \(\frac { 5 }{ 8 } \)

Explanation:
Given,
Mary Jane has \(\frac { 3 }{ 8 } \) of a medium pizza left.
Hector has \(\frac { 2 }{ 8 } \) of another medium pizza left.
To find how much pizza do they have altogether we have to add both the fractions.
\(\frac { 3 }{ 8 } \) + \(\frac { 2 }{ 8 } \) = \(\frac { 5 }{ 8 } \)
Therefore Mary Jane and Hector has \(\frac { 5 }{ 8 } \) pizza altogether.
Thus the correct answer is option c.

Question 2.
Jeannie ate \(\frac{1}{4}\) of an apple. Kelly ate \(\frac{2}{4}\) of the apple. How much did they eat in all?
Options:
a. \(\frac{1}{4}\)
b. \(\frac{2}{8}\)
c. \(\frac{3}{8}\)
d. \(\frac{3}{4}\)

Answer: \(\frac { 3 }{ 4 } \)

Explanation:
Given,
Jeannie ate \(\frac { 1 }{ 4 } \) of an apple.
Kelly ate \(\frac { 2 }{ 4 } \) of the apple.
\(\frac { 1 }{ 4 } \) + \(\frac { 2 }{ 4 } \) = \(\frac { 3 }{ 4 } \)
Thus the correct answer is option d.

Spiral Review

Question 3.
Karen is making 14 different kinds of greeting cards. She is making 12 of each kind. How many greeting cards is she making?
Options:
a. 120
b. 132
c. 156
d. 168

Answer: 168

Explanation:
Given,
Karen is making 14 different kinds of greeting cards.
She is making 12 of each kind.
To find how many greeting cards she is making we have to multiply 14 and 12.
14 × 12 = 168.
Thus the correct answer is option d.

Question 4.
Jefferson works part time and earns $1,520 in four weeks. How much does he earn each week?
Options:
a. $305
b. $350
c. $380
d. $385

Answer: $380

Explanation:
Jefferson works part-time and earns $1,520 in four weeks.
1520 – 4 weeks
? – 1 week
1520/4 = $380
Thus the correct answer is option c

Question 5.
By installing efficient water fixtures, the average American can reduce water use to about 45 gallons of water per day. Using such water fixtures, about how many gallons of water would the average American use in December?
Options:
a. about 1,200 gallons
b. about 1,500 gallons
c. about 1,600 gallons
d. about 2,000 gallons

Answer: about 1,500 gallons

Explanation:
Given,
By installing efficient water fixtures, the average American can reduce water use to about 45 gallons of water per day.
1 day – 45 gallons
31 days – ?
45 × 31 = 1395 gallons
The number near to 1395 is 1500 gallons.
Thus the correct answer is option b.

Question 6.
Collin is making a bulletin board and note center. He is using square cork tiles and square dry-erase tiles. One of every 3 squares will be a cork square. If he uses 12 squares for the center, how many will be cork squares?
Options:
a. 3
b. 4
c. 6
d. 8

Answer: 4

Explanation:
Given that,
Collin is making a bulletin board and note center.
He is using square cork tiles and square dry-erase tiles.
One of every 3 squares will be a cork square.
12/3 = 4
Thus the correct answer is option b.

Common Core – Add and Subtract Fractions – Page No. 139

Subtract Fractions Using Models

Subtract. Use fraction strips to help.

Question 1.

Answer: 3/5

Explanation:
Given the fraction, 4/5 and 1/5
The denominators of both the fractions are the same so subtract the numerators.
4/5 – 1/5 = 3/5

Question 2.
\(\frac{3}{4}-\frac{1}{4}\) = \(\frac{□}{□}\)

Answer: 2/4

Explanation:
Given the fractions \(\frac { 3}{ 4 } \) and [/latex] \frac { 1}{ 4 } [/latex]
The denominators of both the fractions are the same so subtract the numerators.
\(\frac { 3}{ 4 } – \frac { 1}{ 4 } = \frac { 2 }{ 4 } \)

Question 3.
\(\frac{5}{6}-\frac{1}{6}\) = \(\frac{□}{□}\)

Answer: 4/6

Explanation:
Given the fractions \(\frac { 5 }{ 6 } \) and [/latex] \frac { 1 }{ 6 } [/latex]
The denominators of both the fractions are the same so subtract the numerators.
\(\frac { 5}{ 6 } – \frac { 1}{ 6 } = \frac { 4 }{ 6 } \)

Question 4.
\(\frac{7}{8}-\frac{1}{8}\) = \(\frac{□}{□}\)

Answer: 6/8

Explanation:
Given the fractions \(\frac { 7 }{ 8 } \) and [/latex] \frac { 1 }{ 8 } [/latex]
The denominators of both the fractions are the same so subtract the numerators.
\(\frac { 7}{ 8 } – \frac { 1}{ 8 } = \frac { 6 }{ 8 } \)

Question 5.
1 – \(\frac{2}{3}\) = \(\frac{□}{□}\)

Answer: 1/3

Explanation:
Given the fractions \(\frac { 1 }{ 3 } \) and [/latex] \frac { 2 }{ 3 } [/latex]
The denominators of both the fractions are the same so subtract the numerators.
\(\frac { 1}{ 3 } – \frac { 2}{ 3 } = \frac { 1}{ 3 } \)

Question 6.
\(\frac{8}{10}-\frac{2}{10}\) = \(\frac{□}{□}\)

Answer: 6/10

Explanation:
Given the fractions \(\frac { 8 }{ 10 } \) and [/latex] \frac { 2 }{ 10 } [/latex]
The denominators of both the fractions are the same so subtract the numerators.
\(\frac { 8}{ 10 } – \frac { 2}{ 10 } = \frac { 6 }{ 10 } \)

Question 7.
\(\frac{3}{4}-\frac{1}{4}\) = \(\frac{□}{□}\)

Answer: 2/4

Explanation:
Given the fractions \(\frac { 3 }{ 4 } \) and [/latex] \frac { 1 }{ 4 } [/latex]
The denominators of both the fractions are the same so subtract the numerators.
\(\frac { 3}{ 4 } – \frac { 1}{ 4 } = \frac { 2 }{ 4 } \)

Question 8.
\(\frac{7}{6}-\frac{5}{6}\) = \(\frac{□}{□}\)

Answer: 2/6

Explanation:
Given the fractions \(\frac { 7 }{ 6 } \) and [/latex] \frac { 5 }{ 6 } [/latex]
The denominators of both the fractions are the same so subtract the numerators.
\(\frac { 7}{ 6 } – \frac {5}{ 6 } = \frac { 2 }{ 6 } \)

Problem Solving

Use the table for 9 and 10.

Question 9.
Ena is making trail mix. She buys the items shown in the table. How many more pounds of pretzels than raisins does she buy?
\(\frac{□}{□}\)

Answer: 5/8 pound

Explanation:
Given that,
Ena is making trail mix.
pretzels = 7/8
Raisins = 2/8
To find the number of more pounds of pretzels than raisins she buy
we have to subtract both the fractions.
7/8 – 2/8 = 5/8

Question 10.
How many more pounds of granola than banana chips does she buy?
\(\frac{□}{□}\)

Answer: 2/8 pound

Explanation:
Granola = 5/8
Banana Chips = 3/8
To find How many more pounds of granola than banana chips does she buy we have to subtract both the fractions.
5/8 – 3/8 = 2/8 pounds

Common Core – Add and Subtract Fractions – Page No. 140

Lesson Check

Question 1.
Lee reads for \(\frac{3}{4}\) hour in the morning and \(\frac{2}{4}\) hour in the afternoon. How much longer does Lee read in the morning than in the afternoon?
Options:
a. 5 hours
b. \(\frac{5}{4}\) hours
c. \(\frac{4}{4}\) hour
d. \(\frac{1}{4}\) hour

Answer: \(\frac { 1}{ 4} \)

Explanation:
Given,
Lee reads for \(\frac { 3}{ 4} \) hour in the morning and \(\frac {2}{ 4} \) hour in the afternoon.
\(\frac { 3}{ 4} \) – \(\frac {2}{ 4} \) = \(\frac { 1}{ 4} \)
Lee read \(\frac { 1}{ 4} \) hour in the morning than in the afternoon.
Thus the correct answer is option d.

Question 2.
Which equation does the model below represent?

Options:
a. \(\frac{3}{6}-\frac{2}{6}=\frac{1}{6}\)
b. \(\frac{2}{6}-\frac{1}{6}=\frac{1}{6}\)
c. \(\frac{5}{6}-\frac{3}{6}=\frac{2}{6}\)
d. 1 – \(\frac{3}{6}\) = \(\frac{3}{6}\)

Answer: \(\frac { 5}{ 6} – \frac { 3}{ 6} = \frac { 2}{ 6} \)

Explanation:
From the above figure we can say that \(\frac { 5}{ 6} – \frac { 3}{ 6} = \frac { 2}{ 6} \)
Thus the correct answer is option c.

Spiral Review

Question 3.
A city received 2 inches of rain each day for 3 days. The meteorologist said that if the rain had been snow, each inch of rain would have been 10 inches of snow. How much snow would that city have received in the 3 days?
Options:
a. 20 inches
b. 30 inches
c. 50 inches
d. 60 inches

Answer: 60 inches

Explanation:
Given,
A city received 2 inches of rain each day for 3 days.
2 × 3 inches = 6 inches
The meteorologist said that if the rain had been snow, each inch of rain would have been 10 inches of snow.
6 × 10 inches = 60 inches
Therefore the city has received 60 inches of snow in 3 days.
Thus the correct answer is option d.

Question 4.
At a party there were four large submarine sandwiches, all the same size. During the party, \(\frac{2}{3}\) of the chicken sandwich, \(\frac{3}{4}\) of the tuna sandwich, \(\frac{7}{12}\) of the roast beef sandwich, and \(\frac{5}{6}\) of the veggie sandwich were eaten. Which sandwich had the least amount left?
Options:
a. chicken
b. tuna
c. roast beef
d. veggie

Answer: veggie

Explanation:
Given,
At a party there were four large submarine sandwiches, all the same size. During the party, \(\frac { 2}{ 3} \) of the chicken sandwich, \(\frac { 3}{ 4} \) of the tuna sandwich, \(\frac { 7}{ 12} \) of the roast beef sandwich, and \(\frac { 5}{ 6} \) of the veggie sandwich were eaten.
Compare the fractions \(\frac { 2}{ 3} \), \(\frac { 3}{ 4} \) , \(\frac { 7}{ 12} \) and \(\frac { 5}{ 6} \).
Among all the fractions veggie has the least fraction.
Thus the correct answer is option d.

Question 5.
Deena uses \(\frac{3}{8}\) cup milk and \(\frac{2}{8}\) cup oil in a recipe. How much liquid does she use in all?
Options:
a. \(\frac{1}{8}\) cup
b. \(\frac{5}{8}\) cup
c. \(\frac{6}{8}\) cup
d. 5 cups

Answer: \(\frac {5}{ 8} \) cup

Explanation:
Given,
Deena uses \(\frac { 3}{ 8} \) cup milk and \(\frac { 2}{ 8} \) cup oil in a recipe.
\(\frac { 3}{ 8} \) + \(\frac { 2}{ 8} \) = \(\frac {5}{ 8} \) cup
Therefore she used \(\frac {5}{ 8} \) cup of milk in all.
Thus the correct answer is option b.

Question 6.
In the car lot, \(\frac{4}{12}\) of the cars are white and \(\frac{3}{12}\) of the cars are blue. What fraction of the cars in the lot are either white or blue?
Options:
a. \(\frac{1}{12}\)
b. \(\frac{7}{24}\)
c. \(\frac{7}{12}\)
d. 7

Answer: \(\frac { 7}{ 12} \)

Explanation:
Given,
In the car lot, \(\frac { 4}{ 12} \) of the cars are white and \(\frac { 3}{ 12} \) of the cars are blue.
\(\frac { 4}{ 12} \) + \(\frac { 3}{ 12} \) = \(\frac { 7}{ 12} \)
Thus the correct answer is option c.

Common Core – Add and Subtract Fractions – Page No. 141

Add and Subtract Fractions

Find the sum or difference.

Question 1.

Answer: 12/12

Explanation:
The denominators of both the fractions are the same so add the numerators.
\(\frac{4}{12}\) + \(\frac{8}{12}\)
= \(\frac{12}{12}\)

Question 2.
\(\frac{3}{6}-\frac{1}{6}\) = \(\frac{□}{□}\)

Answer: 2/6

Explanation:
The denominators of both the fractions are the same so Subtract the numerators.
\(\frac{3}{6}\) – \(\frac{1}{6}\)
= \(\frac{2}{6}\)

Question 3.
\(\frac{4}{5}-\frac{3}{5}\) = \(\frac{□}{□}\)

Answer: 1/5

Explanation:
The denominators of both the fractions are the same so Subtract the numerators.
\(\frac{4}{5}\) – \(\frac{3}{5}\)
= \(\frac{1}{5}\)

Question 4.
\(\frac{6}{10}+\frac{3}{10}\) = \(\frac{□}{□}\)

Answer: 9/10

Explanation:
The denominators of both the fractions are the same so add the numerators.
\(\frac{6}{10}+\frac{3}{10}\) = \(\frac{9}{10}\)

Question 5.
1 – \(\frac{3}{8}\) = \(\frac{□}{□}\)

Answer: 5/8

Explanation:
The denominators of both the fractions are the same so Subtract the numerators.
1 – \(\frac{3}{8}\)
= \(\frac{8}{8}\) – \(\frac{3}{8}\)
= \(\frac{5}{8}\)

Question 6.
\(\frac{1}{4}+\frac{2}{4}\) = \(\frac{□}{□}\)

Answer: 3/4

Explanation:
The denominators of both the fractions are the same so add the numerators.
\(\frac{1}{4}+\frac{2}{4}\) = \(\frac{3}{4}\)

Question 7.
\(\frac{9}{12}-\frac{5}{12}\) = \(\frac{□}{□}\)

Answer: 4/12

Explanation:
The denominators of both the fractions are the same so Subtract the numerators.
\(\frac{9}{12}-\frac{5}{12}\) = \(\frac{4}{12}\)

Question 8.
\(\frac{5}{6}-\frac{2}{6}\) = \(\frac{□}{□}\)

Answer: 3/6

Explanation:
The denominators of both the fractions are the same so Subtract the numerators.
\(\frac{5}{6}-\frac{2}{6}\) = \(\frac{3}{6}\)

Question 9.
\(\frac{2}{3}+\frac{1}{3}\) = \(\frac{□}{□}\)

Answer: 3/3 = 1

Explanation:
The denominators of both the fractions are the same so add the numerators.
\(\frac{2}{3}+\frac{1}{3}\) = \(\frac{3}{3}\) = 1

Problem Solving

Use the table for 10 and 11.

Question 10.
Guy finds how far his house is from several locations and makes the table shown. How much farther away from Guy’s house is the library than the cafe?
\(\frac{□}{□}\)

Answer: \(\frac{5}{10}\) mile

Explanation:
The distance from Guy’s house to the library is \(\frac{9}{10}\) mile
The distance from Guy’s house to the cafe is \(\frac{4}{10}\) mile
To find how much farther away from Guy’s house is the library than the cafe subtract both the fractions.
\(\frac{9}{10}\) – \(\frac{4}{10}\) = \(\frac{5}{10}\) mile

Question 11.
If Guy walks from his house to school and back, how far does he walk?
\(\frac{□}{□}\)

Answer: 10/10 mile

Explanation:
The distance from Guy’s house to school = \(\frac{5}{10}\) mile
From school to house \(\frac{5}{10}\) mile
\(\frac{5}{10}\) + \(\frac{5}{10}\) = \(\frac{10}{10}\) mile

Common Core – Add and Subtract Fractions – Page No. 142

Lesson Check

Question 1.
Mr. Angulo buys \(\frac{5}{8}\) pound of red grapes and \(\frac{3}{8}\) pound of green grapes. How many pounds of grapes did Mr. Angulo buy in all?
Options:
a. \(\frac{1}{8}\) pound
b. \(\frac{2}{8}\) pound
c. 1 pound
d. 2 pounds

Answer: 1 pound

Explanation:
Given that,
Mr. Angulo buys \(\frac{5}{8}\) pound of red grapes and \(\frac{3}{8}\)pound of green grapes.
\(\frac{5}{8}\) + \(\frac{3}{8}\)
= \(\frac{8}{8}\)
= 1
Thus the correct answer is option c.

Question 2.
Which equation does the model below represent?

Options:
a. \(\frac{7}{8}+\frac{2}{8}=\frac{9}{8}\)
b. \(\frac{5}{8}-\frac{2}{8}=\frac{3}{8}\)
c. \(\frac{8}{8}-\frac{5}{8}=\frac{3}{8}\)
d. \(\frac{7}{8}-\frac{2}{8}=\frac{5}{8}\)

Answer: \(\frac{7}{8}\) – \(\frac{2}{8}\) = \(\frac{5}{8}\)

Explanation:
By seeing the above figure we can say that, the equation of the model is
\(\frac{7}{8}\) – \(\frac{2}{8}\) = \(\frac{5}{8}\)
Thus the correct answer is option d.

Spiral Review

Question 3.
There are 6 muffins in a package. How many packages will be needed to feed 48 people if each person has 2 muffins?
Options:
a. 4
b. 8
c. 16
d. 24

Answer: 16

Explanation:
There are 6 muffins in a package.
Number of people = 48
48/6 = 8
Also given that each person gets 2 muffins.
8 × 2 = 16
Thus the correct answer is option c.

Question 4.
Camp Oaks gets 32 boxes of orange juice and 56 boxes of apple juice. Each shelf in the cupboard can hold 8 boxes of juice. What is the least number of shelves
needed for all the juice boxes?
Options:
a. 4
b. 7
c. 11
d. 88

Answer: 11

Explanation:
Given,
Camp Oaks gets 32 boxes of orange juice and 56 boxes of apple juice.
Each shelf in the cupboard can hold 8 boxes of juice.
First, add the boxes of orange juice and apple juice.
32 + 56 = 88 boxes of juice
Now divide 88 by 8
88/8 = 11
Thus the correct answer is option c.

Question 5.
A machine makes 18 parts each hour. If the machine operates 24 hours a day, how many parts can it make in one day
Options:
a. 302
b. 332
c. 362
d. 432

Answer: 432

Explanation:
Given,
A machine makes 18 parts each hour.
Multiply the number of parts with the number of hours.
18 × 24 = 432 parts in a day.
Thus the correct answer is option d.

Question 6.
Which equation does the model below represent?

Options:
a. \(\frac{5}{6}-\frac{4}{6}=\frac{1}{6}\)
b. \(\frac{4}{5}-\frac{1}{5}=\frac{3}{5}\)
c. \(\frac{5}{5}-\frac{4}{5}=\frac{1}{5}\)
d. \(\frac{6}{6}-\frac{4}{6}=\frac{2}{6}\)

Answer: \(\frac{5}{6}\) – \(\frac{4}{6}\) = \(\frac{1}{6}\)

Explanation:
By observing the figure we can say that the equation is \(\frac{5}{6}\) – \(\frac{4}{6}\) = \(\frac{1}{6}\).
Thus the correct answer is option a.

Common Core – Add and Subtract Fractions – Page No. 143

Rename Fractions and Mixed Numbers

Write the mixed number as a fraction.

Question 1.
2 \(\frac{3}{5}\)

 

Question 2.
4 \(\frac{1}{3}\)
\(\frac{□}{□}\)

Answer: \(\frac{13}{3}\)

Explanation:
\(\frac{3}{3}\) + \(\frac{3}{3}\) + \(\frac{3}{3}\) + \(\frac{3}{3}\) + \(\frac{1}{3}\) = \(\frac{13}{3}\)

Question 3.
1 \(\frac{2}{5}\)
\(\frac{□}{□}\)

Answer: \(\frac{7}{5}\)

Explanation:
\(\frac{5}{5}\) + \(\frac{2}{5}\) = \(\frac{7}{5}\)

Question 4.
3 \(\frac{3}{2}\)
\(\frac{□}{□}\)

Answer: \(\frac{9}{2}\)

Explanation:
\(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{1}{2}\) = \(\frac{9}{2}\)

Question 5.
4 \(\frac{1}{8}\)
\(\frac{□}{□}\)

Answer: \(\frac{33}{8}\)

Explanation:
\(\frac{8}{8}\) + \(\frac{8}{8}\) + \(\frac{8}{8}\) + \(\frac{8}{8}\) + \(\frac{1}{8}\) = \(\frac{33}{8}\)

Question 6.
1 \(\frac{7}{10}\)
\(\frac{□}{□}\)

Answer: \(\frac{17}{10}\)

Explanation:
\(\frac{10}{10}\) + \(\frac{7}{10}\) = \(\frac{17}{10}\)

Question 7.
5 \(\frac{1}{2}\)
\(\frac{□}{□}\)

Answer: \(\frac{11}{2}\)

Explanation:
\(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{1}{2}\) = \(\frac{11}{2}\)

Question 8.
2 \(\frac{3}{8}\)
\(\frac{□}{□}\)

Answer: \(\frac{19}{8}\)

Explanation:
\(\frac{8}{8}\) + \(\frac{8}{8}\) + \(\frac{3}{8}\)

Write the fraction as a mixed number.

Question 9.
\(\frac{31}{6}\)
______ \(\frac{□}{□}\)

Answer: 5 \(\frac{1}{6}\)

Explanation:
\(\frac{6}{6}\) + \(\frac{6}{6}\) + \(\frac{6}{6}\) + \(\frac{6}{6}\) + \(\frac{6}{6}\) + \(\frac{1}{6}\)
1 + 1 + 1 + 1 + 1 + \(\frac{1}{6}\) = 5 \(\frac{1}{6}\)

Question 10.
\(\frac{20}{10}\)
______ \(\frac{□}{□}\)

Answer: 2

Explanation:
\(\frac{10}{10}\) + \(\frac{10}{10}\) = 1 + 1 = 2

Question 11.
\(\frac{15}{8}\)
______ \(\frac{□}{□}\)

Answer: 1 \(\frac{7}{8}\)

Explanation:
\(\frac{8}{8}\) + \(\frac{7}{8}\)
1 + \(\frac{7}{8}\) = 1 \(\frac{7}{8}\)

Question 12.
\(\frac{13}{6}\)
______ \(\frac{□}{□}\)

Answer: 2 \(\frac{1}{6}\)

Explanation:
\(\frac{6}{6}\) + \(\frac{6}{6}\) + \(\frac{1}{6}\)
= 1 + 1 + \(\frac{1}{6}\) = 2 \(\frac{1}{6}\)

Question 13.
\(\frac{23}{10}\)
______ \(\frac{□}{□}\)

Answer: 2 \(\frac{3}{10}\)

Explanation:
\(\frac{10}{10}\) + \(\frac{10}{10}\) + \(\frac{3}{10}\)
1 + 1 + \(\frac{3}{10}\) = 2 \(\frac{3}{10}\)

Question 14.
\(\frac{19}{5}\)
______ \(\frac{□}{□}\)

Answer: 3 \(\frac{4}{5}\)

Explanation:
\(\frac{5}{5}\) + \(\frac{5}{5}\) + \(\frac{5}{5}\) + \(\frac{4}{5}\)
1 + 1 + 1 + \(\frac{4}{5}\) = 3 \(\frac{4}{5}\)

Question 15.
\(\frac{11}{3}\)
______ \(\frac{□}{□}\)

Answer: 3 \(\frac{2}{3}\)

Explanation:
\(\frac{3}{3}\) + \(\frac{3}{3}\) + \(\frac{3}{3}\) + \(\frac{2}{3}\)
= 1 + 1 + 1 \(\frac{2}{3}\)
= 3 \(\frac{2}{3}\)

Question 16.
\(\frac{9}{2}\)
______ \(\frac{□}{□}\)

Answer: 4 \(\frac{1}{2}\)

Explanation:
\(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{1}{2}\)
= 1 + 1 + 1 + 1 + \(\frac{1}{2}\)
= 4 \(\frac{1}{2}\)

Question 17.
A recipe calls for 2 \(\frac{2}{4}\) cups of raisins, but Julie only has a \(\frac{1}{4}\) -cup measuring cup. How many \(\frac{1}{4}\) cups does Julie need to measure out 2 \(\frac{2}{4}\) cups of raisins?
She needs ______ \(\frac{1}{4}\) cups

Answer: 10 \(\frac{1}{4}\) cups

Explanation:
Given,
A recipe calls for 2 \(\frac{2}{4}\) cups of raisins, but Julie only has a \(\frac{1}{4}\) -cup measuring cup.
\(\frac{4}{4}\) + \(\frac{4}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\)
= 10 \(\frac{1}{4}\) cups

Question 18.
If Julie needs 3 \(\frac{1}{4}\) cups of oatmeal, how many 14 cups of oatmeal will she use?
She will use ______ \(\frac{1}{4}\) cups of oatmeal

Answer: 13 \(\frac{1}{4}\) cups of oatmeal

Explanation:
\(\frac{4}{4}\) + \(\frac{4}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\)
= 13 \(\frac{1}{4}\)
Therefore Julie needs 13 \(\frac{1}{4}\) cups of oatmeal.

Common Core – Add and Subtract Fractions – Page No. 144

Lesson Check

Question 1.
Which of the following is equivalent to \(\frac{16}{3}\)?
Options:
a. 3 \(\frac{1}{5}\)
b. 3 \(\frac{2}{5}\)
c. 5 \(\frac{1}{3}\)
d. 5 \(\frac{6}{3}\)

Answer: 5 \(\frac{1}{3}\)

Explanation:
Convert from improper fraction to the mixed fraction.
\(\frac{16}{3}\) = \(\frac{3}{3}\) + \(\frac{3}{3}\) + \(\frac{3}{3}\) + \(\frac{3}{3}\) + \(\frac{3}{3}\) + \(\frac{1}{3}\)
= 5 \(\frac{1}{3}\)
Thus the correct answer is option c.

Question 2.
Stacey filled her \(\frac{1}{2}\) cup measuring cup seven times to have enough flour for a cake recipe. How much flour does the cake recipe call for?
Options:
a. 3 cups
b. 3 \(\frac{1}{2}\) cups
c. 4 cups
d. 4 \(\frac{1}{2}\) cups

Answer: 3 \(\frac{1}{2}\) cups

Explanation:
Given,
Stacey filled her \(\frac{1}{2}\)cup measuring cup seven times to have enough flour for a cake recipe.
\(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{2}{2}\) + \(\frac{1}{2}\)
1 + 1 + 1 + \(\frac{1}{2}\)
= 3 \(\frac{1}{2}\) cups
Thus the correct answer is option b.

Spiral Review

Question 3.
Becki put some stamps into her stamp collection book. She put 14 stamps on each page. If she completely filled 16 pages, how many stamps did she put in the book?
Options:
a. 224
b. 240
c. 272
d. 275

Answer: 224

Explanation:
Becki put some stamps into her stamp collection book.
She put 14 stamps on each page.
If she completely filled 16 pages
Multiply 14 with 16 pages.
14 × 16 = 224 pages
Thus the correct answer is option a.

Question 4.
Brian is driving 324 miles to visit some friends. He wants to get there in 6 hours. How many miles does he need to drive each hour?
Options:
a. 48 miles
b. 50 miles
c. 52 miles
d. 54 miles

Answer: 54 miles

Explanation:
Brian is driving 324 miles to visit some friends. He wants to get there in 6 hours.
Divide the number of miles by hours.
324/6 = 54 miles
Thus the correct answer is option d.

Question 5.
During a bike challenge, riders have to collect various colored ribbons. Each \(\frac{1}{2}\) mile they collect a red ribbon, each \(\frac{1}{8}\) mile they collect a green ribbon, and each \(\frac{1}{4}\) mile they collect a blue ribbon. Which colors of ribbons will be collected at the \(\frac{3}{4}\) mile marker?
Options:
a. red and green
b. red and blue
c. green and blue
d. red, green, and blue

Answer: green and blue

Explanation:
Given,
During a bike challenge, riders have to collect various colored ribbons.
Each \(\frac{1}{2}\) mile they collect a red ribbon, each \(\frac{1}{8}\) mile they collect a green ribbon, and each \(\frac{1}{4}\) mile they collect a blue ribbon.
Green and Blue colors of ribbons will be collected at the \(\frac{3}{4}\) mile marker.
Thus the correct answer is option c.

Question 6.
Stephanie had \(\frac{7}{8}\) pound of bird seed. She used \(\frac{3}{8}\) pound to fill a bird feeder. How much bird seed does Stephanie have left?
Options:
a. \(\frac{3}{8}\) pound
b. \(\frac{4}{8}\) pound
c. 1 pound
d. \(\frac{10}{8}\) pound

Answer: \(\frac{4}{8}\) pound

Explanation:
Given,
Stephanie had \(\frac{7}{8}\) pound of bird seed.
She used \(\frac{3}{8}\) pound to fill a bird feeder.
\(\frac{7}{8}\) – \(\frac{3}{8}\) = \(\frac{4}{8}\) pound
Thus the correct answer is option b.

Common Core – Add and Subtract Fractions – Page No. 145

Add and Subtract Mixed Numbers

Find the sum. Write the sum as a mixed number, so the fractional part is less than 1.

Question 1.

Question 2.
4 \(\frac{1}{2}\)
+ 2 \(\frac{1}{2}\)
_______ \(\frac{□}{□}\)

Answer: 7

4 \(\frac{1}{2}\)
+2 \(\frac{1}{2}\)
6 \(\frac{2}{2}\) = 6 + 1 = 7

Question 3.
2 \(\frac{2}{3}\)
+ 3 \(\frac{2}{3}\)
_______ \(\frac{□}{□}\)

Answer: 6 \(\frac{1}{3}\)

Explanation:
2 \(\frac{2}{3}\)
+3 \(\frac{2}{3}\)
5 \(\frac{4}{3}\)
= 5 + 1 \(\frac{1}{3}\)
= 6 \(\frac{1}{3}\)

Question 4.
6 \(\frac{4}{5}\)
+ 7 \(\frac{4}{5}\)
_______ \(\frac{□}{□}\)

Answer: 14 \(\frac{3}{5}\)

Explanation:
6 \(\frac{4}{5}\)
+7 \(\frac{4}{5}\)
13 \(\frac{8}{5}\)
13 + 1 \(\frac{3}{5}\)
= 14 \(\frac{3}{5}\)

Question 5.
9 \(\frac{3}{6}\)
+ 2 \(\frac{2}{6}\)
_______ \(\frac{□}{□}\)

Answer: 11 \(\frac{5}{6}\)

Explanation:
9 \(\frac{3}{6}\)
+2 \(\frac{2}{6}\)
11 \(\frac{5}{6}\)

Question 6.
8 \(\frac{4}{12}\)
+ 3 \(\frac{6}{12}\)
_______ \(\frac{□}{□}\)

Answer: 11 \(\frac{10}{12}\)

Explanation:
8 \(\frac{4}{12}\)
+3 \(\frac{6}{12}\)
11 \(\frac{10}{12}\)

Question 7.
4 \(\frac{3}{8}\)
+ 1 \(\frac{5}{8}\)
_______ \(\frac{□}{□}\)

Answer: 6

Explanation:
4 \(\frac{3}{8}\)
+1 \(\frac{5}{8}\)
5 \(\frac{8}{8}\)
= 5 + 1 = 6

Question 8.
9 \(\frac{5}{10}\)
+ 6 \(\frac{3}{10}\)
_______ \(\frac{□}{□}\)

Answer: 15 \(\frac{8}{10}\)

Explanation:
9 \(\frac{5}{10}\)
+6 \(\frac{3}{10}\)
15 \(\frac{8}{10}\)

Find the difference.

Question 9.
6 \(\frac{7}{8}\)
– 4 \(\frac{3}{8}\)
_______ \(\frac{□}{□}\)

Answer: 2 \(\frac{4}{8}\)

Explanation:
6 \(\frac{7}{8}\)
-4 \(\frac{3}{8}\)
2 \(\frac{4}{8}\)

Question 10.
4 \(\frac{2}{3}\)
– 3 \(\frac{1}{3}\)
_______ \(\frac{□}{□}\)

Answer: 1 \(\frac{1}{3}\)

Explanation:
4 \(\frac{2}{3}\)
-3 \(\frac{1}{3}\)
1 \(\frac{1}{3}\)

Question 11.
6 \(\frac{4}{5}\)
– 3 \(\frac{3}{5}\)
_______ \(\frac{□}{□}\)

Answer: 3 \(\frac{1}{5}\)

Explanation:
6 \(\frac{4}{5}\)
-3 \(\frac{3}{5}\)
3 \(\frac{1}{5}\)

Question 12.
7 \(\frac{3}{4}\)
– 2 \(\frac{1}{4}\)
_______ \(\frac{□}{□}\)

Answer: 5 \(\frac{1}{2}\)

Explanation:
7 \(\frac{3}{4}\)
-2 \(\frac{1}{4}\)
5 \(\frac{2}{4}\) = 5 \(\frac{1}{2}\)

Problem Solving

Question 13.
James wants to send two gifts by mail. One package weighs 2 \(\frac{3}{4}\) pounds. The other package weighs 1 \(\frac{3}{4}\) pounds. What is the total weight of the packages?
_______ \(\frac{□}{□}\)

Answer: 4 \(\frac{1}{2}\)

Explanation:
2 \(\frac{3}{4}\)
+ 1 \(\frac{3}{4}\)
4 \(\frac{1}{2}\)

Question 14.
Tierra bought 4 \(\frac{3}{8}\) yards blue ribbon and 2 \(\frac{1}{8}\) yards yellow ribbon for a craft project. How much more blue ribbon than yellow ribbon did Tierra buy?
_______ \(\frac{□}{□}\)

Answer: 2 \(\frac{1}{4}\)

Explanation:
Given,
4 \(\frac{3}{8}\)
-2 \(\frac{1}{8}\) 
2 \(\frac{1}{4}\)

Common Core – Add and Subtract Fractions – Page No. 146

Lesson Check

Question 1.
Brad has two lengths of copper pipe to fit together. One has a length of 2 \(\frac{5}{12}\) feet and the other has a length of 3 \(\frac{7}{12}\) feet. How many feet of pipe does he have in all?
Options:
a. 5 feet
b. 5 \(\frac{6}{12}\) feet
c. 5 \(\frac{10}{12}\)
d. 6 feet

Answer: 5 feet

Explanation:
Given,
Brad has two lengths of copper pipe to fit together. One has a length of 2 \(\frac{5}{12}\) feet and the other has a length of 3 \(\frac{7}{12}\) feet.
Add both the lengths
2 \(\frac{5}{12}\) + 3 \(\frac{7}{12}\)
= 5 \(\frac{12}{12}\) = 5 feet
Thus the correct answer is option a.

Question 2.
A pattern calls for 2 \(\frac{1}{4}\)yards of material and 1 \(\frac{1}{4}\)yards of lining. How much total fabric is needed?
Options:
a. 2 \(\frac{2}{4}\) yards
b. 3 yards
c. 3 \(\frac{1}{4}\) yards
d. 3 \(\frac{2}{4}\) yards

Answer: 3 \(\frac{2}{4}\) yards

Explanation:
Given,
A pattern calls for 2 \(\frac{1}{4}\) yards of material and 1 \(\frac{1}{4}\) yards of lining.
2 \(\frac{1}{4}\) + 1 \(\frac{1}{4}\)
= 3 + \(\frac{1}{4}\) + \(\frac{1}{4}\)
= 3 \(\frac{2}{4}\) yards
Thus the correct answer is option d.

Spiral Review

Question 3.
Shanice has 23 baseball trading cards of star players. She agrees to sell them for $16 each. How much will she get for the cards?
Options:
a. $258
b. $358
c. $368
d. $468

Answer: $368

Explanation:
Given,
Shanice has 23 baseball trading cards of star players. She agrees to sell them for $16 each.
To find how much will she get for the cards
23 × 16 = 368
Therefore she will get $368 for the cards.
Thus the correct answer is option c.

Question 4.
Nanci is volunteering at the animal shelter. She wants to spend an equal amount of time playing with each dog. She has 145 minutes to play with all 7 dogs. About how much time can she spend with each dog?
Options:
a. about 10 minutes
b. about 20 minutes
c. about 25 minutes
d. about 26 minutes

Answer: about 20 minutes

Explanation:
Given,
Nanci is volunteering at the animal shelter. She wants to spend an equal amount of time playing with each dog. She has 145 minutes to play with all 7 dogs.
145/7 = 20.7
Therefore she can spend about 20 minutes with each dog.
Thus the correct answer is option b.

Question 5.
Frieda has 12 red apples and 15 green apples. She is going to share the apples equally among 8 people and keep any extra apples for herself. How many apples
will Frieda keep for herself?
Options:
a. 3
b. 4
c. 6
d. 7

Answer: 3

Explanation:
Given,
Frieda has 12 red apples and 15 green apples.
She is going to share the apples equally among 8 people and keep any extra apples for herself.
12 + 15 = 27
27/8
27 – 24 = 3
Thus Frieda keep for herself 3 apples.
Thus the correct answer is option a.

Question 6.
The Lynch family bought a house for $75,300. A few years later, they sold the house for $80,250. How much greater was the selling price than the purchase price?
Options:
a. $4,950
b. $5,050
c. $5,150
d. $5,950

Answer: $4,950

Explanation:
Given,
The Lynch family bought a house for $75,300.
A few years later, they sold the house for $80,250.
$80,250 – $75,300 = $4,950
Thus the correct answer is option a.

Common Core – Add and Subtract Fractions – Page No. 147

Record Subtraction with

Find the difference.

Question 1.

Question 2.
6
– 3 \(\frac{2}{5}\)
_______ \(\frac{□}{□}\)

Answer: 2 \(\frac{3}{5}\)

Explanation:
First subtract the whole numbers
6 – 3 = 3
Next subtract the fractions,
3 – \(\frac{2}{5}\) = 2 \(\frac{3}{5}\)

Question 3.
5 \(\frac{1}{4}\)
– 2 \(\frac{3}{4}\)
_______ \(\frac{□}{□}\)

Answer: 2 \(\frac{1}{2}\)

Explanation:
First subtract the whole numbers
5 – 2 = 3
Next subtract the fractions,
\(\frac{1}{4}\) – \(\frac{3}{4}\) = – \(\frac{1}{2}\)
3 – \(\frac{1}{2}\)
= 2 \(\frac{1}{2}\)

Question 4.
9 \(\frac{3}{8}\)
– 8 \(\frac{7}{8}\)
_______ \(\frac{□}{□}\)

Answer: \(\frac{1}{2}\)

Explanation:
First subtract the whole numbers
9 – 8 = 1
Next subtract the fractions,
\(\frac{3}{8}\) – \(\frac{7}{8}\)
= – \(\frac{4}{8}\)
= – \(\frac{1}{2}\)
= 1 – \(\frac{1}{2}\)
= \(\frac{1}{2}\)

Question 5.
12 \(\frac{3}{10}\)
– 7 \(\frac{7}{10}\)
_______ \(\frac{□}{□}\)

Answer: 4 \(\frac{3}{5}\)

Explanation:
First subtract the whole numbers
12 – 7 = 5
Next subtract the fractions,
\(\frac{3}{10}\) – \(\frac{7}{10}\) = – \(\frac{4}{10}\)
5 – \(\frac{4}{10}\)
5 – \(\frac{2}{5}\) = 4 \(\frac{3}{5}\)

Question 6.
8 \(\frac{1}{6}\)
– 3 \(\frac{5}{6}\)
_______ \(\frac{□}{□}\)

Answer: 4 \(\frac{1}{3}\)

Explanation:
First subtract the whole numbers
8 – 3 = 5
Next subtract the fractions,
\(\frac{1}{6}\) – \(\frac{5}{6}\) = – \(\frac{2}{3}\)
5 – \(\frac{2}{3}\) = 4 \(\frac{1}{3}\)

Question 7.
7 \(\frac{3}{5}\)
– 4 \(\frac{4}{5}\)
_______ \(\frac{□}{□}\)

Answer: 2 \(\frac{4}{5}\)

Explanation:
First subtract the whole numbers
7 – 4 = 3
Next subtract the fractions,
\(\frac{3}{5}\) – \(\frac{4}{5}\) = – \(\frac{1}{5}\)
3 – \(\frac{1}{5}\) = 2 \(\frac{4}{5}\)

Question 8.
10 \(\frac{1}{2}\)
– 8 \(\frac{1}{2}\)
_______ \(\frac{□}{□}\)

Answer: 2

Explanation:
First subtract the whole numbers
10 – 8 = 2
\(\frac{1}{2}\) – \(\frac{1}{2}\) = 0

Question 9.
7 \(\frac{1}{6}\)
– 2 \(\frac{5}{6}\)
_______ \(\frac{□}{□}\)

Answer: 4 \(\frac{1}{3}\)

Explanation:
First subtract the whole numbers
7 – 2 = 5
Next subtract the fractions,
\(\frac{1}{6}\) – \(\frac{5}{6}\) = – \(\frac{4}{6}\)
5 – \(\frac{4}{6}\) = 4 \(\frac{1}{3}\)

Question 10.
9 \(\frac{3}{12}\)
– 4 \(\frac{7}{12}\)
_______ \(\frac{□}{□}\)

Answer: 2 \(\frac{2}{3}\)

Explanation:
First subtract the whole numbers
9 – 4 = 5
Next subtract the fractions,
\(\frac{3}{12}\) – \(\frac{7}{12}\) = – \(\frac{4}{12}\) = – \(\frac{1}{3}\)
5 – \(\frac{1}{3}\) = 2 \(\frac{2}{3}\)

Question 11.
9 \(\frac{1}{10}\)
– 8 \(\frac{7}{10}\)
_______ \(\frac{□}{□}\)

Answer: \(\frac{2}{5}\)

Explanation:
First subtract the whole numbers
9 – 8 = 1
Next subtract the fractions,
\(\frac{1}{10}\) – \(\frac{7}{10}\) = – \(\frac{6}{10}\)
1 – \(\frac{3}{5}\) = \(\frac{2}{5}\)

Question 12.
9 \(\frac{1}{3}\)
– \(\frac{2}{3}\)
_______ \(\frac{□}{□}\)

Answer: 8 \(\frac{2}{3}\)

Explanation:
9 \(\frac{1}{3}\)
– \(\frac{2}{3}\)
8 \(\frac{2}{3}\)

Question 13.
3 \(\frac{1}{4}\)
– 1 \(\frac{3}{4}\)
_______ \(\frac{□}{□}\)

Answer: 1 \(\frac{1}{2}\)

3 \(\frac{1}{4}\)
– 1 \(\frac{3}{4}\)
1 \(\frac{1}{2}\)

Question 14.
4 \(\frac{5}{8}\)
– 1 \(\frac{7}{8}\)
_______ \(\frac{□}{□}\)

Answer: 2 \(\frac{3}{4}\)

Explanation:
First subtract the whole numbers
4 – 1 = 3
Next subtract the fractions,
\(\frac{5}{8}\) – \(\frac{7}{8}\) = – \(\frac{1}{4}\)
3 – \(\frac{1}{4}\) = 2 \(\frac{3}{4}\)

Question 15.
5 \(\frac{1}{12}\)
– 3 \(\frac{8}{12}\)
_______ \(\frac{□}{□}\)

Answer: 1 \(\frac{5}{12}\)

Explanation:
First subtract the whole numbers
5 – 3 = 2
Next subtract the fractions,
\(\frac{1}{12}\) – \(\frac{8}{12}\) = – \(\frac{7}{12}\)
2 – \(\frac{7}{12}\) = 1 \(\frac{5}{12}\)

Question 16.
7
– 1 \(\frac{3}{5}\)
_______ \(\frac{□}{□}\)

Answer: 5 \(\frac{2}{5}\)

Explanation:
7
– 1 \(\frac{3}{5}\)
5 \(\frac{2}{5}\)

Problem Solving

Question 17.
Alicia buys a 5-pound bag of rocks for a fish tank. She uses 1 \(\frac{1}{8}\) pounds for a small fish bowl. How much is left?
_______ \(\frac{□}{□}\)

Answer: 3 \(\frac{7}{8}\)

Explanation:
Given,
Alicia buys a 5-pound bag of rocks for a fish tank. She uses 1 \(\frac{1}{8}\) pounds for a small fish bowl.
First subtract the whole numbers
5 – 1 = 4
4 – 1 \(\frac{1}{8}\)
= 3 \(\frac{7}{8}\)

Question 18.
Xavier made 25 pounds of roasted almonds for a fair. He has 3 \(\frac{1}{2}\) pounds left at the end of the fair. How many pounds of roasted almonds did he sell at the fair?
_______ \(\frac{□}{□}\)

Answer: 21 \(\frac{1}{2}\)

Explanation:
Given,
Xavier made 25 pounds of roasted almonds for a fair.
He has 3 \(\frac{1}{2}\) pounds left at the end of the fair.
First subtract the whole numbers
25 – 3 = 22
22 – \(\frac{1}{2}\) = 21 \(\frac{1}{2}\)

Common Core – Add and Subtract Fractions – Page No. 148

Lesson Check

Question 1.
Reggie is making a double-layer cake. The recipe for the first layer calls for 2 \(\frac{1}{4}\) cups sugar. The recipe for the second layer calls for 1 \(\frac{1}{4}\) cups sugar. Reggie has 5 cups of sugar. How much will he have left after making both recipes?
Options:
a. 1 \(\frac{1}{4}\) cups
b. 1 \(\frac{2}{4}\) cups
c. 2 \(\frac{1}{4}\) cups
d. 2 \(\frac{2}{4}\) cups

Answer: 1 \(\frac{2}{4}\) cups

Explanation:
Given,
Reggie is making a double-layer cake. The recipe for the first layer calls for 2 \(\frac{1}{4}\) cups sugar.
The recipe for the second layer calls for 1 \(\frac{1}{4}\) cups sugar.
Reggie has 5 cups of sugar.
2 \(\frac{1}{4}\) + 1 \(\frac{1}{4}\) = 3 \(\frac{1}{2}\)
5 – 3 \(\frac{1}{2}\) = 1 \(\frac{2}{4}\) cups
Thus the correct answer is option b.

Question 2.
Kate has 4 \(\frac{3}{8}\) yards of fabric and needs 2 \(\frac{7}{8}\) yards to make a skirt. How much extra fabric will she have left after making the skirt?
Options:
a. 2 \(\frac{4}{8}\) yards
b. 2 \(\frac{2}{8}\) yards
c. 1 \(\frac{4}{8}\) yards
d. 1 \(\frac{2}{8}\) yards

Answer: 1 \(\frac{4}{8}\) yards

Explanation:
Given,
Kate has 4 \(\frac{3}{8}\) yards of fabric and needs 2 \(\frac{7}{8}\) yards to make a skirt.
First, subtract the whole numbers
4 – 2 = 2
Next, subtract the fractions,
\(\frac{3}{8}\) – \(\frac{7}{8}\) = – \(\frac{4}{8}\)
2 – \(\frac{4}{8}\) = 1 \(\frac{4}{8}\) yards
Thus the correct answer is option c.

Spiral Review

Question 3.
Paulo has 128 glass beads to use to decorate picture frames. He wants to use the same number of beads on each frame. If he decorates 8 picture frames, how many beads will he put on each frame?
Options:
a. 6
b. 7
c. 14
d. 16

Answer: 16

Explanation:
Given,
Paulo has 128 glass beads to use to decorate picture frames. He wants to use the same number of beads on each frame
128/8 = 16
Thus the correct answer is option d.

Question 4.
Madison is making party favors. She wants to make enough favors so each guest gets the same number of favors. She knows there will be 6 or 8 guests at the party. What is the least number of party favors Madison should make?
Options:
a. 18
b. 24
c. 30
d. 32

Answer: 24

Explanation:
Given,
Madison is making party favors. She wants to make enough favors so each guest gets the same number of favors.
She knows there will be 6 or 8 guests at the party.
To find the least number of party favors, we have to consider the number of guests.
In this case, there are two possibilities—6 or 8.
For 6: 6, 12, 18, 24 (Add 6 to each number)
For 8: 8, 16, 24 (Add 8 to each number)
Now in both series, the least number (that is in common) is 24. Hence, Madison should make at least 24 party favors.
Thus the correct answer is option b.

Question 5.
A shuttle bus makes 4 round-trips between two shopping centers each day. The bus holds 24 people. If the bus is full on each one-way trip, how many passengers are carried by the bus each day?
Options:
a. 96
b. 162
c. 182
d. 192

Answer: 96

Explanation:
Given,
A shuttle bus makes 4 round-trips between two shopping centers each day. The bus holds 24 people.
4 × 24 = 96
Thus the correct answer is option a.

Question 6.
To make a fruit salad, Marvin mixes 1 \(\frac{3}{4}\) cups of diced peaches with 2 \(\frac{1}{4}\) cups of diced pears. How many cups of peaches and pears are in the fruit salad?
Options:
a. 4 cups
b. 3 \(\frac{2}{4}\) cups
c. 3 \(\frac{1}{4}\) cups
d. 3 cups

Answer: 4 cups

Explanation:
Given,
To make a fruit salad, Marvin mixes 1 \(\frac{3}{4}\) cups of diced peaches with 2 \(\frac{1}{4}\) cups of diced pears.
1 \(\frac{3}{4}\) + 2 \(\frac{1}{4}\)
= 4 cups
Thus the correct answer is option a.

Common Core – Add and Subtract Fractions – Page No. 149

Fractions and Properties of Addition

Use the properties and mental math to find the sum.

Question 1.

Question 2.
\(10 \frac{1}{8}+\left(3 \frac{5}{8}+2 \frac{7}{8}\right)\)
_______ \(\frac{□}{□}\)

Answer: 16 \(\frac{5}{8}\)

Explanation:
Given,
\(10 \frac{1}{8}+\left(3 \frac{5}{8}+2 \frac{7}{8}\right)\)
First add the whole numbers in the bracket.
3 + 2 = 5
10 \(\frac{1}{8}\) + 5 + \(\frac{5}{8}\) + \(\frac{7}{8}\)
10 \(\frac{1}{8}\) + 5 + \(\frac{12}{8}\)
10 + 5 = 15
15 + \(\frac{1}{8}\) + \(\frac{12}{8}\)
15 + \(\frac{13}{8}\)
16 \(\frac{5}{8}\)
\(10 \frac{1}{8}+\left(3 \frac{5}{8}+2 \frac{7}{8}\right)\) = 16 \(\frac{5}{8}\)

Question 3.
\(8 \frac{1}{5}+\left(3 \frac{2}{5}+5 \frac{4}{5}\right)\)
_______ \(\frac{□}{□}\)

Answer: 17 \(\frac{2}{5}\)

Explanation:
\(8 \frac{1}{5}+\left(3 \frac{2}{5}+5 \frac{4}{5}\right)\)
8 \(\frac{1}{5}\) + 3 \(\frac{2}{5}\) + 5 \(\frac{4}{5}\)
3 + 5 = 8
8 \(\frac{1}{5}\) + 8 + \(\frac{2}{5}\) + \(\frac{4}{5}\)
8 \(\frac{1}{5}\) + 8 + \(\frac{6}{5}\)
8 + 8 = 16
16 + \(\frac{1}{5}\) + \(\frac{6}{5}\)
16 + \(\frac{7}{5}\)
17 \(\frac{2}{5}\)
\(8 \frac{1}{5}+\left(3 \frac{2}{5}+5 \frac{4}{5}\right)\) = 17 \(\frac{2}{5}\)

Question 4.
\(6 \frac{3}{4}+\left(4 \frac{2}{4}+5 \frac{1}{4}\right)\)
_______ \(\frac{□}{□}\)

Answer: 16 \(\frac{1}{2}\)

Explanation:
\(6 \frac{3}{4}+\left(4 \frac{2}{4}+5 \frac{1}{4}\right)\)
First add the whole numbers in the bracket.
6 \(\frac{3}{4}\) + 4 \(\frac{2}{4}\) + 5 \(\frac{1}{4}\)
4 + 5 = 9
6 \(\frac{3}{4}\) + 9 \(\frac{3}{4}\)
6 + 9 = 15
15 + \(\frac{3}{4}\) + \(\frac{3}{4}\)
16 \(\frac{1}{2}\)
\(6 \frac{3}{4}+\left(4 \frac{2}{4}+5 \frac{1}{4}\right)\) = 16 \(\frac{1}{2}\)

Question 5.
\(\left(6 \frac{3}{6}+10 \frac{4}{6}\right)+9 \frac{2}{6}\)
_______ \(\frac{□}{□}\)

Answer: 26 \(\frac{3}{6}\)

Explanation:
\(\left(6 \frac{3}{6}+10 \frac{4}{6}\right)+9 \frac{2}{6}\)
6 \(\frac{3}{6}\) + 10 \(\frac{4}{6}\) + 9 \(\frac{2}{6}\)
First add the whole numbers in the bracket.
6 + 10 = 16
16 + \(\frac{3}{6}\) + \(\frac{4}{6}\) + 9 \(\frac{2}{6}\)
16 + \(\frac{7}{6}\) + 9 \(\frac{2}{6}\)
16 + 9 = 25
25 + \(\frac{7}{6}\) + \(\frac{2}{6}\)
25 + \(\frac{9}{6}\)
= 26 \(\frac{3}{6}\)
\(\left(6 \frac{3}{6}+10 \frac{4}{6}\right)+9 \frac{2}{6}\) = 26 \(\frac{3}{6}\)

Question 6.
\(\left(6 \frac{2}{5}+1 \frac{4}{5}\right)+3 \frac{1}{5}\)
_______ \(\frac{□}{□}\)

Answer: 11 \(\frac{2}{5}\)

Explanation:
\(\left(6 \frac{2}{5}+1 \frac{4}{5}\right)+3 \frac{1}{5}\)
6 \(\frac{2}{5}\) + 1 \(\frac{4}{5}\) + 3 \(\frac{1}{5}\)
First add the whole numbers in the bracket.
6 + 1 = 7
7 \(\frac{2}{5}\) + \(\frac{4}{5}\) + 3 \(\frac{1}{5}\)
7 + \(\frac{6}{5}\) + 3 \(\frac{1}{5}\)
7 + 3 = 10
10 + \(\frac{6}{5}\) + \(\frac{1}{5}\)
10 + \(\frac{7}{5}\) = 11 \(\frac{2}{5}\)
Therefore \(\left(6 \frac{2}{5}+1 \frac{4}{5}\right)+3 \frac{1}{5}\) = 11 \(\frac{2}{5}\)

Question 7.
\(7 \frac{7}{8}+\left(3 \frac{1}{8}+1 \frac{1}{8}\right)\)
_______ \(\frac{□}{□}\)

Answer: 12 \(\frac{1}{8}\)

Explanation:
\(7 \frac{7}{8}+\left(3 \frac{1}{8}+1 \frac{1}{8}\right)\)
7 \(\frac{7}{8}\) + 3 \(\frac{1}{8}\) + 1 \(\frac{1}{8}\)
First add the whole numbers in the bracket.
3 + 1 = 4
7 \(\frac{7}{8}\) + 4 + \(\frac{1}{8}\) + \(\frac{1}{8}\)
7 \(\frac{7}{8}\) + 4 +\(\frac{2}{8}\)
7 + 4 = 11
11 + \(\frac{7}{8}\) + \(\frac{2}{8}\)
11 + \(\frac{9}{8}\) = 12 \(\frac{1}{8}\)
Thus \(7 \frac{7}{8}+\left(3 \frac{1}{8}+1 \frac{1}{8}\right)\) = 12 \(\frac{1}{8}\)

Question 8.
\(14 \frac{1}{10}+\left(20 \frac{2}{10}+15 \frac{7}{10}\right)\)
_______ \(\frac{□}{□}\)

Answer: 50

Explanation:
\(14 \frac{1}{10}+\left(20 \frac{2}{10}+15 \frac{7}{10}\right)\)
First add the whole numbers in the bracket.
14 \(\frac{1}{10}\) + 20 \(\frac{2}{10}\) + 15 \(\frac{7}{10}\)
20 + 15 = 35
14 \(\frac{1}{10}\) + 35 + \(\frac{2}{10}\) + \(\frac{7}{10}\)
14 \(\frac{1}{10}\) + 35 \(\frac{9}{10}\)
49 \(\frac{1}{10}\) + \(\frac{9}{10}\)
49 + 1 = 50
Thus \(14 \frac{1}{10}+\left(20 \frac{2}{10}+15 \frac{7}{10}\right)\) = 50

Question 9.
\(\left(13 \frac{2}{12}+8 \frac{7}{12}\right)+9 \frac{5}{12}\)
_______ \(\frac{□}{□}\)

Answer: 31 \(\frac{2}{12}\)

Explanation:
\(\left(13 \frac{2}{12}+8 \frac{7}{12}\right)+9 \frac{5}{12}\)
13 \(\frac{2}{12}\) + 8 \(\frac{7}{12}\) + 9 \(\frac{5}{12}\)
First add the whole numbers in the bracket.
13 + 8 = 21
21 + \(\frac{2}{12}\) + \(\frac{7}{12}\) + 9 \(\frac{5}{12}\)
21 + \(\frac{9}{12}\) + 9 \(\frac{5}{12}\)
30 + \(\frac{9}{12}\) + \(\frac{5}{12}\) = 31 \(\frac{2}{12}\)
Thus \(\left(13 \frac{2}{12}+8 \frac{7}{12}\right)+9 \frac{5}{12}\) = 31 \(\frac{2}{12}\)

Problem Solving

Question 10.
Nate’s classroom has three tables of different lengths. One has a length of 4 \(\frac{1}{2}\) feet, another has a length of 4 feet, and a third has a length of 2 \(\frac{1}{2}\) feet. What is the length of all three tables when pushed end to end?
_______ \(\frac{□}{□}\)

Answer: 11

Explanation:
Given,
Nate’s classroom has three tables of different lengths. One has a length of 4 \(\frac{1}{2}\) feet, another has a length of 4 feet, and a third has a length of 2 \(\frac{1}{2}\) feet.
4 \(\frac{1}{2}\) + 4 + 2 \(\frac{1}{2}\)
4 + 4 + 2 = 10
\(\frac{1}{2}\) + \(\frac{1}{2}\) = 1
10 + 1 = 11
Therefore the length of all three tables when pushed end to end is 11 feet.

Question 11.
Mr. Warren uses 2 \(\frac{1}{4}\) bags of mulch for his garden and another 4 \(\frac{1}{4}\) bags for his front yard. He also uses \(\frac{3}{4}\) bag around a fountain. How many total bags of mulch does Mr. Warren use?
_______ \(\frac{□}{□}\)

Answer: 7 \(\frac{1}{4}\)

Explanation:
Given,
Mr. Warren uses 2 \(\frac{1}{4}\) bags of mulch for his garden and another 4 \(\frac{1}{4}\) bags for his front yard.
He also uses \(\frac{3}{4}\) bag around a fountain.
2 \(\frac{1}{4}\) + 4 \(\frac{1}{4}\) + \(\frac{3}{4}\)
2 + 4 = 6
6 + \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{3}{4}\)
= 7 \(\frac{1}{4}\)

Common Core – Add and Subtract Fractions – Page No. 150

Lesson Check

Question 1.
A carpenter cut a board into three pieces. One piece was 2 \(\frac{5}{6}\) feet long. The second piece was 3 \(\frac{1}{6}\) feet long. The third piece was 1 \(\frac{5}{6}\) feet long. How long was the board?
Options:
a. 6 \(\frac{5}{6}\) feet
b. 7 \(\frac{1}{6}\) feet
c. 7 \(\frac{5}{6}\) feet
d. 8 \(\frac{1}{6}\) feet

Answer: c. 7 \(\frac{5}{6}\) feet

Explanation:
Given,
A carpenter cut a board into three pieces. One piece was 2 \(\frac{5}{6}\) feet long. The second piece was 3 \(\frac{1}{6}\) feet long.
The third piece was 1 \(\frac{5}{6}\) feet long.
Add three pieces.
2 \(\frac{5}{6}\) + 3 \(\frac{1}{6}\)
= 5 + \(\frac{6}{6}\)
= 5 + 1 = 6
6 + 1 \(\frac{5}{6}\)
= 7 \(\frac{5}{6}\) feet
Thus the correct answer is option c.

Question 2.
Harry works at an apple orchard. He picked 45 \(\frac{7}{8}\) pounds of apples on Monday. He picked 42 \(\frac{3}{8}\) pounds of apples on Wednesday. He picked 54 \(\frac{1}{8}\) pounds of apples on Friday. How many pounds of apples did Harry pick those three days?
Options:
a. 132 \(\frac{3}{8}\) pounds
b. 141 \(\frac{3}{8}\) pounds
c. 142 \(\frac{1}{8}\) pounds
d. 142 \(\frac{3}{8}\) pounds

Answer: 142 \(\frac{3}{8}\) pounds

Explanation:
Given,
Harry works at an apple orchard. He picked 45 \(\frac{7}{8}\) pounds of apples on Monday.
He picked 42 \(\frac{3}{8}\) pounds of apples on Wednesday.
He picked 54 \(\frac{1}{8}\) pounds of apples on Friday.
45 \(\frac{7}{8}\) + 42 \(\frac{3}{8}\) + 54 \(\frac{1}{8}\)
Add the whole numbers first
45 + 42 + 54 = 141
141 + \(\frac{7}{8}\) + \(\frac{3}{8}\) + \(\frac{1}{8}\)
141 + 1 \(\frac{3}{8}\)
= 142 \(\frac{3}{8}\) pounds
Thus the correct answer is option d.

Spiral Review

Question 3.
There were 6 oranges in the refrigerator. Joey and his friends ate 3 \(\frac{2}{3}\) oranges. How many oranges were left?
Options:
a. 2 \(\frac{1}{3}\) oranges
b. 2 \(\frac{2}{3}\) oranges
c. 3 \(\frac{1}{3}\) oranges
d. 9 \(\frac{2}{3}\) oranges

Answer: 9 \(\frac{2}{3}\) oranges

Explanation:
Given,
There were 6 oranges in the refrigerator.
Joey and his friends ate 3 \(\frac{2}{3}\) oranges.
6 + 3 \(\frac{2}{3}\)
= 9 \(\frac{2}{3}\) oranges
Thus the correct answer is option d.

Question 4.
Darlene was asked to identify which of the following numbers is prime. Which number should she choose?
Options:
a. 2
b. 12
c. 21
d. 39

Answer: 2

Explanation:
A prime number is an integer, or whole number, that has only two factors 1 and itself.
In the above options, all are composite numbers except 2.
Therefore 2 is a prime number.
Thus the correct answer is option a.

Question 5.
A teacher has 100 chairs to arrange for an assembly. Which of the following is NOT a way the teacher could arrange the chairs?
Options:
a. 10 rows of 10 chairs
b. 8 rows of 15 chairs
c. 5 rows of 20 chairs
d. 4 rows of 25 chairs

Answer: 8 rows of 15 chairs

Explanation:
A teacher has 100 chairs to arrange for an assembly.
15 × 8 = 120
So, 8 rows of 15 chairs are not the way to arrange the chairs.
Thus the correct answer is option b.

Question 6.
Nic bought 28 folding chairs for $16 each. How much money did Nic spend on chairs?
Options:
a. $196
b. $348
c. $448
d. $600

Answer: c. $448

Explanation:
Given,
Nic bought 28 folding chairs for $16 each.
28 × 16 = 448
Thus the correct answer is option c.

Common Core – Add and Subtract Fractions – Page No. 151

Read each problem and solve.

Question 1.
Each child in the Smith family was given an orange cut into 8 equal sections. Each child ate \(\frac{5}{8}\) of the orange. After combining the leftover sections, Mrs. Smith noted that there were exactly 3 full oranges left. How many children are in the Smith family?

Question 2.
Val walks 2 \(\frac{3}{5}\) miles each day. Bill runs 10 miles once every 4 days. In 4 days, who covers the greater distance?
_________

Answer: Val

Explanation:
Given,
Val walks 2 \(\frac{3}{5}\) miles each day. Bill runs 10 miles once every 4 days.
2 \(\frac{3}{5}\) × 4
Convert from mixed fraction to the improper fraction.
2 \(\frac{3}{5}\) = \(\frac{13}{5}\) × 4 = 10.4
10.4 > 10
Thus Val covers the greater distance.

Question 3.
Chad buys peanuts in 2-pound bags. He repackages them into bags that hold \(\frac{5}{6}\) pound of peanuts. How many 2-pound bags of peanuts should Chad buy so that he can fill the \(\frac{5}{6}\) -pound bags without having any peanuts left over?
_________ 2-pound bags

Answer: 5

Explanation:
Given,
Chad buys peanuts in 2-pound bags. He repackages them into bags that hold \(\frac{5}{6}\) pound of peanuts.
\(\frac{5}{6}\) + \(\frac{5}{6}\) + \(\frac{5}{6}\) + \(\frac{5}{6}\) + \(\frac{5}{6}\)
Thus 5 2-pound bags of peanuts are left.

Question 4.
A carpenter has several boards of equal length. He cuts \(\frac{3}{5}\) of each board. After cutting the boards, the carpenter notices that he has enough pieces left over to make up the same length as 4 of the original boards. How many boards did the carpenter start with?
_________

Answer: 10

Explanation:
Given,
A carpenter has several boards of equal length. He cuts \(\frac{3}{5}\) of each board. After cutting the boards, the carpenter notices that he has enough pieces left over to make up the same length as 4 of the original boards.
4 of the original boards have a summed length of 20 units. 5 x 4 = 20.
Since 2/5 is left from each board, you simply add them until the 2’s add to 20.
So, 2 x 10 = 20. Hence, there are 10 2/5 boards.
That’s just 4 of the boards that the 2/5 make up, but that should also mean that there are 10 3/5 boards as well.
30/5 + 20/5 = 50/5 = 10

Common Core – Add and Subtract Fractions – Page No. 152

Lesson Check

Question 1.
Karyn cuts a length of ribbon into 4 equal pieces, each 1 \(\frac{1}{4}\) feet long. How long was the ribbon?
Options:
a. 4 feet
b. 4 \(\frac{1}{4}\) feet
c. 5 feet
d. 5 \(\frac{1}{4}\) feet

Answer: 5 feet

Explanation:
Given,
Karyn cuts a length of ribbon into 4 equal pieces, each 1 \(\frac{1}{4}\) feet long.
1 \(\frac{1}{4}\) × 4
Convert from the mixed fraction to the improper fraction.
1 \(\frac{1}{4}\) = \(\frac{5}{4}\)
\(\frac{5}{4}\) × 4 = 5 feet
Thus the correct answer is option c.

Question 2.
Several friends each had \(\frac{2}{5}\) of a bag of peanuts left over from the baseball game. They realized that they could have bought 2 fewer bags of peanuts between them. How many friends went to the game?
Options:
a. 6
b. 5
c. 4
d. 2

Answer: 5

Explanation:
Given,
Several friends each had \(\frac{2}{5}\) of a bag of peanuts left over from the baseball game.
They realized that they could have bought 2 fewer bags of peanuts between them
2 ÷ \(\frac{2}{5}\) = 5
Thus the correct answer is option b.

Spiral Review

Question 3.
A frog made three jumps. The first was 12 \(\frac{5}{6}\) inches. The second jump was 8 \(\frac{3}{6}\) inches. The third jump was 15 \(\frac{1}{6}\) inches. What was the total distance the frog jumped?
Options:
a. 35 \(\frac{3}{6}\) inches
b. 36 \(\frac{1}{6}\) inches
c. 36 \(\frac{3}{6}\) inches
d. 38 \(\frac{1}{6}\) inches

Answer: 36 \(\frac{3}{6}\) inches

Explanation:
Given,
A frog made three jumps. The first was 12 \(\frac{5}{6}\) inches. The second jump was 8 \(\frac{3}{6}\) inches. The third jump was 15 \(\frac{1}{6}\) inches.
First add the whole numbers
12 + 8 + 15 = 35
Next add the fractions,
\(\frac{5}{6}\) + \(\frac{3}{6}\) + \(\frac{1}{6}\) = 1 \(\frac{3}{6}\)
35 + \(\frac{3}{6}\) = 36 \(\frac{3}{6}\) inches
Thus the correct answer is option c.

Question 4.
LaDanian wants to write the fraction \(\frac{4}{6}\) as a sum of unit fractions. Which expression should he write?
Options:
a. \(\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}\)
b. \(\frac{2}{6}+\frac{2}{6}\)
c. \(\frac{3}{6}+\frac{1}{6}\)
d. \(\frac{1}{6}+\frac{1}{6}+\frac{2}{6}\)

Answer: \(\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}\)

Explanation:
Given,
LaDanian wants to write the fraction \(\frac{4}{6}\) as a sum of unit fractions.
The unit fraction for \(\frac{4}{6}\) is \(\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}\)
Thus the correct answer is option a.

Question 5.
Greta made a design with squares. She colored 8 out of the 12 squares blue. What fraction of the squares did she color blue?
Options:
a. \(\frac{1}{4}\)
b. \(\frac{1}{3}\)
c. \(\frac{2}{3}\)
d. \(\frac{3}{4}latex]

Answer: [latex]\frac{2}{3}\)

Explanation:
Given,
Greta made a design with squares. She colored 8 out of the 12 squares blue.
\(\frac{8}{12}\)
= \(\frac{2}{3}\)
Thus the correct answer is option c.

Question 6.
The teacher gave this pattern to the class: the first term is 5 and the rule is add 4, subtract 1. Each student says one number. The first student says 5. Victor is tenth in line. What number should Victor say?
Options:
a. 17
b. 19
c. 20
d. 21

Answer:
given
a=5
d=4-1=3
to find t10
tn=a + (n-1) d
t10=5 + (10-1) 3
t10=5 + 27
t10 = 32
victor is tenth in line,therefore he should say the number 32

Common Core – Add and Subtract Fractions – Page No. 153

Lesson 7.1

Use the model to write an equation.

Question 1.

Type below:
_________

Answer: 1/6 + 3/6 = 4/6

Explanation:
From the figure, we can see that the shaded fraction of the first circle is 1/6.
The shaded fraction of the second circle is 3/6
The shaded fraction of the third circle is 4/6.

Question 2.

Type below:
_________

Answer: 5/8

Explanation:
From the above figure, we can say that the fraction of the shaded part is 5/8.

Use the model to solve the equation.

Question 3.
\(\frac{3}{10}+\frac{5}{10}\) =

\(\frac{□}{□}\)

Answer: \(\frac{8}{10}\)

Explanation:
The shaded part of the first figure is 3/10
The shaded part of the second figure is 5/10
\(\frac{3}{10}+\frac{5}{10}\) = \(\frac{8}{10}\)

Question 4.
\(\frac{7}{12}-\frac{6}{12}\) =

\(\frac{□}{□}\)

Answer: \(\frac{1}{12}\)

Explanation:
The shaded part of the above figure is 7/12. Out of which 6/12 are subtracted.
\(\frac{7}{12}-\frac{6}{12}\) = \(\frac{1}{12}\)

Lesson 7.2

Write the fraction as a sum of unit fractions.

Question 5.
\(\frac{2}{3}\) =
Type below:
_________

Answer: The unit fraction of \(\frac{2}{3}\) is \(\frac{1}{3}\) + \(\frac{1}{3}\)

Question 6.
\(\frac{3}{10}\) =
Type below:
_________

Answer: The unit fraction of \(\frac{3}{10}\) is \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\)

Question 7.
\(\frac{4}{6}\) =
Type below:
_________

Answer: The unit fraction of \(\frac{4}{6}\) is \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\)

Question 8.
\(\frac{5}{12}\) =
Type below:
_________

Answer: The unit fraction of \(\frac{5}{12}\) is \(\frac{1}{12}\) + \(\frac{1}{12}\) + \(\frac{1}{12}\) + \(\frac{1}{12}\) + \(\frac{1}{12}\)

Lessons 7.3–7.5

Find the sum or difference. Use fraction strips to help.

Question 9.
\(\frac{3}{8}+\frac{2}{8}\) =
\(\frac{□}{□}\)

Answer: \(\frac{5}{8}\)

Question 10.
\(\frac{4}{5}+\frac{1}{5}\) =
\(\frac{□}{□}\)

Answer: 1

Question 11.
\(\frac{6}{10}+\frac{1}{10}\) =
\(\frac{□}{□}\)

Answer: \(\frac{7}{10}\)

Question 12.
\(\frac{5}{6}-\frac{4}{6}\) =
\(\frac{□}{□}\)

Answer: \(\frac{1}{6}\)

Question 13.
\(\frac{3}{4}-\frac{1}{4}\) =
\(\frac{□}{□}\)

Answer: \(\frac{1}{2}\)

Question 14.
1 – \(\frac{7}{12}\) =
\(\frac{□}{□}\)

Answer: \(\frac{5}{12}\)

Question 15.
\(\frac{7}{10}-\frac{3}{10}\) =
\(\frac{□}{□}\)

Answer: \(\frac{4}{10}\)

Question 16.
\(\frac{2}{6}+\frac{4}{6}\) =
\(\frac{□}{□}\)

Answer: 1

Question 17.
\(\frac{5}{8}-\frac{4}{8}\) =
\(\frac{□}{□}\)

Answer: \(\frac{1}{8}\)

Common Core – Add and Subtract Fractions – Page No. 154

Lesson 7.6

Write each mixed number as a fraction and each fraction as a mixed number.

Question 1.
4 \(\frac{2}{3}\) =
\(\frac{□}{□}\)

Answer: \(\frac{14}{3}\)

Explanation:
First multiply 4 and 3
4 × 3 = 12
And then add 2 to 12
12 + 2 = 14
Thus the fraction of the mixed fraction is \(\frac{14}{3}\).

Question 2.
6 \(\frac{1}{4}\) =
\(\frac{□}{□}\)

Answer: \(\frac{25}{4}\)

Explanation:
First multiply 6 and 4
6 × 4 = 24
And then add 1 to 24
24 + 1 = 25
Thus the fraction of the mixed fraction is \(\frac{25}{4}\)

Question 3.
\(\frac{11}{3}\) =
_______ \(\frac{□}{□}\)

Answer: 3 \(\frac{2}{3}\)

Explanation:
Convert from improper fraction to the mixed fraction.
3 × 3 = 9
9 + 2 = 11
\(\frac{11}{3}\) = 3 \(\frac{2}{3}\)

Question 4.
\(\frac{16}{15}\) =
_______ \(\frac{□}{□}\)

Answer: 1 \(\frac{1}{15}\)

Explanation:
Given,
Convert from improper fraction to the mixed fraction.
15 × 1 = 15
15 + 1 = 16
\(\frac{16}{15}\) = 1 \(\frac{1}{15}\)

Lessons 7.7–7.8

Find the sum or difference.

Question 5.
\(3 \frac{1}{4}+2 \frac{3}{4}\) =
_______ \(\frac{□}{□}\)

Answer: 6

Explanation:
Given,
\(3 \frac{1}{4}+2 \frac{3}{4}\)
First add the whole numbers
3 + 2 = 5
\(\frac{1}{4}\) + \(\frac{3}{4}\) = 1
5 + 1 = 6
\(3 \frac{1}{4}+2 \frac{3}{4}\) = 6

Question 6.
\(1 \frac{5}{12}+2 \frac{1}{12}\) =
_______ \(\frac{□}{□}\)

Answer: 3 \(\frac{6}{12}\)

Explanation:
Given,
\(1 \frac{5}{12}+2 \frac{1}{12}\)
First add the whole numbers
1 + 2 = 3
3 \(\frac{5}{12}\) + \(\frac{1}{12}\) = 3 \(\frac{6}{12}\)

Question 7.

\(9 \frac{5}{6}-7 \frac{1}{6}\) =
_______ \(\frac{□}{□}\)

Answer: 2 \(\frac{4}{6}\)

Explanation:
Given,
\(9 \frac{5}{6}-7 \frac{1}{6}\)
First subtract the whole numbers
9 – 7 = 2
5/6 – 1/6 = \(\frac{4}{6}\)
2 + \(\frac{4}{6}\) = 2 \(\frac{4}{6}\)
Thus \(9 \frac{5}{6}-7 \frac{1}{6}\) = 2 \(\frac{4}{6}\)

Question 8.

\(9 \frac{3}{10}-1 \frac{7}{10}\) =
_______ \(\frac{□}{□}\)

Answer: 7 \(\frac{6}{10}\)

Explanation:
Given,
\(9 \frac{3}{10}-1 \frac{7}{10}\)
First subtract the whole numbers
9 – 1 = 8
3/10 – 7/10 = – 4/10
8 – 4/10 = 7 \(\frac{6}{10}\)

Lesson 7.9

Use the properties and mental math to find the sum.

Question 9.
\(\left(1 \frac{1}{4}+4\right)+2 \frac{3}{4}\)
_______ \(\frac{□}{□}\)

Answer: 8

Explanation:
Given,
\(\left(1 \frac{1}{4}+4\right)+2 \frac{3}{4}\)
1 \(\frac{1}{4}\) + 4 + 2 \(\frac{3}{4}\)
Add the whole numbers
1 + 4 = 5
5 \(\frac{1}{4}\) + 2 \(\frac{3}{4}\)
5 + 2 = 7
\(\frac{1}{4}\) + \(\frac{3}{4}\) = 1
7 + 1 = 8

Question 10.
\(\frac{3}{5}+\left(90 \frac{2}{5}+10\right)\)
_______ \(\frac{□}{□}\)

Answer: 101

Explanation:
Given,
\(\frac{3}{5}+\left(90 \frac{2}{5}+10\right)\)
Add the whole numbers
90 + 10 = 100
3/5 + 2/5 = 5/5 = 1
100 + 1 = 101

Question 11.
\(3 \frac{2}{6}+\left(2 \frac{1}{6}+\frac{4}{6}\right)\)
_______ \(\frac{□}{□}\)

Answer: 6 \(\frac{1}{6}\)

Explanation:
Given,
\(3 \frac{2}{6}+\left(2 \frac{1}{6}+\frac{4}{6}\right)\)
1/6 + 4/6 = 5/6
3 \(\frac{2}{6}\) + 2 \(\frac{5}{6}\) = 6 \(\frac{1}{6}\)

Question 12.
\(\left(\frac{5}{8}+2 \frac{3}{8}\right)+1 \frac{3}{8}\)
_______ \(\frac{□}{□}\)

Answer: 4 \(\frac{3}{8}\)

Explanation:
Given,
\(\left(\frac{5}{8}+2 \frac{3}{8}\right)+1 \frac{3}{8}\)
5/8 + 3/8 = 8/8 = 1
2 + 1 = 3
3 + 1 3/8 = 4 \(\frac{3}{8}\)

Lesson 7.10

Question 13.
Adrian jogs \(\frac{3}{4}\) mile each morning. How many days will it take him to jog 3 miles?
____ days

Answer: 4 days

Explanation:
Given,
Adrian jogs \(\frac{3}{4}\) mile each morning.
\(\frac{3}{4}\)/3 = 4
Thus it will take 4 days for him to jog 3 miles.

Question 14.
Trail mix is sold in 1-pound bags. Mary will buy some trail mix and re-package it so that each of the 15 members of her hiking club gets one \(\frac{2}{5}\) -pound bag. How many 1-pound bags of trail mix should Mary buy to have enough trail mix without leftovers?
____ 1-pound bags

Answer: 6 1-pound bags

Explanation:
Given,
Trail mix is sold in 1-pound bags. Mary will buy some trail mix and re-package it so that each of the 15 members of her hiking club gets one \(\frac{2}{5}\) -pound bag.
15 × \(\frac{2}{5}\) = 6
Therefore Mary should buy 6 1-pound bags to have enough trail mix without leftovers.

Conclusion:
I wish the information shared in Go Math Grade 4 Answer Key Homework Practice FL Chapter 7 Add and Subtract Fractions pdf is helpful for all the students and teachers. Test yourself by solving the problems in HMH Go Math Grade 4 Answer Key Chapter 7 Add and Subtract Fractions. Stay tuned to get the pdfs of all the chapters of Grade 4 Go Math Answer Key. All the Best!!!

Go Math Grade 4 Answer Key Homework Practice FL Chapter 3 Multiply 2-Digit Numbers helps the parents to make their child understand the concepts of multiplication. It is very important for students to learn the fundamentals in primary schools. Or else you will face many issues in the secondary standards. We help the students to overcome the difficulties of basics of maths by providing the Answer Key for Go Math Grade 4 Homework Practice FL Chapter 3 Multiply 2-Digit Numbers.

Go Math Grade 4 Answer Key Homework Practice FL Chapter 3 Multiply 2-Digit Numbers

Refer Go Math Grade 4 Answer Key Homework Practice FL Chapter 3 Multiply 2-Digit Numbers by downloading the pdf for free. We have presented the step by steps explanation for all the questions here. All you have to do is to click on the below links and get the simple techniques to solve the solutions.

Lesson: 1 – Multiply by Tens

• Common Core – Multiply 2-Digit Numbers – Page No. 51
• Common Core – Multiply 2-Digit Numbers – Page No. 52

Lesson: 2 – Estimate Products

• Common Core – Multiply 2-Digit Numbers – Page No. 53
• Common Core – Multiply 2-Digit Numbers – Page No. 54

Lesson: 3 – Investigate • Area Models and Partial Products

• Common Core – Multiply 2-Digit Numbers – Page No. 55
• Common Core – Multiply 2-Digit Numbers – Page No. 56

Lesson: 4 – Multiply Using Partial Products

• Common Core – Multiply 2-Digit Numbers – Page No. 57
• Common Core – Multiply 2-Digit Numbers – Page No. 58

Lesson: 5 – Multiply with Regrouping

• Common Core – Multiply 2-Digit Numbers – Page No. 59
• Common Core – Multiply 2-Digit Numbers – Page No. 60

Lesson: 6 – Choose a Multiplication Method

• Common Core – Multiply 2-Digit Numbers – Page No. 61
• Common Core – Multiply 2-Digit Numbers – Page No. 62

Lesson: 7 – Problem Solving • Multiply 2-Digit Numbers

• Common Core – Multiply 2-Digit Numbers – Page No. 63
• Common Core – Multiply 2-Digit Numbers – Page No. 64

Lesson: 8

• Common Core – Multiply 2-Digit Numbers – Page No. 65
• Common Core – Multiply 2-Digit Numbers – Page No. 66

Common Core – Multiply 2-Digit Numbers – Page No. 51

Multiply by Tens

Choose a method. Then find the product.

Question 1.
16 × 60 = 960
Use the halving-and-doubling strategy.
Find half of 16: 16 ÷ 2 = 8.
Multiply this number by 60: 8 × 60 = 480
Double this result: 2 × 480 = 960

Question 2.
80 × 22 = _____

Answer: 1760

Explanation:
By using the place value method, Multiply 80 × 22
You can think of 80 as 8 tens
80 × 22 = (22 × 8) tens
= 176 tens
= 176 × 10 = 1760
80 × 22 = 1760

Question 3.
30 × 52 = _____

Answer: 1560

Explanation:
Use the Associative Property
You can think of 30 as 3 × 10
30 × 52 = (3 × 10) × 52
= 3 × (10 × 52)
= 3 × 520
= 1560
30 × 52 = 1560

Question 4.
60 × 20 = _____

Answer: 1200

Explanation:
60 × 20
Use the halving and doubling strategy
half of the 60 to make the problem simpler
60/ 2 = 30
Multiply 30 with 20
30 × 20 = 600
Double the 600
2 × 600= 1200
60 × 20 = 1200

Question 5.
40 × 35 = _____

Answer: 1400

Explanation:
By using the Associative Property 40 × 35
You can think of 40 as 4 × 10
40 × 35 = (4 × 10) × 35
= 4 × (10 × 35)
= 4 × 350
= 1400
40 × 35 = 1400

Question 6.
10 × 90 = _____

Answer: 900

Explanation:
By using the place value method, Multiply 10 x 90
You can think of 90 as 9 tens
10 × 90 = (10 × 9) tens
= 90 tens
= 10 × 90 = 900

Question 7.
31 × 50 = _____

Answer: 1,550

Explanation:
Use the place value method to multiply 31 × 50
You can think of 50 as 5 tens
31 × 50 = 31 × 5 tens
= 155 tens
= 1,550
31 × 50 = 1,550

Problem Solving

Question 8.
Kenny bought 20 packs of baseball cards. There are 12 cards in each pack. How many cards did Kenny buy?
_____ cards

Answer: 240 cards

Explanation:
From the given data,
Kenny bought 20 packs of basketball cards
There are 12 cards in each pack = 12 × 20 cards
Use the associative property
You can write 20 as 2 × 10
12 × 20 = 12 × (2 × 10)
= (12 × 2) × 10
= (24) × 10
= 240 cards
Kenny bought 240 cards

Question 9.
The Hart family drove 10 hours to their vacation spot. They drove an average of 48 miles each hour. How many miles did they drive in all?
_____ miles

Answer: 480 miles

Explanation:
As per the given data,
Hart family drove 10 hours to their vacation spot
The average speed per each hour is = 48 miles
Total miles = 48 × 10
Use the halving and doubling strategy
Half of the 48 to make the problem simpler
48/ 2 = 24
Multiply 24 with 10 = 24 × 10 = 240
Double the value = 2 × 240 = 480 miles
Total miles drove by hart family = 480 miles.

Common Core – Multiply 2-Digit Numbers – Page No. 52

Lesson Check

Question 1.
For the school play, 40 rows of chairs are set up. There are 22 chairs in each row. How many chairs are there in all?
Options:
a. 800
b. 840
c. 880
d. 8,800

Answer: 880

Explanation:
As per the given data
For the school play, 40 rows of chairs are available. 22 chairs are available in each row.
Then total chairs in school play are = 22 × 40
By using the place value method
You can think of 40 as 4 tens
22 × 40 = 22 × 4 tens
= 88 tens
= 880
Total chairs in school are = 880
Thus the answer is option c.

Question 2.
At West School, there are 20 classrooms. Each classroom has 20 students. How many students are at West School?
Options:
a. 40
b. 400
c. 440
d. 4,000

Answer: 400

Explanation:
From the given data,
Total classrooms in west school = 20
Number of students per each classroom = 20
Then, total students at West School = 20 × 20
By using the associative property
You can think of 20 as 2 × 10
20 × 20 = 20 × (2 × 10)
= (20 × 2) × 10
=(40) × 10
=400
Total number of students at West School = 400
Thus the answer is option b.

Spiral Review

Question 3.
Alex has 48 stickers. This is 6 times the number of stickers Max has. How many stickers does Max have?
Options:
a. 6
b. 7
c. 8
d. 9

Answer: 8

Explanation:
As per the give data,
Alex has 48 stickers
That means, X= 48
This is 6 times the number of stickers max has = Y = 6X = 48
Then, number of stickers with Max = Y = X = 48/6 = 8
Number of stickers with Max = Y = 8 Stickers.
Thus the answer is option c.

Question 4.
Ali’s dog weighs 8 times as much as her cat. Together, the two pets weigh 54 pounds. How much does Ali’s dog weigh?
Options:
a. 6 pounds
b. 42 pounds
c. 46 pounds
d. 48 pounds

Answer: 48 pounds

Explanation:
From the given data,
Ali’s cat weight = X
Ali’s dog weight = 8 times as much as Ali’s cat = 8X
Together, the two pets weight = (X + 8X) = 54 pounds
9X = 54 pounds
X = 54/9 pounds = 6 pounds
Then, Ali’s dog weight = 8X =8 x 6 = 48 pounds.
Thus the answer is option d.

Question 5.
Allison has 3 containers with 25 crayons in each. She also has 4 boxes of markers with 12 markers in each box. She gives 10 crayons to a friend. How many crayons and markers does Allison have now?
Options:
a. 34
b. 113
c. 123
d. 133

Answer: 113

Explanation:
As per the given data,
Allison has 3 containers with 25 crayons in each = X = 3 × 25 = 75
Allison has 4 boxes of markers with 12 markers in each box = Y = 4 × 12 = 48
Allison gives 10 crayons to a friend = Z = 75 – 10 = 65
Now, total number of crayons and markers with Allison = Y + Z = 48 + 65 = 113
Thus the answer is option b.

Question 6.
The state of Utah covers 82,144 square miles. The state of Montana covers 145,552 square miles. What is the total area of the two states?
Options:
a. 63,408 square miles
b. 223,408 square miles
c. 227,696 square miles
d. 966,992 square miles

Answer: 227,696 square miles

Explanation:
From the given data,
The state of Utah covers 82,144 square miles
The state of Montana covers 145,552 square miles
Then, Total area of the two states = 82,144 + 145,552
The total area of two states = 227,696 square miles.
Thus the answer is option c.

Common Core – Multiply 2-Digit Numbers – Page No. 53

Estimate Products

Estimate the product. Choose a method.

Question 1.
38 × 21
38 × 21
↓        ↓
40 × 20
800

Question 2.
63 × 19
Estimate: _______

Answer: 1200

Explanation:
63     19
↓        ↓
60     20
Use mental math
60 × 20 = 1200

Question 3.
27 × $42
Estimate: _______

Answer: 1200

Explanation:
27     42
↓        ↓
30      40
Use mental math
30 × $40 = $1200

Question 4.
73 × 67
Estimate: _______

Answer: 4900

Explanation:
73      67

      
70      70
Use mental math
70 × 70 = 4900

Question 5.
37 × $44
Estimate: _______

Answer: 1600

Explanation:
37     44
↓        ↓
40     40
Use mental math
40 × $40 = $1600

Question 6.
85 × 71
Estimate: _______

Answer: 6300

Explanation:
85     71
↓        ↓
90     70
Use mental math
90 × 70 = 6300

Question 7.
88 × 56
Estimate: _______

Answer: 5400

Explanation:
88     56
↓        ↓
90      60
Use mental math
90 × 60 = 5400

Question 8.
97 × 13
Estimate: _______

Answer: 1000

Explanation:
97     13
↓        ↓
100    10
Use mental math
100 × 10 = 1000

Question 9.
92 × 64
Estimate: _______

Answer: 5400

Explanation:
92     64
↓        ↓
90      60
Use mental math
90 × 60 = 5400

Problem Solving

Question 10.
A dime has a diameter of about 18 millimeters. About how many millimeters long would a row of 34 dimes be?
about ______ millimeters

Answer:

about 600 millimeters

Explanation:
From the given data,
A dime has a diameter of about 18 millimeters
Then, 34 dimes diameter = 18 × 34
18 x 34
↓        ↓
20 × 30 = 600
So, 34 dimes have a diameter of about 600 millimeters long

Question 11.
A half-dollar has a diameter of about 31 millimeters. About how many millimeters long would a row of 56 half-dollars be?
about ______ millimeters

Answer: 1800 millimeters

Explanation:
As per the given data,
A half – dollar has a diameter of about 31 millimeters
Then, 56 half-dollars diameter = 31 × 56
31     56
↓        ↓
30     60
So, 56 half-dollars have a diameter of about 1800 millimeters long.

Common Core – Multiply 2-Digit Numbers – Page No. 54

Lesson Check

Question 1.
Which is the best estimate for the product
43 × 68?
Options:
a. 3,500
b. 2,800
c. 2,400
d. 280

Answer: 2,800

Explanation:
Round to the nearest tens
43 × 68
↓        ↓
40 × 70
Use mental math
4 × 7 = 28
40 × 70 = 2800
Estimated product of 43 × 68 = 2800
The correct answer is option b.

Question 2.
Marissa burns 93 calories each time she plays fetch with her dog. She plays fetch with her dog once a day. About how many calories will Marissa burn playing fetch with her dog in 28 days?
Options:
a. 4,000
b. 2,700
c. 2,000
d. 270

Answer: 2,700

Explanation:
From the given data,
Marissa burned calories each time when she plays fetch with her dog= 93 calories
Then, Marissa burned calories in 28 days while playing fetch with her dog = 28 × 93
Round to the nearest tens
28 × 93
↓        ↓
30 × 90
Then, estimated burned calories in 28 days by Marissa = 2700 calories
The correct answer is option b.

Spiral Review

Question 3.
Use the model to find 3 × 126.

Options:
a. 368
b. 378
c. 468
d. 478

Answer: 378

Explanation:
From the above Figure,
3 × 126 = 3 × 100 + 3 × 20 + 3 × 6
= 300 + 60 + 18
= 378
3 × 126 = 378
The correct answer is option b.

Question 4.
A store sells a certain brand of jeans for $38. One day, the store sold 6 pairs of jeans of that brand. How much money did the store make from selling the 6 pairs of jeans?
Options:
a. $188
b. $228
c. $248
d. $288

Answer: $228

Explanation:
As per the given data,
A store sells a certain brand of jeans for rupees = $38
One day, the store sold 6 pairs of jeans of that brand = 6 × $38
6 × $38 = $228
The total amount of 6 pairs of jeans = $228
The correct answer is option b.

Question 5.
The Gateway Arch in St. Louis, Missouri, weighs about 20,000 tons. Which amount could be the exact number of tons the Arch weighs?
Options:
a. 31,093 tons
b. 25,812 tons
c. 17,246 tons
d. 14,096 tons

Answer: 17,246 tons

Explanation:
From the given data,
The Gateway Arch in St.Louis, Missouri weight = about 20,000 tons
From the available options, 17,246 tons is closer to 20,000 tons
Then, the exact number of tons the Arch weighs = 17,246 tons
The correct answer is option c.

Question 6.
Which is another name for 23 ten thousands?
Options:
a. 23,000,000
b. 2,300,000
c. 230,000
d. 23,000

Answer: 230,000

Explanation:
As per the data,
Another name for 23 ten thousands = 23 × 10,000
= 230,000
Another name for 23 ten thousand = 230,000
The correct answer is option c.

Common Core – Multiply 2-Digit Numbers – Page No. 55

Area Models and Partial Products

Draw a model to represent the product.
Then record the product.

Question 1.
13 × 42

Question 2.
18 × 34 = _____

Answer:

300 + 40 + 240 + 32 = 612

Question 3.
22 × 26 = _____

Answer:

400 + 120 + 40 + 12 = 572

Question 4.
15 × 33 = _____

Answer:

300 + 30 + 150 + 15 = 495

Question 5.
23 × 29 = _____

Answer:

400 + 180 + 60 + 27 = 667

Question 6.
19 × 36 = _____

Answer:

300 + 60 + 270 + 54 = 684

Problem Solving

Question 7.
Sebastian made the following model to find the product 17 × 24.

Is his model correct? Explain.
i. yes
ii. no

Answer: no

200 + 40 + 140 + 28 = 408

Question 8.
Each student in Ms. Sike’s kindergarten class has a box of crayons. Each box has 36 crayons. If there are 18 students in Ms. Sike’s class, how many crayons are
there in all?
_____ crayons

Answer: 648 crayons

Explanation:
From the given information,
Each student in Ms.Sike’s kindergarten class has a box of crayons
Crayons in each box = 36 Crayons
Number of students in Mr.Sike’s class = 18 students
Total crayons = 18 × 36

300 + 60 + 240 + 48 = 648

Common Core – Multiply 2-Digit Numbers – Page No. 56

Lesson Check

Question 1.
Which product does the model below represent?

Options:
a. 161
b. 230
c. 340
d. 391

Answer: 391

Explanation:
200 + 30 + 140 + 21 = 391
17 × 23 = 391
The correct answer is option d.

Question 2.
Which product does the model below represent?

Options:
a. 219
b. 225
c. 244
d. 275

Answer: 225

Explanation:
130 + 20 + 65 + 10 = 225
15 × 15 = 225
The correct answer is option b.

Spiral Review

Question 3.
Mariah builds a tabletop using square tiles. There are 12 rows of tiles and 30 tiles in each row. How many tiles in all does Mariah use?
Options:
a. 100
b. 180
c. 360
d. 420

Answer: 360

Explanation:
From the given data,
Mariah builds a tabletop using square tiles
Square contains 12 rows of tiles and 30 tiles in each row = 12 × 30
12 × 30 = 360 tiles
Total tiles used by Mariah = 360 tiles
The correct answer is option c.

Question 4.
Trevor bakes 8 batches of biscuits, with 14 biscuits in each batch. He sets aside 4 biscuits from each batch for a bake sale and puts the rest in a jar. How many biscuits does Trevor put in the jar?
Options:
a. 112
b. 80
c. 50
d. 32

Answer: 80

Explanation:
As per the given data,
Number of biscuits baked by Trevor = 8 batches
Number of biscuits in each batch = 14 biscuits
So, total biscuits = 14 × 8 = 112
Trevor sets aside 4 biscuits from each batch for a bake = 8 × 4 = 32 biscuits are aside for a bake
Trevor kept rest of biscuits in a jar = 112 – 32 = 80
So, 80 biscuits are put in the jar by Trevor.
The correct answer is option b.

Question 5.
Li feeds her dog 3 cups of food each day. About how many cups of food does her dog eat in 28 days?
Options:
a. 60 cups
b. 70 cups
c. 80 cups
d. 90 cups

Answer: 80 cups

Explanation:
As per the given data,
Li feeds her dog per day = 3 cups of food
Then, Li feeds her dog for 28 days = 3 × 28 = 84 cups of food
So, Li feeds her dog with 84 cups of food in 28 days.
The correct answer is option c.

Question 6.
Which symbol makes the number sentence true?
4 ■ 0 = 0
Options:
a. +
b. –
c. ×
d. ÷

Answer: ×

Explanation:
4 x 0 = 0

Common Core – Multiply 2-Digit Numbers – Page No. 57

Multiply Using Partial Products

Record the product.

Question 1.
2 3
× 7 9
1, 4 0 0
———
2 1 0
1 8 0
+ 2 7
———
1, 8 17

Question 2.
5 6
× 3 2
———
________

Answer: 1,792

Explanation:

Question 3.
8 7
× 6 4
———
________

Answer: 5,568

Explanation:

Question 4.
3 3
× 2 5
———
________

Answer: 825

Explanation:

Question 5.
9 4
× 1 2
———
________

Answer: 1,128

Explanation:

Question 6.
5 1
× 7 7
———
________

Answer: 3,927

Explanation:

Question 7.
6 9
× 4 9
———
________

Answer: 3,381

Explanation:

Question 8.
8 6
× 8 4
———
________

Answer: 7,224

Explanation:

Question 9.
9 8
× 4 2
———
________

Answer: 4,116

Explanation:

Question 10.
7 3
× 3 7
———
________

Answer: 2,701

Explanation:

Question 11.
8 5
× 5 1
———
________

Answer: 4,335

Explanation:

Problem Solving

Question 12.
Evelyn drinks 8 glasses of water a day, which is 56 glasses of water a week. How many glasses of water does she drink in a year? (1 year = 52 weeks)
______ glasses

Answer: 2,912 glasses

Explanation:
As per the given data,
Evelyn drinks 8 glasses of water a day
Evelyn drinks water per week = 56 glasses
Then, the number of glasses per 52 weeks = 52 × 56

Total number of glasses of water drink by Evelyn per year = 2912 glasses of water

Question 13.
Joe wants to use the Hiking Club’s funds to purchase new walking sticks for each of its 19 members. The sticks cost $26 each. The club has $480. Is this enough money to buy each member a new walking stick? If not, how much more money is needed?
Is the money enough? ________
How much more is needed? ________

Answer:
This amount is not enough to buy walking sticks
Still, $14 amount is needed to buy walking sticks

Explanation:
From the given data,
Joe wants to use the Hiking club funds to purchase new walking sticks for each of its 19 members
Cost per each stick = $26
Total walking sticks cost per 19 members = $26 × 19

Total cost for walking sticks for 19 members = $494
The club has = $480
This amount is not enough to buy walking sticks.
Still, $14 amount is needed to buy walking sticks.

Common Core – Multiply 2-Digit Numbers – Page No. 58

Lesson Check

Question 1.
A carnival snack booth made $76 selling popcorn in one day. It made 22 times as much selling cotton candy. How much money did the snack booth make selling
cotton candy?
Options:
a. $284
b. $304
c. $1,562
d. $1,672

Answer: $1,672

Explanation:
As per the given data,
A carnival snack booth made popcorn in one day = $76
It made 22 times as much selling cotton candy
Then, total selling cotton candy made by snack booth = $76 × 22

So, $1672 money snack booth will get for selling cotton candy.
Thus the correct answer is option d.

Question 2.
What are the partial products of
42 × 28?
Options:
a. 800, 80, 40, 16
b. 800, 16
c. 800, 40, 320, 16
d. 80, 16

Answer: 800, 40, 320, 16

Explanation:

So, partial products of 42 x 28 are 800, 40, 320, 16
Thus the correct answer is option c.

Spiral Review

Question 3.
Last year, the city library collected 117 used books for its shelves. This year, it collected 3 times as many books. How many books did it collect this year?
Options:
a. 832
b. 428
c. 351
d. 72

Answer: 351

Explanation:
From the given data,
Last year, the number of used books collected by the city library by its shelves = 117 books
This year, it collected 3 times as many books = 3 × 117 =351 books
Total number of books collected by the city library for this year = 351 books
Thus the correct answer is option c.

Question 4.
Washington Elementary has 232 students. Washington High has 6 times as many students. How many students does Washington High have?
Options:
a. 1,392
b. 1,382
c. 1,292
d. 1,281

Answer: 1,392

Explanation:
As per the given data,
The number of students in Washington elementary = 232 students
Washington High has 6 times as many students = 6 x 232 = 1392
Total number of students in Washington High = 1392 students
Thus the correct answer is option a.

Question 5.
What are the partial products of 35 × 7?
Options:
a. 10, 12
b. 21, 35
c. 210, 35
d. 350, 21

Answer: 210, 35

Explanation:
Partial products of 35 x 7 are 210, 35
Thus the correct answer is option c.

Question 6.
Shelby has ten $5 bills and thirteen $10 bills. How much money does Shelby have in all?
Options:
a. $15
b. $60
c. $63
d. $180

Answer: $180

Explanation:
From the given data,
Shelby has ten $5 bills and thirteen $10 bills = (10 x $5) + (13 x $10)
= ($50) + ($130)
=$180
Total money with Shelby = $180
Thus the correct answer is option d.

Common Core – Multiply 2-Digit Numbers – Page No. 59

Multiply with Regrouping
Estimate. Then find the product.

Question 1.
Estimate: 2,700
Think: 87 is close to 90 and 32 is close to 30.
90 × 30 = 2,700

Question 2.
7 3
× 2 8
———
Estimate: _______
Product: _______

Answer:
Estimate: 2,100
Product: 2,044

Explanation:
Estimate: 73 is close to 70; 28 is close to 30.
So, 70 × 30 = 2,100.
Product: Write 73 as 7 tens and 3 ones. Multiply 28 by 3 ones.
2
28
× 73
——–
84 <– 3 × 28
Multiply 28 by 7 tens
5
28
× 73
——–
1960 <– 70 × 28
Add the partial products.
84 + 1960 = 2,044.
So, 73 × 28 = 2,044.

Question 3.
4 8
× 3 8
———
Estimate: _______
Product: _______

Answer:
Estimate: 2,000
Product: 1,824

Explanation:
48 is close to 50 and 38 is close to 40.
Estimate: 50 × 40 = 2,000
40 × 38 = 1520
8 × 38 = 304
1520 + 304 = 1824.
Product: 1,824

Question 4.
5 9
× 5 2
———
Estimate: _______
Product: _______

Answer:
Estimate: 3,000
Product: 3,068

Explanation:
59 is close to 60 and 52 is close to 50.
Estimate: 60 × 50 = 3,000
50 × 52 = 2600
9 × 52 = 468
2600 + 468 = 3068.
Product: 3,068.

Question 5.
8 4
× 4 0
———
Estimate: _______
Product: _______

Answer:
Estimate: 3,200
Product: 3,360

Explanation:
84 is close to 80 and 40 is close to 40.
Estimate: 80 × 40 = 3,200
80 × 40 = 3,200
4 × 40 = 160
3200 + 160 = 3,360.
Product: 3,360.

Question 6.
8 3
× 7 7
———
Estimate: _______
Product: _______

Answer:
Estimate: 6,400
Product: 6,391

Explanation:
83 is close to 80 and 77 is close to 80.
Estimate: 80 × 80 = 6,400
80 × 77 = 6,160
3 × 77 = 231
6,160 + 231 = 6,391.
Product: 6,391.

Question 7.
9 1
× 1 9
———
Estimate: _______
Product: _______

Answer:

Estimate: 1,800
Product: 1,729

Explanation:
91 is close to 90 and 19 is close to 20.
Estimate: 90 × 20 = 1,800
90 × 19 = 1,710
1 × 19 = 19
1,710+ 19 = 1,729.
Product: 1,729.

Problem Solving

Question 8.
Baseballs come in cartons of 84 baseballs. A team orders 18 cartons of baseballs. How many baseballs does the team order?
______ baseballs

Answer: 1,512 baseballs

Explanation:
Given,
Baseballs come in cartons of 84 baseballs.
A team orders 18 cartons of baseballs.
To find total baseballs, 84 × 18
80 × 18 = 1,440
4 × 18 = 72
84 × 18 = 1,512
Thus the team order 1512 baseballs.

Question 9.
There are 16 tables in the school lunch room. Each table can seat 22 students. How many students can be seated at lunch at one time?
______ students

Answer: 352 students

Explanation:
Given,
There are 16 tables in the school lunch room.
Each table can seat 22 students.
Total Students = 16 × 22
10 × 22 = 220
6 × 22 = 132
220 + 132 = 352.
352 students can be seated at lunch at one time.

Common Core – Multiply 2-Digit Numbers – Page No. 60

Lesson Check

Question 1.
The art teacher has 48 boxes of crayons. There are 64 crayons in each box. Which is the best estimate of the number of crayons the art teacher has?
Options:
a. 2,400
b. 2,800
c. 3,000
d. 3,500

Answer: 3,000

Explanation:
Given,
The art teacher has 48 boxes of crayons. There are 64 crayons in each box.
Total number of crayons = 48 × 64
48 is close to 50; 64 is close to 60
50 × 60 = 3,000.
The art teacher has about 3, 000 crayons.
The correct answer is option c.

Question 2.
A basketball team scored an average of 52 points in each of 15 games. How many points did the team score in all?
Options:
a. 500
b. 312
c. 780
d. 1,000

Answer: 780

Explanation:
Given,
A basketball team scored an average of 52 points in each of 15 games.
Total Points = 52 × 15
50 × 15 = 750
2 × 15 = 30
750 + 30 = 780.
The basketball team scored 780 points in total.
The correct answer is option c.

Spiral Review

Question 3.
One Saturday, an orchard sold 83 bags of apples. There are 27 apples in each bag. Which expression represents the total number of apples sold?
Options:
a. 16 + 6 + 56 + 21
b. 160 + 60 + 56 + 21
c. 160 + 60 + 560 + 21
d. 1,600 + 60 + 560 + 21

Answer: 1,600 + 60 + 560 + 21

Explanation:
Total number of apples sold = 83 × 27
80 × 27 = 2,160
3 × 27 = 81
2,160 + 81 = 2,241.
The total number of apples sold = 2,241.
16 + 6 + 56 + 21 = 99 not equal to 2,241
160 + 60 + 56 + 21 = 297 not equal to 2,241
160 + 60 + 560 + 21 = 801 not equal to 2,241
1,600 + 60 + 560 + 21 = 2,241 equal to 2,241
1,600 + 60 + 560 + 21 = 2,241 is correct.
The correct answer is option d.

Question 4.
Hannah has a grid of squares that has 12 rows with 15 squares in each row. She colors 5 rows of 8 squares in the middle of the grid blue. She colors the rest of the squares red. How many squares does Hannah color red?
Options:
a. 40
b. 140
c. 180
d. 220

Answer: 140

Explanation:
Hannah has a grid of squares that has 12 rows with 15 squares in each row = 12 × 15 = 180.
She colors 5 rows of 8 squares in the middle of the grid blue.
The grid of squares in blue = 5 × 8 = 40.
The grid of squares in red = 180 – 40 = 140.
The correct answer is option b.

Question 5.
Gabriella has 4 times as many erasers a Leona. Leona has 8 erasers. How many erasers does Gabriella have?
Options:
a. 32
b. 24
c. 12
d. 2

Answer: 32

Explanation:
Given,
Gabriella has 4 times as many erasers a Leona.
Leona has 8 erasers.
Gabriella have 4 x 8 = 32 erasers.
The correct answer is option a.

Question 6.
Phil has 3 times as many rocks as Peter. Together, they have 48 rocks. How many more rocks does Phil have than Peter?
Options:
a. 36
b. 24
c. 16
d. 12

Answer: 24

Explanation:
Phil has 3 times as many rocks as Peter. Together, they have 48 rocks
If Peter has x rocks, Phil has 3x rocks
3x + x = 48.
4x = 48.
x = 48/4 = 12.
Peter has 12 rocks. Phil has 3 × 12 = 36 rocks.
Phil has 36 – 12 = 24 more rocks than Peter.
The correct answer is option b.

Common Core – Multiply 2-Digit Numbers – Page No. 61

Choose a Multiplication Method

Estimate. Then choose a method to find the product.

Question 1.
Estimate: 1,200
3 1
× 4 3
——-
9 3
+ 1, 2 4 0
———–
1, 3 3 3

Question 2.
6 7
× 8 5
———-
Estimate: _________
Product: _________

Answer:
Estimate: 6,300
Product: 5,695

Explanation:
Estimate: 67 is close to 70; 85 is close to 90.
70 × 90 = 6,300.
Product: 67 × 85
80 × 6 tens = 480 tens
80 × 7 ones = 560 ones
5 × 6 tens = 30 tens
5 × 7 ones = 35 ones.
Add partial products.
4800 + 560 + 300 + 35 = 5,695.

Question 3.
6 8
× 3 8
———-
Estimate: _________
Product: _________

Answer:
Estimate: 2,800
Product: 2,584

Explanation:
Estimate: 68 is close to 70; 38 is close to 40.
70 × 40 = 2,800.
Product: 68 × 38
30 × 6 tens = 180 tens
30 × 8 ones = 240 ones
8 × 6 tens = 48 tens
8 × 8 ones = 64 ones.
Add partial products.
1800 + 240 + 480 + 64 = 2,584.

Question 4.
9 5
× 1 7
———-
Estimate: _________
Product: _________

Answer:
Estimate: 1,700
Product: 1,615

Explanation:
Estimate: 95 is close to 100.
100 × 17 = 1,700.
Product: 95 × 17
10 × 9 tens = 90 tens
10 × 5 ones = 50 ones
7 × 9 tens = 63 tens
7 × 5 ones = 35 ones.
Add partial products.
900 + 50 + 630 + 35 = 1,615.

Question 5.
4 9
× 5 4
———-
Estimate: _________
Product: _________

Answer:
Estimate: 2,500
Product: 2,646

Explanation:
Estimate: 49 is close to 50; 54 is close to 50.
50 × 50 = 2,500.
Product: 49 × 54
50 × 4 tens = 200 tens
50 × 9 ones = 450 ones
4 × 4 tens = 16 tens
4 × 9 ones = 36 ones.
Add partial products.
2000 + 450 + 160 + 36 = 2,646.

Question 6.
9 1
× 2 6
———-
Estimate: _________
Product: _________

Answer:
Estimate: 2,700
Product: 2,366

Explanation:
Estimate: 91 is close to 90; 26 is close to 30.
90 × 30 = 2,700.
Product: 49 × 54
20 × 9 tens = 180 tens
20 × 1 ones = 20 ones
6 × 9 tens = 54 tens
6 × 1 ones = 6 ones.
Add partial products.
1800 + 20 + 540 + 6 = 2,366.

Question 7.
8 2
× 1 9
———-
Estimate: _________
Product: _________

Answer:
Estimate: 1,600
Product: 1,558

Explanation:
Estimate: 82 is close to 80; 19 is close to 20.
80 × 20 = 1,600.
Product: 82 × 19
10 × 8 tens = 80 tens
10 × 2 ones = 20 ones
9 × 8 tens = 72 tens
9 × 2 ones = 18 ones.
Add partial products.
800 + 20 + 720 + 18 = 1,558.

Question 8.
4 6
× 2 7
———-
Estimate: _________
Product: _________

Answer:
Estimate: 1,500
Product: 1,242

Explanation:
Estimate: 46 is close to 50; 27 is close to 30.
50 × 30 = 1,500.
Product: 46 × 27
20 × 4 tens = 80 tens
20 × 6 ones = 120 ones
7 × 4 tens = 28 tens
7 × 6 ones = 42 ones.
Add partial products.
800 + 120 + 280 + 42 = 1,242.

Question 9.
4 1
× 3 3
———-
Estimate: _________
Product: _________

Answer:
Estimate: 1,200
Product: 1,353

Explanation:
Estimate: 41 is close to 40; 33 is close to 30.
40 × 30 = 1,200.
Product: 41 × 33
30 × 4 tens = 120 tens
30 × 1 ones = 30 ones
3 × 4 tens = 12 tens
3 × 1 ones = 3 ones.
Add partial products.
1200 + 30 + 120 + 3 = 1,353.

Question 10.
9 7
× 1 3
———-
Estimate: _________
Product: _________

Answer:
Estimate: 1,300
Product: 1,261

Explanation:
Estimate: 97 is close to 100.
100 × 13 = 1,300.
Product: 97 × 13
10 × 9 tens = 90 tens
10 × 7 ones = 70 ones
3 × 9 tens = 27 tens
3 × 7 ones = 21 ones.
Add partial products.
900 + 70 + 270 + 21 = 1,261.

Question 11.
7 5
× 6 9
———-
Estimate: _________
Product: _________

Answer:
Estimate: 5,600
Product: 5,195

Explanation:
Estimate: 75 is close to 80; 69 is close to 70.
80 × 70 = 5,600.
Product: 75 × 69
60 × 7 tens = 420 tens
60 × 5 ones = 300 ones
9 × 7 tens = 63 tens
9 × 5 ones = 45 ones.
Add partial products.
4200 + 300 + 630 + 45 = 5,195.

Problem Solving

Question 12.
A movie theatre has 26 rows of seats. There are 18 seats in each row. How many seats are there in all?
_____ seats

Answer: 468 seats

Explanation:
Given,
A movie theatre has 26 rows of seats.
There are 18 seats in each row.
26 x 18 = 468 seats.
20 x 18 = 360
6 x 18 = 108
108+360 = 468.
Therefore there are 468 seats in all.

Question 13.
Each class at Briarwood Elementary collected at least 54 cans of food during the food drive. If there are 29 classes in the school, what was the least number of
cans collected?
_____ cans

Answer: 1,566 cans

Explanation:
Each class at Briarwood Elementary collected at least 54 cans of food.
If there are 29 classes in the school,
the least number of cans collected = 54 x 29 = 1,566 cans.

Common Core – Multiply 2-Digit Numbers – Page No. 62

Lesson Check

Question 1.
A choir needs new robes for each of its 46 singers. Each robe costs $32. What will be the total cost for all 46 robes?
Options:
a. $1,472
b. $1,372
c. $1,362
d. $230

Answer: $1,472

Explanation:
Given,
A choir needs new robes for each of its 46 singers. Each robe costs $32.
46 × $32
40 × $32 = $1,280
6 × $32 = $192
$1,280 + $192 = $1,472
The correct answer is option a.

Question 2.
A wall on the side of a building is made up of 52 rows of bricks with 44 bricks in each row. How many bricks make up the wall?
Options:
a. 3,080
b. 2,288
c. 488
d. 416

Answer: 2,288

Explanation:
Given,
A wall on the side of a building is made up of 52 rows of bricks with 44 bricks in each row.
52 × 44
50 × 44 = 2,200
2 × 44 = 88
2,200 + 88 = 2,288.
2,288 bricks make up the wall.
The correct answer is option b.

Spiral Review

Question 3.
Which expression shows how to multiply 4 × 362 by using place value and expanded form?
Options:
a. (4 × 3) + (4 × 6) + (4 × 2)
b. (4 × 300) + (4 × 600) +(4 × 200)
c. (4 × 300) + (4 × 60) + (4 × 20)
d. (4 × 300) + (4 × 60) + (4 × 2)

Answer: (4 × 300) + (4 × 60) + (4 × 2)

Explanation:
4 × 362 = 1,448
a. (4 × 3) + (4 × 6) + (4 × 2) = 12 + 24 + 8 = 44 not equal to 1,448.
b. (4 × 300) + (4 × 600) +(4 × 200) = 1200 + 2400 + 800 = 4,400 not equal to 1,448.
c. (4 × 300) + (4 × 60) + (4 × 20) = 1200 + 240 + 80 = 1,520 not equal to 1,448.
d. (4 × 300) + (4 × 60) + (4 × 2) = 1200 + 240 + 8 = 1,448 equal to 1,448.
The correct answer is option d.

Question 4.
Use the model below. What is the product 4 × 492?

Options:
a. 16 + 36 + 8 = 60
b. 160 + 36 + 8 = 204
c. 160 + 360 + 8 = 528
d. 1,600 + 360 + 8 = 1,968

Answer: 1,600 + 360 + 8 = 1,968

1,600 + 360 + 8 = 1,968
The correct answer is option d.

Question 5.
What is the sum 13,094 + 259,728?
Options:
a. 272,832
b. 272,822
c. 262,722
d. 262,712

Answer: 262,722

Explanation:
13,094 + 259,728 = 262,722
The correct answer is option c.

Question 6.
During the 2008–2009 season, there were 801,372 people who attended the home hockey games in Philadelphia. There were 609,907 people who attended the home hockey games in Phoenix. How much greater was the home attendance in Philadelphia than in Phoenix that season?
Options:
a. 101,475
b. 191,465
c. 201,465
d. 202,465

Answer: 191,465

Explanation:
Given,
During the 2008–2009 season, there were 801,372 people who attended the home hockey games in Philadelphia.
There were 609,907 people who attended the home hockey games in Phoenix.
801,372 – 609,907 = 191,465
Philadelphia attendance is 191,465 greater than in Phoenix that season.
The correct answer is option b.

Common Core – Multiply 2-Digit Numbers – Page No. 63

Problem Solving Multiply 2 – Digit numbers

Solve each problem. Use a bar model to help.

Question 1.
Mason counted an average of 18 birds at his bird feeder each day for 20 days. Gloria counted an average of 21 birds at her bird feeder each day for 16 days. How many more birds did Mason count at his feeder than Gloria counted at hers?

Birds counted by Mason: 18 × 20 = 360
Birds counted by Gloria: 21 × 16 = 336
Draw a bar model to compare.
Subtract. 360 – 336 = 24
So, Mason counted 24 more birds.

Question 2.
The 24 students in Ms. Lee’s class each collected an average of 18 cans for recycling. The 21 students in Mr. Galvez’s class each collected an average of 25 cans for recycling. How many more cans were collected by Mr. Galvez’s class than Ms. Lee’s class?
_____ more cans

Answer: 93 more cans

Explanation:
The number of cans collected by Ms. Lee’s class = 18 × 24 = 432.
The number of cans collected by Mr. Galvez’s class = 25 × 21 = 525.
Use Bar Model

Subtract. 525 – 432 = 93 more cans.
So, Mr. Galvez’s class collected 93 more cans than Ms. Lee’s class.

Question 3.
At East School, each of the 45 classrooms has an average of 22 students. At West School, each of the 42 classrooms has an average of 23 students. How many more students are at East School than at West School?
_____ more students

Answer: 24 more students

Explanation:
Students in East school = 45 × 22 = 990.
Students in West School = 42 × 23 = 966.
Use Bar Model

Subtract. 990 – 966 = 24.
So, East School has 24 students more than West School.

Question 4.
A zoo gift shop orders 18 boxes of 75 key rings each and 15 boxes of 80 refrigerator magnets each. How many more key rings than refrigerator magnets does the gift shop order?
_____ more key rings

Answer: 150 more key rings

Explanation:
Number of Key Rings = 75 x 18 = 1,350.
Number of Refrigerator Magnets= 80 x 15 = 1,200.
Use Bar Model

Subtract. 1,350 – 1,200 = 150.
So, key rings are 150 more than refrigerator magnets.

Common Core – Multiply 2-Digit Numbers – Page No. 64

Lesson Check

Question 1.
Ace Manufacturing ordered 17 boxes with 85 ball bearings each. They also ordered 15 boxes with 90 springs each. How many more ball bearings than springs did they order?
Options:
a. 5
b. 85
c. 90
d. 95

Answer: 95

Explanation:
Number of ball bearings = 85 × 17 = 1,445.
Number of springs = 90 × 15 = 1,350.
Use Bar Model

Subtract. 1,445 – 1,350 = 95.
So, ball bearings are 95 more than springs.
The correct answer is option d.

Question 2.
Elton hiked 16 miles each day on a 12-day hiking trip. Lola hiked 14 miles each day on her 16-day hiking trip. In all, how many more miles did Lola hike than Elton hiked?
Options:
a. 2 miles
b. 18 miles
c. 32 miles
d. 118 miles

Answer: 32 miles

Explanation:
Hiking trip by Elton = 12 × 16 = 192.
Hiking trip by Lola = 16 × 14 = 224.
Use Bar Model

Subtract. 224 – 192 = 32.
So, the Hiking trip by Lola is 32 times more than the Hiking trip by Elton.
The correct answer is option c.

Spiral Review

Question 3.
An orchard has 24 rows of apple trees. There are 35 apple trees in each row. How many apple trees are in the orchard?
Options:
a. 59
b. 192
c. 740
d. 840

Answer: 840

Explanation:
An orchard has 24 rows of apple trees. There are 35 apple trees in each row.
24 × 35 = 840 apple trees are in the orchard.
The correct answer is option d.

Question 4.
An amusement park reported 354,605 visitors last summer. What is this number rounded to the nearest thousand?
Options:
a. 354,600
b. 355,000
c. 360,000
d. 400,000

Answer: 355,000

Explanation:
An amusement park reported 354,605 visitors last summer. 4,605 is close to 5,000.
So, the answer is 355,000.
The correct answer is option b.

Question 5.
Attendance at the football game was 102,653. What is the value of the digit 6?
Options:
a. 6
b. 60
c. 600
d. 6,000

Answer: 600

Explanation:
Digit 6 is at hundreds of positions.
So, the answer is 6 x 100 = 600.
The correct answer is option c.

Question 6.
Jill’s fish weighs 8 times as much as her parakeet. Together, the pets weigh 63 ounces. How much does the fish weigh?
Options:
a. 7 ounces
b. 49 ounces
c. 55 ounces
d. 56 ounces

Answer: 56 ounces

Explanation:
Let Jill’s parakeet = X.
Jill’s fish weighs 8 times as much as her parakeet = 8X.
Together, the pets weigh 63 ounces.
X + 8X = 63.
9X = 63.
X = 63/9 = 7.
So, Jill’s parakeet =7.
Jill’s fish = 7 × 8 = 56 ounces.
The correct answer is option d.

Common Core – Multiply 2-Digit Numbers – Page No. 65

Lesson 3.1

Choose a method. Then find the product.

Question 1.
12 × 60 = _____

Answer: 720

Explanation:
By using the place value method
You can take 10 as 1 ten
12 × 60 = 12 × 6 ten
= 72 ten
12 × 60 = 720

Question 2.
56 × 40 = _____

Answer: 2240

Explanation:
56 × 40
By using the associative property
You can think of 40 as (4 × 10)
56 × 40 = 56 × (4 × 10)
= (56 × 4) × 10
= 224 × 10
56 × 40 = 2240

Question 3.
30 × 40 = _____

Answer: 1200

Explanation:
30 × 40
By using the place value method
You can take 30 as 3 tens
30 × 40 = 30 × 4 tens
= 120 tens
30 × 40 = 1200

Question 4.
50 × 67 = _____

Answer: 3350

Explanation:
By using the place value method
You can take 50 as 5 tens
50 x 67 = 67 x 5 tens
= 335 tens
50 × 67 = 3350

Lesson 3.2

Estimate the product. Choose a method.

Question 5.
33 × 76 = _____

Answer: 2400

Round to the nearest tens.
33 is close to 30; 76 is close to 80;
Use the mental math
30 × 80  = 2400
So, estimated product of 33 × 76 = 2400

Question 6.
43 × 90 = _____

Answer: 3600

Explanation:
Round to the nearest tens.
43 is close to 40; 90 is close to 90;
Use the mental math, then
9 × 4 = 36
90 × 40 = 3,600
So, estimated product of 43 × 90 = 3,600

Question 7.
47 × $ 66 = _____

Answer: $3500

Explanation:
Round to the nearest tens.
47 is close to 50; 66 is close to 70;
Use the mental math, then
50 × 70 = 3,500
So, estimated product of 50 × 70 = $3,500

Question 8.
12 × 81 = _____

Answer: 800

Explanation:
Round to the nearest tens.
12 is close to 10; 81 is close to 80;
Use mental math, then
10 × 80 = 800
So, the estimated product of 12 × 81 = 800

Question 9.
46 × 47 = _____

Answer: 2500

Explanation:
Round to the nearest tens.
46 is close to 50; 47 is close to 50;
Use mental math, then
50 × 50 = 2500
So, the estimated product of 46 × 47 = 2500

Question 10.
58 × 79 = _____

Answer: 4800

Explanation:
Round to the nearest tens.
58 is close to 60; 79 is close to 80;
Use mental math, then
60 × 80 = 4800
So, the estimated product of 58 × 79 = 4800

Question 11.
24 × 73 = _____

Answer: 1400

Explanation:
Round to the nearest tens.
24 is close to 20; 73 is close to 70;
Use mental math, then
20 × 70 = 1400
So, the estimated product of 24 × 73 = 1400

Question 12.
68 × 36 = _____

Answer: 2800

Explanation:
Round to the nearest tens.
68 is close to 70; 36 is close to 40;
Use mental math, then
70 × 40 = 2800
So, the estimated product of 68 × 36 = 2800

Lesson 3.3

Draw a model to represent the product.
Then record the product.

Question 13.
41 × 16 = _____

Answer: 656

Explanation:

400 + 240 + 10 + 6 = 656

Question 14.
39 × 52 = _____

Answer: 2028

Explanation:

1500 + 60 + 450 + 18 = 2028

Question 15.
94 × 36 = _____

Answer: 3384

Explanation:

2700 + 540 + 120 + 24 = 3384

Common Core – Multiply 2-Digit Numbers – Page No. 66

Lesson 3.4

Record the product.

Question 1.
5 3
× 3 7
———
________

Answer: 1961

Question 2.
4 8
× 47
———
________

Answer: 2256

Question 3.
6 5
× 2 8
———
________

Answer: 1820

Question 4.
9 2
× 7 9
———
________

Answer: 7268

Lessons 3.5–3.6

Estimate. Then choose a method to find the product.

Question 5.
4 8
× 2 1
———
Estimate: ________
Product: ________

Answer:

Explanation:
48 × 21
Estimate: Think 48 is close to 50; 21 is close to 20.
50 x 20 = 1000
Product:
10 x 5 tens = 50 tens
50 x 2 ones = 100 ones
2 x 2 tens = 40 tens
4 x 2 ones = 8 ones.
Add partial products.
500 + 100 + 400 + 8 = 1008.

Question 6.
$ 7 2
× 4 6
———
Estimate: ________
Product: ________

Answer: 3312

Estimate: Think 72 is close to 70; 46 is close to 50.
70 × 50 = 3500
Product:
70 x 4 tens = 280 tens
50 x 2 ones = 100 ones
4 x 10 tens = 40 tens
4 x 6 ones = 24 ones.
Add partial products.
2800 + 100 + 400 + 12 = 3312

Question 7.
$ 3 9
× 5 8
———
Estimate: ________
Product: ________

Answer: 2262

Estimate: Think 39 is close to 40; 58 is close to 60.
40 × 60 = 2400
Product:
30 x 5 tens = 150 tens
9 x 8 ones = 72 ones
8 x 3 tens = 24 tens
9 x 5 tens = 45 tens.
Add partial products.
1500 + 240 + 450 + 72 = 2262

Question 8.
27 × $ 19
Estimate: ________
Product: ________

Answer: 513

Estimate: Think 27 is close to 30; 19 is close to 20.
30 × 20 = 600
Product:
20 x 9 ones = 180 ones
9 x 7 ones = 63 ones
20 x 1 tens = 20 tens
7 x 10 ones = 70 ones.
Add partial products.
180 + 70 + 63 + 200 = 513

Question 9.
97 × 32
Estimate: ________
Product: ________

Answer: 3104

Estimate: Think 97 is close to 100; 32 is close to 30.
100 × 30 = 3000
Product:
30 x 9 tens = 270 tens
30 x 7 ones = 210 ones
2 x 9 tens = 18 tens
2 x 7 ones = 14 ones.
Add partial products.
2700 + 210 + 14 + 180 = 3104

Question 10.
44 × 69
Estimate: ________
Product: ________

Answer: 3036

Estimate: Think 44 is close to 40; 69 is close to 70.
100 × 30 = 3000
Product:
40 x 6 tens = 240 tens
40 x 9 ones = 360 ones
4 x 6 tens = 24 tens
4 x 9 ones = 36 ones.
Add partial products
2400 + 360 + 240 + 36 = 3036

Question 11.
Last week, Ms. Simpson worked 28 hours. She stocked shelves for 45 minutes each hour for 14 of those hours. The rest of the time she worked in customer service. How many minutes last week did Ms. Simpson work in customer service? (Hint: 1 hour = 60 minutes)
______ minutes

Answer: 1050 minutes

Explanation:
Given,
Last week, Ms. Simpson worked 28 hours.
She stocked shelves for 45 minutes each hour for 14 of those hours.
The rest of the time she worked in customer service.
45 × 14 = 630
She worked 630 minutes stocking shelves, which equals 10 hours and 30 minutes.
After that, she worked another 17 hours and 30 minutes in customer service.
17 × 60 = 1020
1020 + 30 = 1050
Ms. Simpson worked 1050 minutes in customer service.

Question 12.
The after-school craft center has 15 boxes of 64 crayons each. In 12 of the boxes, 28 of the crayons have not been used. All the rest have been used. How many of the crayons in the center have been used?
______ crayons

Answer: 624 crayon

Explanation:
In 12 of the boxes, 28 crayons have not been used; this leaves 64-28=36 crayons that have been used. 12(36) = 432 crayons have been used in these boxes.
3 full boxes have been used; this is 3(64) = 192 crayons.
Together this makes 432 + 192 = 624 crayons that have been used.

Conclusion:

I wish the explanation provided in our Go Math Grade Chapter 3 Homework Practice FL Multiply 2-Digit Numbers is beneficial for all the 4th standard students in scoring the marks in the exams. To solve more questions check out to Go Math Grade Chapter 3 Multiply 2-Digit Numbers pdf. All the Best Guys!!!!

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Go Math Grade 4 Answer Key Homework Practice FL Chapter 5 Factors, Multiples, and Patterns

The students who are lagging in the Factors, Multiples, and Patterns can learn through our Go Math Answer Key. Just tap the link and start preparing now. Refer Go Math Grade 4 Answer Key Homework Practice FL Chapter 5 Factors, Multiples, and Patterns to enhance your skills and score well in the exams.

Lesson: 1 – Model Factors

• Common Core – Factors, Multiples, and Patterns – Page No. 97
• Common Core – Factors, Multiples, and Patterns – Page No. 98

Lesson: 2

• Common Core – Factors, Multiples, and Patterns – Page No. 99
• Common Core – Factors, Multiples, and Patterns – Page No. 100

Lesson: 3 – Problem Solving Common Factors

• Common Core – Factors, Multiples, and Patterns – Page No. 101
• Common Core – Factors, Multiples, and Patterns – Page No. 102

Lesson: 4 – Factors and Multiples

• Common Core – Factors, Multiples, and Patterns – Page No. 103
• Common Core – Factors, Multiples, and Patterns – Page No. 104

Lesson: 5 – Prime and Composite Numbers

• Common Core – Factors, Multiples, and Patterns – Page No. 105
• Common Core – Factors, Multiples, and Patterns – Page No. 106

Lesson: 6 – Number Patterns

• Common Core – Factors, Multiples, and Patterns – Page No. 107
• Common Core – Factors, Multiples, and Patterns – Page No. 108

Lesson: 7

• Common Core – Factors, Multiples, and Patterns – Page No. 109
• Common Core – Factors, Multiples, and Patterns – Page No. 110

Common Core – Factors, Multiples, and Patterns – Page No. 97

Model Factors

Use tiles to find all the factors of the product.

Record the arrays on grid paper and write the factors shown.

Question 1.

Question 2.
Write the factors of: 30
Type below:
_________

Answer: The Factors of 30 are: 1,2,3,5,6,10,15,30.

Explanation:
Factors are the numbers that divide the original number completely. Here, we can see the numbers which give the result as 30 when multiplied together.
1 × 30 =30
2 × 15 = 30
3 × 10 = 30
5 × 6 = 30
6 × 5 = 30
10 × 3 = 30
15 × 2 = 30
30 × 1 = 30
So the factors of 30 are 1,2,3.5,6,10,15,30.

Question 3.
Write the factors of: 45
Type below:
_________

Answer: The Factors of 45 are:1,3,5,9,15,45

Explanation:
Factors are the numbers that divide the original number completely. Here, we can see the numbers which give the result as 45 when multiplied together.
1×45=45
3×15=45
5×9=45
9×5=45
15×3=45
45×1=45
So the factors of 45 are: 1,3,5,9,15,45.

Question 4.
Write the factors of: 19
Type below:
_________

Answer: The Factors of 19 are: 1,19

Explanation:
Since 19 is a Prime number that means it is divisible by 1 and itself.
1 × 19 = 19
19 × 1 = 19
So the factors of 19 are 1,19.

Question 5.
Write the factors of: 40
Type below:
_________

Answer:

The Factors of 40 are:1,2,4,5,8,10,20,40.

Explanation:
Factors are the numbers that divide the original number completely.
1×40=40
2×20=40
4×10=40
5×8=40
8×5=40
10×4=40
20×2=40
40×1=40
The Factors of 40 are: 1,2,4,5,8,10,20,40.

Question 6.
Write the factors of: 36
Type below:
_________

Answer: The Factors Of 36 are:1,2,3,4,6,9,12,18,36.

Explanation:
Factors are the numbers which divides the original number completely.
1×36=36
2×18=36
3×12=36
4×9=36
6×6=36
9×4=36
12×3=36
18×3=36
36×1=36.
The factors of 36 are:1,2,3,4,6,9,12,18,36

Question 7.
Write the factors of: 22
Type below:
_________

Answer: The Factors Of 22 are:1,2,11,22.

Explanation:
Factors are the numbers that divide the original number completely.
1×22=22
2×11=22
11×2=22
22×1=22.
The factors of 22 are:1,2,11,22.

Question 8.
Write the factors of: 4
Type below:
_________

Answer: The Factors Of 4 are: 1,2,4.

Explanation:
Factors are the numbers that divide the original number completely.
1×4=4
2×2=4
4×1=4.
The Factors Of 4 are 1,2,4.

Question 9.
Write the factors of: 26
Type below:
_________

Answer: The Factors Of 26 are:1,2,13,26.

Explanation:
Factors are the numbers that divide the original number completely. Here, we can see the numbers which give the result as 26 when multiplied together.
1×26=26
2×13=26
13×2=26
26×1=26.
So the factors of 26 are:1,2,13,26.

Question 10.
Write the factors of: 49
Type below:
_________

Answer: The Factors Of 49 are: 1,7,49.

Explanation:
Factors are the numbers that divide the original number completely.
1×49=49
7×7=49
49×1=49.
The Factors Of 49 are 1,7,49.

Question 11.
Write the factors of: 32
Type below:
_________

Answer: The Factors Of 32 are:1,2,4,8,16,32.

Explanation:
Factors are the numbers that divide the original number completely. Here, we can see the numbers which give the result as 32 when multiplied together.
1×32=32
2×16=32
4×8=32
8×4=32
16×2=32
32×1=32.
So the factors of 32 are:1,2,4,8,16,32.

Question 12.
Write the factors of: 23
Type below:
_________

Answer: The Factors Of 23 are: 1,23.

Explanation:
Since 23 is a Prime number that means it is divisible by 1 and itself.
1×23=23
23×1=23.
So the factors of 23 are 1,23.

Question 13.
Brooke has to set up 70 chairs in equal rows for the class talent show. But, there is not room for more than 20 rows. What are the possible number of rows that Brooke could set up?
Type below:
_________

Answer: 2,5,7,10,14.

Explanation:
Let the possible no.of rows be X, As there is no room for more than 20 rows so there should not be more than 20 rows.X should be less than or equal to 20 (X<=20).
As Brooke has 70 chairs to set up in equal rows we will find the factors of 70 and in that, we must pick up the numbers which are less than equal to 20.
Therefore the factors of 70 are 2,5,7,10,14.

Question 14.
Eduardo thinks of a number between 1 and 20 that has exactly 5 factors. What number is he thinking of?
_________

Answer: 16

Explanation:
If find factors for 1 to 20 we don’t get exactly 5 factors for any number except 16.
So the answer is 16.
Thus Eduardo might be thinking of the number 16.

Common Core – Factors, Multiples, and Patterns – Page No. 98

Lesson Check

Question 1.
Which of the following lists all the factors of 24?
Options:
a. 1, 4, 6, 24
b. 1, 3, 8, 24
c. 3, 4, 6, 8
d. 1, 2, 3, 4, 6, 8, 12, 24

Answer: 1, 2, 3, 4, 6, 8, 12, 24

Explanation:
Factors are the numbers that divide the original number completely.
Here, we can see the numbers which give the result as 24 when multiplied together.
1×24=24
2×12=24
3×8=24
4×6=24
6×4=4
8×3=24
12×2=24
24×1=24
So the factors of 24 are:1, 2, 3, 4, 6, 8, 12, 24.
Thus the correct answer is option d.

Question 2.
Natalia has 48 tiles. Which of the following shows a factor pair for the number 48?
Options:
a. 4 and 8
b. 6 and 8
c. 2 and 12
d. 3 and 24

Answer: 6 and 8

Explanation:
Given that, Natalia has 48 tiles.
We have to find the factor pair of the number 48.
6 and 8 are factor pairs for 48 because 6×8=48.
Thus the correct answer is option b.

Spiral Review

Question 3.
The Pumpkin Patch is open every day. If it sells 2,750 pounds of pumpkins each day, about how many pounds does it sell in 7 days?
Options:
a. 210 pounds
b. 2,100 pounds
c. 14,000 pounds
d. 21,000 pounds

Answer: 21,000 pounds

Explanation:
Given that, The Pumpkin Patch is open every day.
Let’s round off 2750 pounds to 3000 pounds. In one day 3000 pounds pumpkins were sold out, and in
7 days?? —- 3000×7= 21,000 pounds.
It sold 21,000 pounds in 7 days.
Thus the correct answer is option d.

Question 4.
What is the remainder in the division problem modeled below?

Options:
a. 2
b. 3
c. 5
d. 17

Answer: 2

Explanation:
We can see in the above figure 3 circles with 5 sub circles inside it and a pair of sub circles.
Here total sub circles are (3×5)+2=17.
If we divide 17 with 3 then we will get a reminder as 2.
So the answer is 2.
Thus the correct answer is option a.

Question 5.
Which number sentence is represented by the following array?

Options:
a. 4 × 5 = 20
b. 4 × 4 = 16
c. 5 × 2 = 10
d. 5 × 5 = 25

Answer: 4 × 5 = 20

Explanation:
By seeing the above figure we can say that there are 4 rows and 5 columns.
As we can see 4 rows and 5 squares.
Multiply the number of rows with the number of columns.
So 4 × 5 = 20.
Thus the correct answer is option a.

Question 6.
Channing jogs 10 miles a week. How many miles will she jog in 52 weeks?
Options:
a. 30 miles
b. 120 miles
c. 200 miles
d. 520 miles

Answer: 520 miles

Explanation:
No.of weeks = 52. So 1 week = 10 miles,
then 52 weeks =?????
52 × 10 = 520 miles.
Thus the correct answer is option d.

Common Core – Factors, Multiples, and Patterns – Page No. 99

Is 6 a factor of the number? Write yes or no.

Question 1.

Question 2.
56
_____

Answer: No

Explanation:
The factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56 .
56 is not divisible by 6.
So the answer is No.

Question 3.
42
_____

Answer: Yes

Explanation:
The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42.
Since 42 is divisible by 6.
So the answer is yes.

Question 4.
66
_____

Answer: Yes

Explanation:
Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66
66 is divisible by 6.
So the answer is yes.

Is 5 a factor of the number? Write yes or no.

Question 5.
38
_____

Answer: No

Explanation:
If the end is 0 or 5 then the number is divisible by 5.
The factors of 38 are 1, 2, 19, 38.
As the number is 38 the answer is No.

Question 6.
45
_____

Answer: Yes

Explanation:
45 is divisible by 5.
The factors of 45 are 1,3,5,9,15,45.
So the answer is Yes.

Question 7.
60
_____

Answer: Yes

Explanation:
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
60 is a factor of 5 because 60 is divisible by 5.

Question 8.
39
_____

Answer: No

Explanation:
The factors of 39 are 1,3,13,39.
As 39 is not divisible by 5.
So the answer is No.

List all the factor pairs

Question 9.
Factors of 12
_____ × _____ = 12; ( _____ , _____ )
_____ × _____ = 12; ( _____ , _____ )
_____ × _____ = 12; ( _____ , _____ )

Answer:
1 × 12 = 12; ( 1 , 12 )
2 × 6 = 12; ( 2, 6 )
3 × 4 = 12; ( 3 , 4 )

Question 10.
Factors of 25
_____ × _____ = 25; ( _____ , _____ )
_____ × _____ = 25; ( _____ , _____ )

Answer:
1 ×25 = 25; ( 1 , 25 )
5 × 5 = 25; ( 5 , 5 )

Question 11.
List all the factor pairs for 48.
Type below:
_________

Answer:
Factor pairs of 48 are (1,48),(2,24),(3,16),(4,12),(6,8),(12,2),(6,3),(24,2),(48,1).

Explanation:
Factor pairs are the pairs when we multiplied both numbers will get the result. Here factor pairs for 48 are
1×48=48 (1,48)
2×24=48 (2,24)
3×16=48 (3,16)
4×12=48 (4,12)
6×8 =48 (6,8)

Problem Solving

Question 12.
Bryson buys a bag of 64 plastic miniature dinosaurs. Could he distribute them equally into six storage containers and not have any left over?
_____

Answer: No

Explanation:
Given that,
Bryson buys a bag of 64 plastic miniature dinosaurs.
64 is not divisible by 6, So he cannot distribute them equally into six storage containers.

Question 13.
Lori wants to distribute 35 peaches equally into baskets. She will use more than 1 but fewer than 10 baskets. How many baskets does Lori need?
Type below:
_________

Answer: 5 or 7.

Explanation:
First, we need to know the factors of 35.
The factors of 35 are 1,5,7,35. As Lori uses more than 1 but fewer than 10, the answer is 5 or 7. Lori can distribute 35 peaches equally in 5 or 7 baskets.

Common Core – Factors, Multiples, and Patterns – Page No. 100

Lesson Check

Question 1.
Which of the following numbers has 9 as a factor?
Options:
a. 28
b. 30
c. 39
d. 45

Answer: 45

Explanation:
45 is divisible 9.
So the answer is 45.
Thus the correct answer is option d.

Question 2.
Which of the following numbers does NOT have 5 as a factor?
Options:
a. 15
b. 28
c. 30
d. 45

Answer: 28

Explanation:
28 is not divisible by 5.
So 28 is not a factor of 5.
Thus the correct answer is option b.

Spiral Review

Question 3.
Which of the following shows a strategy to use to find 4 × 275?
Options:
a. (4 × 300) + (4 × 25)
b. (4 × 300) – (4 × 25)
c. (4 × 275) – 100
d. (4 × 200) + 75

Answer: (4 × 300) – (4 × 25)

Explanation:
First, we must replace 300-25 in the place of 275 then it becomes 4×(300-25), Now we must use the distributive property of multiplication then (4×300)-(4×25).
So the answer is b.

Question 4.
Jack broke apart 5 × 216 as (5 × 200) + (5 × 16) to multiply mentally. What strategy did Jack use?
Options:
a. the Commutative Property
b. the Associative Property
c. halving and doubling
d. the Distributive Property

Answer: the Distributive Property

Explanation:
Distributive property means if we multiply a sum by a number is the same as multiplying each addend by the number and adding the products. This is the strategy Jack used.
Thus the correct answer is option d.

Question 5.
Jordan has $55. She earns $67 by doing chores. How much money does Jordan have now?
Options:
a. $122
b. $130
c. $112
d. $12

Answer: $122

Explanation:
Jordan has $55, she earns by doing chores is $67.
So the total money is $55+$67=$122.
Thus the correct answer is option a.

Question 6.
Trina has 72 collector’s stamps. She puts 43 of the stamps into a stamp book. How many stamps are left?
Options:
a. 29
b. 31
c. 39
d. 115

Answer: 29

Explanation:
Given,
Trina has 72 collector’s stamps.
She puts 43 of the stamps into a stamp book.
Stamps left are 72-43=29.
Thus the correct answer is option a.

Common Core – Factors, Multiples, and Patterns – Page No. 101

Problem Solving Common Factors

Solve each problem.

Question 1.
Grace is preparing grab bags for her store’s open house. She has 24 candles, 16 pens, and 40 figurines. Each grab bag will have the same number of items, and all the items in a bag will be the same. How many items can Grace put in each bag?

Question 2.
Simon is making wreaths to sell. He has 60 bows, 36 silk roses, and 48 silk carnations. He wants to put the same number of items on each wreath. All the items on a wreath will be the same type. How many items can Simon put on each wreath?
Type below:
_________

Answer: 1,2,3,4,6 or 12 items Simon puts on each wreath.

Explanation:
Given that,
Simon is making wreaths to sell.
He has 60 bows, 36 silk roses, and 48 silk carnations.
He wants to put the same number of items on each wreath.
First we will find the common factors of 36,48,60
factors of 36 are: 1,2,3,4,6,9,12,18,36.
factors of 48 are: 1,2,3,4,6,8,12,16,24,48
factors of 60 are: 1,2,3,4,5,6,10,12,15,20,30,60.
The common factors of 36,48,60 are 1,2,3,4,6,12.
So Simon can put 1,2,3,4,6 or 12 items on each wreath.

Question 3.
Justin has 20 pencils, 25 erasers, and 40 paper clips. He organizes them into groups with the same number of items in each group. All the items in a group will be the same type. How many items can he put in each group?
Type below:
_________

Answer: Justin can put 1 or 5 items in each group.

Explanation:
Given,
Justin has 20 pencils, 25 erasers, and 40 paper clips.
He organizes them into groups with the same number of items in each group.
We will find common factors of 20,25,40.
factors of 20 are: 1,2,4,5,10,20.
factors of 25 are: 1,5,25.
factors of 40 are: 1,2,4,5,8,10,20,40
So common factors are 1 and 5.
Therefore, Justin can put 1 or 5 items in each group.

Question 4.
A food bank has 50 cans of vegetables, 30 loaves of bread, and 100 bottles of water. The volunteers will put the items into boxes. Each box will have the same number of food items and all the items in the box will be the same type. How many items can they put in each box?
Type below:
_________

Answer: 1,2,5, or 10.

Explanation:
Given,
A food bank has 50 cans of vegetables, 30 loaves of bread, and 100 bottles of water.
The volunteers will put the items into boxes.
1,2,5 or 10 are the common factors of 30,50 and 100.
factors for 30 are: 1,2,3,5,6,10,15,30
factors for 50 are: 1,2,5,10,25,50
factors of 100 are: 1,2,4,5,10,20,25,50,100
So the answer is 1,2,5,10.

Question 5.
A debate competition has participants from three different schools: 15 from James Elementary, 18 from George Washington School, and 12 from the MLK Jr. Academy. All teams must have the same number of students. Each team can have only students from the same school. How many students can be on each team?
Type below:
_________

Answer: 3

Explanation:
Given,
A debate competition has participants from three different schools: 15 from James Elementary, 18 from George Washington School, and 12 from the MLK Jr. Academy.
Lets find the common factors of 12,15,18
factors of 12 are: 1,2,3,4,6,12
factors of 15 are: 1,3,5,15
factors of 18 are: 1,2,3,6,9,18
3 is the common factor for 12,15,18
Therefore 3 students can be on each team.

Common Core – Factors, Multiples, and Patterns – Page No. 102

Lesson Check

Question 1.
What are all the common factors of 24, 64, and 88?
Options:
a. 1 and 4
b. 1, 4, and 8
c. 1, 4, 8, and 12
d. 1, 4, 8, and 44

Answer: 1, 4, and 8

Explanation:
factors of 24 are: 1,2,3,4,8,12,24
factors of 64 are: 1,2,4,8,16,32,64
factors of 88 are: 1,2,4,8,11,22,44,88
Thus the correct answer is option b.

Question 2.
Which number is NOT a common factor of 15, 45, and 90?
Options:
a. 3
b. 5
c. 10
d. 15

Answer: 10

Explanation:
As 15 and 45 are not divisible by 10.
Thus the correct answer is option c.

Spiral Review

Question 3.
Dan puts $11 of his allowance in his savings account every week. How much money will he have after 15 weeks?
Options:
a. $165
b. $132
c. $110
d. $26

Answer: $165

Explanation:
Dan puts $11 in his savings account every week.
So after 15 weeks, it will be 15×11=165.
The total money he will have after 15 weeks is $165.
Thus the correct answer is option a.

Question 4.
James is reading a book that is 1,400 pages. He will read the same number of pages each day. If he reads the book in 7 days, how many pages will he read each day?
Options:
a. 20
b. 50
c. 140
d. 200

Answer: 200

Explanation:
Given,
James is reading a book that is 1,400 pages.
He will read the same number of pages each day.
Total no.of.pages is 1400, no.of pages James read each day is 1400÷7= 200
Thus the correct answer is option d.

Question 5.
Emma volunteered at an animal shelter for a total of 119 hours over 6 weeks. Which is the best estimate of the number of hours she volunteered each week?
Options:
a. 10 hours
b. 20 hours
c. 120 hours
d. 714 hours

Answer: 20 hours

Explanation:
Given,
Emma volunteered at an animal shelter for a total of 119 hours over 6 weeks.
Total hours Emma volunteered is 119 hours over 6 weeks.
To find:
how much she volunteered each week is
119÷6= 19.833 i.e 20 hours.
We must round off to the nearest one i.e 20 hours.
Thus the correct answer is option b.

Question 6.
Which strategy can be used to multiply 6 × 198 mentally?
Options:
a. 6 × 198 = (6 × 19) + (6 × 8)
b. 6 × 198 = (6 × 200) + (6 × 2)
c. 6 × 198 = (6 × 200) – (6 × 2)
d. 6 × 198 = (6 + 200) × (6 + 2)

Answer: 6 × 198 = (6 × 200) – (6 × 2)

Explanation:
By Distributive property of multiplication 6×198 can be written as (6 × 200) – (6 × 2).
Thus the correct answer is option c.

Common Core – Factors, Multiples, and Patterns – Page No. 103

Factors and Multiples

Is the number a multiple of 8? Write yes or no.

Question 1.

Question 2.
8
_____

Answer: Yes

Explanation: Since 8×1=8, it is a multiple of 8

Question 3.
20
_____

Answer: No

Explanation: 20 is not a multiple of 8

Question 4.
40
_____

Answer: Yes

Explanation: 8×5=40, So 40 is multiple of 8

List the next nine multiples of each number. Find the common multiples.

Question 5.
Multiples of 4:
Multiples of 7:
Common multiples:
Type below:
__________

Answer:

Multiples of 4: 4,8,12,16,20,24,28,32,36,40.
Multiples of 7: 7,14,21,28,35,42,49,56,63,70.
Common Multiples: 28,

Question 6.
Multiples of 3:
Multiples of 9:
Common multiples:
Type below:
__________

Answer: 9,18,45,54,63, etc.

Explanation:
Multiples of 3: 3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63.
Multiples of 9: 9,18,27,36,45,54,63,72,81,90.
Common multiples: 9,18,45,54,63, etc.

Question 7.
Multiples of 6:
Multiples of 8:
Common multiples:
Type below:
__________

Answer: 24,48,72.

Explanation:
Multiples of 6: 6,12,18,24,30,36,42,48,54,60,66,72,78.
Multiples of 8: 8,16,24,32,40,48,56,64,72,80.
Common multiples: 24,48,72.

Tell whether 24 is a factor or multiple of the number. Write factor, multiple, or neither.

Question 8.
6
__________

Answer: Multiple

Explanation: 6×4=24

Question 9.
36
__________

Answer: Neither

Explanation: 36 is not a factor or multiple of 24.

Question 10.
48
__________

Answer: Factor

Explanation: 24×2= 48, So 48 is a factor of 24

Problem Solving

Question 11.
Ken paid $12 for two magazines. The cost of each magazine was a multiple of $3. What are the possible prices of the magazines?
Type below:
__________

Answer: $3+$9=$12.

Explanation:
As each magazine cost was multiple of $3.
The possible price for 2 magazines are $3+$9=$12, which is a multiple of 3

Question 12.
Jodie bought some shirts for $6 each. Marge bought some shirts for $8 each. The girls spent the same amount of money on shirts. What is the least amount they could have spent?
$ _____

Answer: $24

Explanation:
Given,
Jodie bought some shirts for $6 each.
Marge bought some shirts for $8 each.
The girls spent the same amount of money on shirts.
So multiples of 6 are: 6,12,18,24,30,36,42 and
multiples of 8 are: 8,16,24,32,40. The least amount they could spend is 24. As 24 is the least common multiple.

Common Core – Factors, Multiples, and Patterns – Page No. 104

Lesson Check

Question 1.
Which list shows numbers that are all multiples of 4?
Options:
a. 2, 4, 6, 8
b. 3, 7, 11, 15, 19
c. 4, 14, 24, 34
d. 4, 8, 12, 16

Answer: 4, 8, 12, 16

Explanation:
Multiples of 4 are 4,8,12,16.
Thus the correct answer is option d.

Question 2.
Which of the following numbers is a common multiple of 5 and 9?
Options:
a. 9
b. 14
c. 36
d. 45

Answer: 45

Explanation:
The common multiple of 5 and 9 is
5×9= 45
Thus the correct answer is option d.

Spiral Review

Question 3.
Jenny has 50 square tiles. She arranges the tiles into a rectangular array of 4 rows. How many tiles will be left over?
Options:
a. 0
b. 1
c. 2
d. 4

Answer: 2

Explanation:
As Jenny arranges in 4 rows, each row contains 12 tiles.
So 12×4= 48.
The tiles left are 50 – 48 = 2.
Thus the correct answer is option c.

Question 4.
Jerome added two numbers. The sum was 83. One of the numbers was 45. What was the other number?
Options:
a. 38
b. 48
c. 42
d. 128

Answer: 38

Explanation:
The sum of the two numbers is 83, in that one number is 45.
To find another number we will do subtraction,
i.e 83 – 45 = 38.
Thus the correct answer is option a.

Question 5.
There are 18 rows of seats in the auditorium. There are 24 seats in each row. How many seats are in the auditorium in all?
Options:
a. 42
b. 108
c. 412
d. 432

Answer: 432

Explanation:
Given,
There are 18 rows of seats in the auditorium.
There are 24 seats in each row.
No.of rows= 18, each row has 24 seats.
So total no.of seats are 18×24= 432.
Thus the correct answer is option d.

Question 6.
The population of Riverdale is 6,735. What is the value of the 7 in the number 6,735?
Options:
a. 7
b. 700
c. 735
d. 7,000

Answer: 700

Explanation:
Given,
The population of Riverdale is 6,735.
In 6,735 the 7 is in the Hundreds Place.
So the answer is 7.
Thus the correct answer is option b.

Common Core – Factors, Multiples, and Patterns – Page No. 105

Prime and Composite Numbers

Tell whether the number is prime or composite

Question 1.

Question 2.
68
_________

Answer: Composite number.

Explanation:
The number which has more than two factors is called composite numbers.
The Factors of 68 are: 1,2,4,17,34,69.

Question 3.
52
_________

Answer: Composite number

Explanation:
The number which has more than two factors is called composite numbers.
The Factors of 52 are: 1,2,4,13,26,52.

Question 4.
63
_________

Answer: Composite number

Explanation:
The number which has more than two factors is called composite numbers.
The Factors of 63 are: 1,2,3,7,9,21,63.

Question 5.
75
_________

Answer: Composite number

Explanation:
The number which has more than two factors is called composite numbers.
The Factors of 75 are: 1,3,5,15,25,75

Question 6.
31
_________

Answer: Prime number

Explanation:
31 is a prime number that means it is divisible by 1 and itself.

Question 7.
77
_________

Answer: Composite number

Explanation:
The number which has more than two factors is called composite numbers.
Factors of 77 are 1,7,11,77.

Question 8.
59
_________

Answer: Prime number

Explanation:
59 is a prime number that means it is divisible by 1 and itself.

Question 9.
87
_________

Answer: Composite Number

Explanation:
The number which has more than two factors is called composite numbers.
Factors of 87 are: 1,3,29,87.

Question 10.
72
_________

Answer: Composite Number

Explanation:
The number which has more than two factors is called composite numbers.
Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

Question 11.
49
_________

Answer: Composite Number

Explanation:
The number which has more than two factors is called composite numbers.
Factors of 49 are 1,7,49.

Question 12.
73
_________

Answer: Prime number

Explanation:
A Prime number is a number that is divisible 1 and itself.

Problem Solving

Question 13.
Kai wrote the number 85 on the board. Is 85 prime or composite?
_________

Answer: Composite number

Explanation: The number which has more than two factors is called composite numbers.
Factors of 85 are 1,5,17,85

Question 14.
Lisa says that 43 is a 2-digit odd number that is composite. Is she correct?
_____

Answer: No

Explanation:
43 is a prime number.
A Prime number is a number that is divisible 1 and itself.

Common Core – Factors, Multiples, and Patterns – Page No. 106

Lesson Check

Question 1.
The number 5 is:
Options:
a. prime
b. composite
c. both prime and composite
d. neither prime nor composite

Answer: Prime number

Explanation:
A Prime number is a number that is divisible 1 and itself.
Thus the correct answer is option a.

Question 2.
The number 1 is:
Options:
a. prime
b. composite
c. both prime and composite
d. neither prime nor composite

Answer: neither prime nor composite

Explanation:
A Prime number is a number that is divisible 1 and itself. So prime number should have two divisors but 1 has only one divisor. The number which has more than two factors is called composite numbers. So 1 doesn’t have more than two factors. So 1 is neither Prime nor Composite.
Thus the correct answer is option d.

Spiral Review

Question 3.
A recipe for a vegetable dish contains a total of 924 calories. The dish serves 6 people. How many calories are in each serving?
Options:
a. 134 calories
b. 150 calories
c. 154 calories
d. 231 calories

Answer: 154 calories

Explanation:
Total no.of calories are 924, which serves 6 people.
To find each serving we will perform division
924 ÷ 6 = 154 calories.
Thus the correct answer is option c.

Question 4.
A store clerk has 45 shirts to pack in boxes. Each box holds 6 shirts. What is the fewest boxes the clerk will need to pack all the shirts?
Options:
a. 9
b. 8
c. 7
d. 6

Answer: 8

Explanation:
As the box holds only 6 shirts, 42 shirts are packed in 7 boxes, and the remaining 3 shirts will be packed in another box.
So the total number of boxes is 8.
Thus the correct answer is option b.

Question 5.
Which number rounds to 200,000?
Options:
a. 289,005
b. 251,659
c. 152,909
d. 149,889

Answer: 152,909

Explanation:
152,909 is nearest to 200,000.
Thus the correct answer is option c.

Question 6.
What is the word form of the number 602,107?
Options:
a. six hundred twenty thousand,seventeen
b. six hundred two thousand, one hundred seven
c. six hundred twenty-one thousand, seventeen
d. six hundred two thousand, one hundred seventy

Answer: six hundred two thousand, one hundred seven

Explanation:
Convert the number 602,107 into the word form.
The word form of 602,107 is six hundred two thousand, one hundred seven
Thus the correct answer is option b.

Common Core – Factors, Multiples, and Patterns – Page No. 107

Number Patterns

Use the rule to write the first twelve numbers in the pattern.

Describe another pattern in the numbers.

Question 1.
Rule: Add 8. First-term: 5

Question 2.
Rule: Subtract 7. First-term: 95
Type below:
_________

Answer: 95,88,81,74,67,60,53,46,39,32,25,118,11.

Explanation: 95
95-7= 88
88-7= 81
81-7= 74
74-7= 67
67-7= 60
60-7= 53
53-7= 46
46-7= 39
39-7= 32
32-7= 25
25-7= 18
18-7= 11

Question 3.
Rule: Add 15, subtract 10. First-term: 4
Type below:
_________

Answer: 4,19,9,24,14,29,19,34,24,39,29,44,34.

Explanation: 4
4+15= 19
19-10= 9
9+15= 24
24-10= 14
14+15= 29
29-10= 19
19+15= 34
34-10= 24
24+15= 39
39-10=29
29+15=44
44-10=34

Question 4.
Rule: Add 1, multiply by 2. First-term: 2
Type below:
_________

Answer: 2,4,5,10,11,22,23,46,47,94,95,190.

Explanation: 2
2+1= 2
2×2= 4
4+1= 5
5×2= 10
10+1= 11
11×2= 22
22+1= 23
23×2= 46
46+1= 47
47×2= 94
94+1= 95
95×2= 190.

Problem Solving

Question 5.
Barb is making a bead necklace. She strings 1 white bead, then 3 blue beads, then 1 white bead, and so on. Write the numbers for the first eight beads that are white. What is the rule for the pattern?
Type below:
_________

Answer: The serial numbers of first 8 white beads are = 1, 5, 9, 13, 17, 21, 25, 29

Explanation:
Since there are 3 blue beads after each white beads.
Hence we can design the progression in the following way looking at the sequence:
W,B,B,B,W,B,B,B,W…….
Hence the required formula for white beads serial number is,
N = (X-1)(A+1) + L
Where, A = number of blue beads after each white beads = 3
L = initial position at which the first white bead is placed = 1
X = number of white bead
Putting the values in the above formula our equation becomes,
N = 4(X-1) + 1
Hence we can find out the serial numbers as follows:
N₁ = 4 x 0 + 1 = 1
N₂ = 4×1 + 1 = 5
N₃ = 4×2 + 1 = 9
and so on upto
N₈ = 4 x 7 + 1 = 29

Question 6.
An artist is arranging tiles in rows to decorate a wall. Each new row has 2 fewer tiles than the row below it. If the first row has 23 tiles, how many tiles will be in the seventh row?
_____ tiles

Answer: 11 tiles

Explanation:
Given that,
An artist is arranging tiles in rows to decorate a wall.
Each new row has 2 fewer tiles than the row below it.
23
23-2= 21
21-2= 19
19-2= 17
17-2= 15
15-2= 13
13-2= 11

Common Core – Factors, Multiples, and Patterns – Page No. 108

Lesson Check

Question 1.
The rule for a pattern is add 6. The first term is 5. Which of the following numbers is a term in the pattern?
Options:
a. 6
b. 12
c. 17
d. 22

Answer: 17

Explanation:
Given that,
The rule for a pattern is add 6. The first term is 5.
5+6= 11
11+6= 17
Thus the correct answer is option c.

Question 2.
What are the next two terms in the pattern 3, 6, 5, 10, 9, 18, 17, . . .?
Options:
a. 16, 15
b. 30, 31
c. 33, 34
d. 34, 33

Answer: 34, 33

Explanation: 3
3×2= 6
6-1= 5
5×2= 10
10-1= 9
9×2= 18
18-1= 17
17×2= 34
34-1= 33
Thus the correct answer is option d.

Spiral Review

Question 3.
To win a game, Roger needs to score 2,000 points. So far, he has scored 837 points. How many more points does Roger need to score?
Options:
a. 1,163 points
b. 1,173 points
c. 1,237 points
d. 2,837 points

Answer: 1,163 points

Explanation:
Roger has scored 837 points, He needs to score 2000 points to win, So to know how much more points do Roger needs we need to subtract i.e 2,000-837= 1,163.
Thus the correct answer is option a.

Question 4.
Sue wants to use mental math to find 7 × 53. Which expression could she use?
Options:
a. (7 × 5) + 3
b. (7 × 5) + (7 × 3)
c. (7× 50) + 3
d. (7 × 50) + (7 × 3)

Answer: (7 × 50) + (7 × 3)

Explanation:
Distributive property means if we multiply a sum by a number is the same as multiplying each addend by the number and adding the products.
Thus the correct answer is option d.

Question 5.
Pat listed numbers that all have 15 as a multiple. Which of the following could be Pat’s list?
Options:
a. 1, 3, 5, 15
b. 1, 5, 10, 15
c. 1, 15, 30, 45
d. 15, 115, 215

Answer: 1, 3, 5, 15

Explanation:
Given,
Pat listed numbers that all have 15 as a multiple.
1×15= 15
3×5= 15
5×3= 15
15×1= 15
Thus the correct answer is option a.

Question 6.
Which is a true statement about 7 and 14?
Options:
a. 7 is a multiple of 14.
b. 14 is a factor of 7.
c. 14 is a common multiple of 7 and 14.
d. 21 is a common multiple of 7 and 14.

Answer: 14 is a common multiple of 7 and 14.

Explanation:
7×2=14
14×1=14
Thus the correct answer is option c.

Common Core – Factors, Multiples, and Patterns – Page No. 109

Use tiles to find all the factors of the product. Record the arrays on grid paper and write the factors shown.

Question 1.
Write the factors of: 17
Type below:
_________

Answer: The factors of 17 are: 1, 17

Explanation:
Factors are the numbers that divide the original number completely. Here, we can see the numbers which give the result as 17 when multiplied together.
1 × 17 = 17
17 × 1 = 17
So the factors of 17 are: 1, 17.

Question 2.
Write the factors of: 42
Type below:
_________

Answer: The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42.

Explanation:
Factors are the numbers that divide the original number completely. Here, we can see the numbers which give the result as 42 when multiplied together.
1 × 42 = 42
2 × 21= 42
3 × 14 = 42
6 × 7 = 42
7 × 6 = 42
14 × 3 = 42
21 × 2 = 42
42 × 1 = 42
So the factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42.

Question 3.
Write the factors of: 28
Type below:
_________

Answer: The factors of 28 are: 1, 2, 4, 7, 14, 28.

Explanation:
Factors are the numbers that divide the original number completely. Here, we can see the numbers which give the result as 28 when multiplied together.
1 × 28 = 28
2 × 14 = 28
4 × 7 = 28
7 × 4 = 28
14 × 2 = 28
28 × 1 = 28
So the factors of 28 are:1, 2, 4, 7, 14, 28.

Question 4.
Write the factors of: 50
Type below:
_________

Answer: The factors of 50 are 1, 2, 5, 10, 25, and 50.

Explanation:
Factors are the numbers that divide the original number completely. Here, we can see the numbers which give the result as 50 when multiplied together.
1 × 50 = 50
2 × 25 = 50
5 × 10 = 50
10 × 5 = 50
25 × 2 = 50
50 × 1 = 50
The factors of 50 are 1, 2, 5, 10, 25, and 50.

Is 5 a factor of the number? Write yes or no.

Question 5.
35
_____

Answer: Yes

Explanation:
The factors of 35 are 1, 5, 7, 35. So, the answer is yes.

Question 6.
56
_____

Answer: No

Explanation:
The factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56. So, the answer is no.

Question 7.
51
_____

Answer: No

Explanation:
The factors of 51 are 1, 3, 17, 51. So, the answer is no.

Question 8.
40
_____

Answer: Yes

Explanation:
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40. So, the answer is yes.

List all the factor pairs.

Question 9.
Factors of 16
_____ × _____ = 16; ( _____ , _____ )
_____ × _____ = 16; ( _____ , _____ )
_____ × _____ = 16; ( _____ , _____ )

Answer: The factor pairs of 16 are (1, 16), (2, 8), (4, 4)
1× 16 = 16; ( 1, 16)
2× 8 = 16; ( 2, 8)
4× 4 = 16; ( 4, 4)

Question 10.
Factors of 49
_____ × _____ = 49; ( _____ , _____ )
_____ × _____ = 49; ( _____ , _____ )

Answer: The factors in pairs of number 49 are (1, 49) and (7, 7).
1× 49= 49; ( 1, 49)
7× 7= 49; ( 7, 7)

Question 11.
Hana is putting the fruit she bought into bowls. She bought 8 melons, 12 pears, and 24 apples. She puts the same number of pieces of fruit in each bowl and puts only one type of fruit in each bowl. How many pieces can Hana put in each bowl?
Type below:
_________

Answer:
If she wants the same number of pieces of each kind of fruit in each bowl (same number of melons, the same number of pears, and the same number of apples in each bowl), then she can put 11 pieces in each of the 4 bowls.

Explanation:
To answer this, we find the greatest common factor (GCF) of all 3 numbers. To do this, we find the prime factorization of 8, 12 and 24:
8 = 4 × 2
4 = 2 × 2
8 = 2 × 2× 2
12 = 4 × 3
4 = 2 × 2
12 = 2 × 2 × 3
24 = 4 × 6
4 = 2 × 2
6 = 2 × 3
24 = 2 × 2 × 2 × 3
The GCF is made of all of the common factors. The factors common to all 3 numbers are 2 and 2; 2(2) = 4 for the GCF.
This means we can use 4 bowls.
She has a total of 8+12+24 = 44 pieces of fruit; 44/4 = 11. She would have 11 pieces of fruit in each bowl.

Question 12.
A store owner is arranging clothing on racks. She has 30 sweaters, 45 shirts, and 15 pairs of jeans. She wants to put the same number of items on each rack, with only one type of item on each. How many items can she put on a rack?
Type below:
_________

Answer:
I think what the teacher wants is 15 which is the greatest common factor of all three numbers and the factors of 15 are 1 x 15 and 3 x 5 so she can put one of each, or she can put 3 of each, or she can put 5 of each, or she can put 15 of each.

Common Core – Factors, Multiples, and Patterns – Page No. 110

Is the number a multiple of 9? Write yes or no.

Question 1.
24
_____

Answer: No

Explanation:
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. So the answer is no.

Question 2.
18
_____

Answer: Yes

Explanation:
The factors of 18 are 1, 2, 3, 6, 9, 18. So, the answer is yes.

Question 3.
27
_____

Answer: Yes

Explanation:
The factors of 27 are 1, 3, 9, 27. So, the answer is yes.

Question 4.
42
_____

Answer: No

Explanation:
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42. So the answer is no.

List the next nine multiples of each number.

Find the common multiples.

Question 5.
Multiples of 4:
Multiples of 5:
Common multiples:
Type below:
_________

Answer: 20, 40.

Explanation:
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40.
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50.
Common multiples: 20, 40.

Question 6.
Multiples of 3:
Multiples of 6:
Common multiples:
Type below:
_________

Answer: 6, 12, 18, 24, 30.

Explanation:
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30.
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60.
Common multiples: 6, 12, 18, 24, 30.

Tell whether the number is prime or composite.

Question 7.
39
_____

Answer: Composite

Explanation: The number which has more than two factors is called composite numbers.
The factors of 39 are 1, 13, 39.
Thus 39 is the composite number.

Question 8.
29
_____

Answer: Prime

Explanation: A Prime number is a number that is divisible 1 and itself.
The factors of 29 are 1, 29.
So, 29 is the prime number.

Question 9.
51
_____

Answer: Composite

Explanation: The number which has more than two factors is called composite numbers.
The factors of 51 are 1, 3, 17, 51.
Therefore 51 is the composite number.

Use the rule to write the first twelve numbers in the pattern.

Describe another pattern in the numbers.

Question 10.
Rule: Add 6. First term: 10
Type below:
_________

Answer: 16, 22, 28, 34, 40, 46, 52, 58, 64, 70, 76, 82.

Explanation: 10
10 + 6 = 16
16 + 6 = 22
22 + 6 = 28
28 + 6 = 34
34 + 6 = 40
40 + 6 = 46
46 + 6 = 52
52 + 6 = 58
58 + 6 = 64
64 + 6 = 70
70 + 6 = 76
76 + 6 = 82

Question 11.
Rule: Add 3, subtract 2. First term: 7
Type below:
_________

Answer: 10, 8, 11, 9, 12, 10, 13, 11, 14, 12, 15, 13.

Explanation: 7
7 + 3 = 10
10 – 2 = 8
8 + 3 = 11
11 – 2 = 9
9 + 3 = 12
12 – 2 = 10
10 + 3 = 13
13 – 2 = 11
11 + 3 = 14
14 – 2 = 12
12 + 3 = 15
15 – 2 = 13

Conclusion:

It is very difficult for parents to teach maths to primary school children. Keeping this in mind we have prepared the answers with step-by-step explanation in Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns. We suggest the students to Download Go Math Grade 4 Answer Key Homework Practice FL Chapter 5 Factors, Multiples, and Patterns pdf and start your preparation. All the Best!!