McGraw Hill Math

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 19.1 Metric Units of Length will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 19.1 Metric Units of Length

Exercises
CALCULATE
Question 1.
235 cm = _____________ m
Answer:
235 cm = 2.35 m.

Explanation:
235 cm = ?? m.
Conversion:
1 m = 100 cm.
235 cm = 235 ÷ 100
= 2.35 m.

Question 2.
4235 mm = _____________ m
Answer:
4235 mm = 4.235 m.

Explanation:
4235 mm = ?? m.
Conversion:
1 m = 1,000 mm.
4235 mm = 4235 ÷ 1,000
= 4.235 m.

Question 3.
5.7 km = _____________ cm
Answer:
5.7 km = 570,000 cm.

Explanation:
5.7 km = ?? cm.
Conversion:
1 km = 100,000 cm.
5.7 km = 5.7 × 100,000
= 570,000 cm.

Question 4.
625 km = _____________ mm
Answer:
625 km = 62,50,00,000 mm.

Explanation:
625 km = ?? mm.
Conversion:
1 km = 10,00,000 mm.
625 km =625 × 10,00,000
= 62,50,00,000 mm.

Question 5.
235 cm + 300 mm = _____________ m
Answer:
235 cm + 300 mm = 2.65 m.

Explanation:
235 cm + 300 mm = ?? m.
Conversion:
1 m = 100 cm.
1 m = 1000 mm.
235 cm + 300 mm = (235 ÷ 100) + (300 ÷ 1000)
= 2.35 + 0.3
= 2.65 m.

Question 6.
1.6 km = _____________ cm
Answer:
1.6 km = 160,000 cm.

Explanation:
1.6 km = ?? cm.
Conversion:
1 km = 100,000 cm
1.6 km = 1.6 × 100,000
= 160,000 cm.

Question 7.
5 cm + 5 mm = _____________ m
Answer:
5 cm + 5 mm = 5.005 m.

Explanation:
5 cm + 5 mm = ?? m.
Conversion:
1 m = 100 cm.
1 m = 1000 mm.
5 cm + 5 mm = (500 ÷ 100) + (5 ÷ 1000)
= 5 + 0.005
= 5.005 m.

Question 8.
3.87 m = _____________ mm
Answer:
3.87 m = 3870 mm.

Explanation:
3.87 m = ?? mm.
Conversion:
1 m = 1000 mm.
3.87 m = 3.87 × 1000
= 3870 mm.

Question 9.
5 km + 50 m = _____________ m
Answer:
5 km + 50 m = 5050 m.

Explanation:
5 km + 50 m = ?? m.
Conversion:
1 km = 1000 m.
5 km + 50 m = (5 × 1000) + 50
= 5000 + 50
= 5050 m.

Question 10.
200 km + 200 m = _____________ cm
Answer:
200 km + 200 m = 2,00,20,000 cm.

Explanation:
200 km + 200 m = ?? cm.
Conversion:
1 km = 100,000 cm.
1 m = 100 cm.
200 km + 200 m = (200 × 100,000) + (200 × 100)
= 2,00,00,000 + 20,000
= 2,00,20,000 cm.

Question 11.
400 cm = _____________ km
Answer:
400 cm = 0.004 km.

Explanation:
400 cm = ?? km.
Conversion:
1 km = 100,000 cm.
400 cm = 400 ÷ 100,000
= 0.004 km.

Question 12.
25 m + 10 cm = _____________ cm
Answer:
25 m + 10 cm = 2,510 cm.

Explanation:
25 m + 10 cm = ?? cm.
Conversion:
1 m = 100 cm.
25 m + 10 cm = (25 × 100) + 10
= 2,500 + 10
= 2,510 cm.

Question 13.
45 m + .25 m = _____________ mm
Answer:
45 m + .25 m = 45,250 mm.

Explanation:
45 m + .25 m = ?? mm.
Conversion:
1 m = 1,000 mm.
45 m + .25 m = (45 × 1,000) + (0.25 × 1,000)
= 45,000 + 250
= 45,250 mm.

Question 14.
33 cm + 33 mm + 33 m = _____________ m
Answer:
33 cm + 33 mm + 33 m = 36.033 m.

Explanation:
33 cm + 33 mm + 33 m = ?? m.
Conversion:
1 m = 1,000 mm.
1 m = 100 cm.
33 cm + 33 mm + 33 m = (300 ÷ 100) + (33 ÷ 1000) + 33
= 3 + 0.033 + 33
= 36.033 m.

Question 15.
11 km = _____________ m
Answer:
11 km = 11,000 m.

Explanation:
11 km = ?? m.
Conversion:
1 km = 1,000 m.
11 km = 11 × 1,000
= 11,000 m.

Question 16.
57 m = _____________ km
Answer:
57 m = 0.057 km.

Explanation:
57 m = ?? km.
Conversion:
1 km = 1,000 m.
57 m =57 ÷ 1000
= 0.057 km.

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 18.8 Temperature will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 18.8 Temperature

Exercises
CONVERT
For this exercise F will be the symbol for the temperature in degrees Fahrenheit. C will be for the temperature in degrees Celsius. To convert from one scale to the other, you use one of the following formulas: (F – 32 ) × (\(\frac{5}{9}\)) = C and C × (\(\frac{9}{5}\)) + 32 = F

Question 1.
32° F = ____________ C
Answer:
32° F = 0.95° C.

Explanation:
32° F = ?? C.
Conversion:
1 Celsius = 33.8 Fahrenheit.
32° F = 32 ÷ 33.8
= 0.95° C.

Question 2.
100° C = ____________ F
Answer:
100° C = 3,380° F.

Explanation:
100° C = ?? F.
Conversion:
1 Celsius = 33.8 Fahrenheit.
100° C = 33.8 × 100
= 3,380° F.

Question 3.
-149° F = ____________ C
Answer:
-149° F = 4.41° C.

Explanation:
-149° F = ??  C.
Conversion:
1 Celsius = 33.8 Fahrenheit.
-149° F = -149 ÷  33.8
= 4.41° C.

Question 4.
0° C = ____________ F
Answer:
0° C = 0° F.

Explanation:
0° C = ____________ F
Conversion:
1 Celsius = 33.8 Fahrenheit.
0° C = 33.8 × 0
= 0° F.

Question 5.
100° F = ____________ C
Answer:
100° F = 2.958° F.

Explanation:
100° F = ?? C.
Conversion:
1 Celsius = 33.8 Fahrenheit.
100° F = 100 ÷ 33.8
= 2.958° F.

Question 6.
72° F = ____________ C
Answer:
72° F = 2.130° C.

Explanation:
72° F = ?? C.
Conversion:
1 Celsius = 33.8 Fahrenheit.
72° F = 72 ÷ 33.8
= 2.130° C.

Question 7.
32° C = ____________ F
Answer:
32° C = 1081.6° F.

Explanation:
32° C = ?? F.
Conversion:
1 Celsius = 33.8 Fahrenheit.
32° C = 33.8 × 32
= 1081.6° F.

Question 8.
212° C = ____________ F
Answer:
212° C = 7165.6° F.

Explanation:
212° C = ?? F.
Conversion:
1 Celsius = 33.8 Fahrenheit.
212° C = 33.8 × 212
= 7165.6° F.

Question 9.
40° F = ____________ C
Answer:
40° F = 1.183° C.

Explanation:
40° F = ?? C.
Conversion:
1 Celsius = 33.8 Fahrenheit.
40° F = 40 ÷ 33.8
= 1.183° C.

Question 10.
120° F = ____________ C
Answer:
120° F = 3.550° C.

Explanation:
120° F = ?? C.
Conversion:
1 Celsius = 33.8 Fahrenheit.
120° F = 120 ÷ 33.8
= 3.550° C.

Question 11.
50° C = ____________ F
Answer:
50° C = 1,690° F.

Explanation:
50° C = ?? F.
Conversion:
1 Celsius = 33.8 Fahrenheit.
50° C = 50 × 33.8
= 1,690° F.

Question 12.
50° F = ____________ C
Answer:
50° F = 1.479° C.

Explanation:
50° F = ?? C.
Conversion:
1 Celsius = 33.8 Fahrenheit.
50° F = 50 ÷ 33.8
= 1.479° C.

Question 13.
5° C = ____________ F
Answer:
5° C = 169° F.

Explanation:
5° C = ?? F.
Conversion:
1 Celsius = 33.8 Fahrenheit.
5° C = 33.8 × 5
= 169° F.

Question 14.
-10° F = ____________ C
Answer:
-10° F = 0.295° F.

Explanation:
-10° F = ?? C.
Conversion:
1 Celsius = 33.8 Fahrenheit.
-10° F = -10 ÷ 33.8
= 0.295° F.

Question 15.
-10° C = ____________ F
Answer:
-10° C = 338° F.

Explanation:
-10° C = ?? F.
Conversion:
1 Celsius = 33.8 Fahrenheit.
-10° C = 33.8 × -10
= 338° F.

Question 16.
-30° C = ____________ F
Answer:
-30° C = -1,014° F.

Explanation:
-30° C = ?? F.
Conversion:
1 Celsius = 33.8 Fahrenheit.
-30° C = 33.8 × -30
= -1,014° F.

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 18.7 Time will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 18.7 Time

Exercises
SOLVE
Question 1.
24 hours = ____________ seconds
Answer:
24 hours = 1,440 seconds.

Explanation:
24 hours = ?? seconds
Conversion:
1 hour = 60 seconds.
24 hours = 60 × 24
= 1,440 seconds.

Question 2.
35 days = ____________ hours
Answer:
35 days = 840 hours.

Explanation:
35 days = ?? hours.
Conversion:
1 day = 24 hours.
35 days = 24 × 35
= 840 hours.

Question 3.
365 days = ____________ minutes
Answer:
365 days = 525,600 minutes.

Explanation:
365 days = ?? minutes.
Conversion:
1 day = 1,440 minutes.
365 days = 1,440 × 365
= 525,600 minutes.

Question 4.
12 hours = ____________ days
Answer:
12 hours = 0.5 day or half a day.

Explanation:
12 hours = ?? days.
Conversion:
1 day = 24 hours.
12 hours = 12 ÷ 24
= 0.5 day or half a day.

Question 5.
52 weeks = ____________ days
Answer:
52 weeks = 364 days.

Explanation:
52 weeks = ?? days.
Conversion:
1 week = 7 days.
52 weeks = 7 × 52
= 364 days.

Question 6.
51 hours = ____________ minutes
Answer:
51 hours = 3,060 minutes.

Explanation:
51 hours = ?? minutes.
Conversion:
1 hour = 60 minutes.
51 hours = 60 × 51
= 3,060 minutes.

Question 7.
24 days = ____________ weeks
Answer:
24 days = 3.4 weeks.

Explanation:
24 days = ?? weeks.
Conversion:
1 week = 7 days.
24 days = 24 ÷ 7
= 3.4 weeks.

Question 8.
200 years = ____________ decades
Answer:
200 years = 20 decades.

Explanation:
200 years = ?? decades.
Conversion:
1 decade = 10 years.
200 years = 200 ÷ 10
= 20 decades.

Question 9.
3,000 years = ____________ centuries
Answer:
3,000 years = 30 centuries.

Explanation:
3,000 years = ?? centuries.
Conversion:
1 century = 100 years.
3,000 years = 3,000 ÷ 100
= 30 centuries

Question 10.
42 days = ____________ minutes
Answer:
42 days = 60,480 minutes

Explanation:
42 days = ??  minutes
Conversion:
1 day = 1,440 minutes.
42 days = 1,440 × 42
= 60,480 minutes

Question 11.
2 weeks = ____________ seconds
Answer:
2 weeks = 12,09,600 seconds

Explanation:
2 weeks = ?? seconds
Conversion:
1 week = 604,800 seconds.
2 weeks = 604,800 × 2
= 12,09,600 seconds

Question 12.
45 minutes = ____________ hours
Answer:
45 minutes = 0.75 hours.

Explanation:
45 minutes = ?? hours.
Conversion:
1 hour = 60 minutes.
45 minutes = 45 ÷ 60
= 0.75 hours.

Question 13.
If you got paid $800 and you worked 2.92 days, approximately how much did you make per hour?
Answer:
Amount paid per day = $11.42.

Explanation:
Amount paid = $800.
Number of days = 2.92.
Amount paid per day = Amount paid ÷ Number of days
= $800 ÷ 2.92
= $273.97.
Conversion:
1 day = 24 hours.
Amount paid per day = Amount paid per day ÷ 24
= $273.97 ÷ 24
= $11.42.

Question 14.
How much do you have to pay a rock band that will play for 2 hours and wants to be paid $15/ second?
Answer:
Amount paid for 2 hours = $108,000.

Explanation:
Number of hours = 2.
Amount paid per second = $15.
Conversion:
1 hour = 3,600 seconds.
2 hours = 3,600 × 2
= 7,200 seconds.
=> Amount paid for 2 hours = Amount paid per second × 7,200
= $15 × 7,200
= $108,000.

Question 15.
3 decades = _____________ hours
Assume 365 days per year.
Answer:
3 decades = 262,800 hours.

Explanation:
Conversion:
1 year = 365 days.
1 day = 24 hours.
=> 1 year = 365 × 24
= 8,760 hours.
1 decade = 10 years.
= 10 × 8760 hours
= 87,600 hours.
3 decades = 87,600 × 3
= 262,800 hours.

Question 16.
A man tells you he is 2,270,592,000 seconds old. How many years old is he if you assume 365 days per year?
Answer:
Number of years old a man is = 72.

Explanation:
Number of seconds old a man is = 2,270,592,000.
Conversion:
1 year = 365 days.
1 day = 24 hours.
=> 1 year = 365 × 24
=> 8,760 hours.
1 hour = 3,600 seconds.
8,760 hours = 8,760 × 3600
= 3,15,36,000 seconds.
Number of years old a man is = Number of seconds old a man is ÷ 3,15,36,000 seconds
= 2,270,592,000 ÷ 3,15,36,000 seconds
= 72.

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 18.6 Volume of a Solid will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 18.6 Volume of a Solid

Exercises
SOLVE
Question 1.
A football field measures 360 ft long and 165 ft wide. If a construction company is told that they need to have 3 feet of gravel under the field for proper drainage, how many cubic yards do they need to order?

Answer:
Number of cubic yards they need to order = 178,200.

Explanation:
Length of the football field = 360 feet.
Width of the football field = 165 feet.
Depth of the gravel = 3 feet.
Area of the football = Length of the football field × Width of the football field × Length of the gravel
= 360 × 165
= 59400.
Number of cubic yards they need to order = Area of the football × Depth of the gravel
= 59,400 × 3
= 178,200.

Question 2.
A shoe box has dimensions of 12 inches by 10 inches by 7 inches. How many cubic inches is it?

Answer:
Volume of the shoe box = 840 cubic inches.

Explanation:
Length of the shoe box = 12 inches.
Width of the shoe box = 10 inches.
Height of the shoe box = 7 inches.
Volume of the shoe box = Length of the shoe box × Width of the shoe box × Height of the shoe box
= 12 × 10 × 7
= 120 × 7
= 840 cubic inches.

Question 3.
What is the volume of a cube with sides of 5 ft?

Answer:
Volume of a cube = 125 cubic feet.

Explanation:
Side of the cube = 5 feet.
Volume of a cube = Side of the cube × Side of the cube × Side of the cube
= 5 × 5 × 5
= 25 × 5
= 125 cubic feet.

Question 4.
A shipping box has dimensions of 6 in. by 5 in. by 8 in. If a pound of granola takes up a cubic inch, how many pounds of granola can you put in the box?
Answer:
Number of pounds of granola can you put in the box = 240.

Explanation:
Length of the shipping box = 6 inches.
Width of the shipping box = 5 inches.
Height of the shipping box = 8 inches.
Volume of the shipping box = Length of the shipping box × Width of the shipping box  × Height of the shipping box
= 6 × 5 × 8
= 30 × 8
= 240 cubic inches.
If a pound of granola takes up a cubic inch.
=> Number of pounds of granola can you put in the box = Volume of the shipping box ÷ 1 cubic inch
=> 240 cubic inches ÷ 1 cubic inch
=> 240.

Question 5.
A rectangular solid with sides of 8 ft by 4 ft by 11 ft has what volume?
Answer:
Volume of the rectangular solid = 352 cubic feet.

Explanation:
Length of the rectangular solid = 8 feet.
Width of the rectangular solid = 4 feet.
Height of the rectangular solid = 11 feet.
Volume of the rectangular solid = Length of the rectangular solid × Width of the rectangular solid × Height of the rectangular solid
= 8 × 4 × 11
= 32 × 11
= 352 cubic feet.

Question 6.
A cube that has sides of 16 inches has how many cubic yards of volume?
Answer:
Volume of the cube = 1911.03 cubic yards.

Explanation:
Side of the cube = 16 inches.
Volume of the cube = Side of the cube × Side of the cube × Side of the cube
= 16 × 16 × 16
= 256 × 16
= 4,096 cubic inches.
1 cubic inches = 2.14335 cubic yards
=> 4,096 cubic inches = 4,096 × 2.14335
= > 1911.03 cubic yards.

Question 7.
Jim built a rectangular prism out of \(\frac{1}{2}\) -inch cubes. The prism is 5 cubes long, 2 cubes wide, and 2 cubes tall. What is the volume of the prism?
Answer:
Volume of the prism = 20 cubic cubes.

Explanation:
Volume of the rectangular prism = \(\frac{1}{2}\) -inch cubes.
Length of the prism = 5 cubes.
Width of the prism = 2 cubes.
Height of the prism = 2 cubes.
Volume of the prism = Length of the prism × Width of the prism × Height of the prism
= 5 × 2 × 2
= 10 × 2
= 20 cubic cubes.

Question 8.
Bob is packing a rectangular box with sugar cubes. If the box measures 4.5 inches by 3.5 inches by 2 inches, how many \(\frac{1}{2}\)-inch sugar cubes will fit in the box?
Answer:
Number of sugar cubes fit in the box = 40.

Explanation:
Length of the box = 5 cubes.
Width of the box = 2 cubes.
Height of the box = 2 cubes.
Volume of the box = Length of the box × Width of the box × Height of the box
= 5 × 2 × 2
= 10 × 2
= 20 cubic inches.
Length of the sugar cube = \(\frac{1}{2}\)-inch
Number of sugar cubes fit in the box = Volume of the box ÷ Length of the sugar cube
= 20  ÷ \(\frac{1}{2}\)
= 40 .

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 18.5 Area will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 18.5 Area

Exercises

SOLVE
Question 1.
What is the area of a square with 4 ft sides?
Answer:
Area of square = 16 square feet.

Explanation:
Side of square = 4 feet.
Area of square = Side of square × Side of square
= 4 × 4
= 16 square feet.

Question 2.
If a rectangle has sides of 2 ft and 12 ft, what is its area?
Answer:
Area of a rectangle = 24 square feet.

Explanation:
Length of a rectangle = 12 feet.
Width of a rectangle = 2 feet.
Area of a rectangle = Length of a rectangle × Width of a rectangle
= 12 × 2
= 24 square feet.

Question 3.
There are 9 sq ft in one square yard (3 ft × 3 ft). How many square feet are in a 3-yd by 4-yd rug?
Answer:
Area of the rug = 12 square yards.

Explanation:
Length of the rug = 3-yd
Width of the rug = 4-yd
Area of the rug = Length of the rug × Width of the rug
= 3 yards × 4 yards
= 12 square yards.

Question 4.
How much will the area decrease if you take away 3 feet from each side of a square with 10-ft long sides?
Answer:
91 square feet the area decrease if you take away 3 feet from each side of a square with 10-ft long sides.

Explanation:
Side of square = 3 feet.
Area of square = Side of square × Side of square
= 3 feet × 3 feet
= 9 square feet.
Side of square = 10 feet.
Area of square = Side of square × Side of square
=  10 feet × 10 feet
= 100 square feet.
Difference:
= 100 square feet – 9 square feet
= 91 square feet.

Question 5.
John walks west 20 ft, then 10 ft to the south, then 20 ft to the east, and then returns to his starting point to form a rectangle. What is the area of that rectangle?
Answer:
Area of the rectangle = 60 square feet.

Explanation:
Number of feet John walks to the west = 20 feet.
Number of feet John walks to the south = 10 feet.
Number of feet John walks to the east = 20 feet.
Number of feet John walks to the north = 10 feet
Area of the rectangle = Number of feet John walks to the west + Number of feet John walks to the south + Number of feet John walks to the east + Number of feet John walks to the north
= 20 feet + 10 feet + 20 feet + 10 feet
= 30 feet + 20 feet + 10 feet
= 50 feet + 10 feet
= 60 square feet.

Question 6.
If a square that has sides of 25 ft is split in half, what is the area of each of the pieces?
Answer:
Area of each of the pieces = 156.25 square feet.

Explanation:
If a square that has sides of 25 ft is split in half.
=> Side of the square = 25 feet ÷ 2
= 12.5 feet.
Area of each of the pieces = Side of the square × Side of the square
= 12.5 × 12.5
= 156.25 square feet.

Question 7.
A right triangle has sides of 7 ft, 24 ft, and 25 ft. What is its area?
Answer:
Area of a right triangle = 84 square feet.

Explanation:
Sides of a right triangle = 7 ft, 24 ft, and 25 ft.
Area of a right triangle =  \(\frac{1}{2}\) × Base × Height
= \(\frac{1}{2}\)  × 7 feet × 24 feet
= 7 feet × 12 feet
= 84 square feet.

Question 8.
Which has a larger area, a triangle with a base of 15 ft and a height 25 ft or a square with sides of 14 ft?
Answer:
Area of a square has a larger area than a triangle with a base of 15 ft and a height 25 ft.

Explanation:
Base of the triangle = 15 feet.
Height of triangle = 25 feet.
Area of the triangle = \(\frac{1}{2}\) × Base × Height
= \(\frac{1}{2}\) × 15 feet × 25 feet
= \(\frac{375}{2}\)
= 187.5 square feet.
Side of a square = 14 feet.
Area of a square = Side of a square × Side of a square
= 14 feet × 14 feet
= 196 square feet.

Question 9.
What is the area of a rectangle that is 3.2 inches by 4.8 inches?
Answer:
Area of the rectangle = 15.36 square inches.

Explanation:
Length of the rectangle = 4.8 inches
Width of the rectangle = 3.2 inches.
Area of the rectangle = Length of the rectangle × Width of the rectangle
= 4.8 × 3.2
= 15.36 square inches.

Question 10.

Answer:
Area of the rectangle = 15.

Explanation:
Length of the rectangle = 7.5.
Width of the rectangle = 2.
Area of the rectangle = Length of the rectangle × Width of the rectangle
= 7.5 × 2
= 15.

Question 11.
Kim wants to put carpet on her bedroom floor and needs to find the total area of the floor. If the floor measures 13.5 feet by 12 feet, what is the total area of the floor?
Answer:
Total area of the floor = 162 square feet.

Explanation:
Length of the floor = 13.5 feet.
Width of the floor =  12 feet.
Total area of the floor = Length of the floor × Width of the floor
= 13.5 feet × 12 feet
= 162 square feet.

Question 12.
What is the area of a square with sides of .7 inches?
Answer:
Area of the square = 0.49 square inches.

Explanation:
Side of the square = 0.7 inches.
Area of the square = Side of the square × Side of the square
= 0.7 × 0.7
= 0.49 square inches.

Question 13.

Answer:
Area of the square = 25.

Explanation:
Side of the square = 5.
Area of the square = Side of the square × Side of the square
= 5 × 5
= 25.

Question 14.
If Aaron wants to lay a tile floor in a room that is 12 feet long and 9 feet wide, how 5 many 1 ft. square tiles will he need?
Answer:
Area of the tile floor = 108 square feet.

Explanation:
Length of the tile floor = 12 feet.
Width of the tile floor = 9 feet.
Area of the tile floor = Length of the tile floor × Width of the tile floor
= 12 feet × 9 feet.
= 108 square feet.

Question 15.
What is the area of a triangle with base and height 5cm?
Answer:
Area of the triangle = 12.5 square cm.

Explanation:
Base of the triangle = 5 cm.
Height of the triangle = 5 cm.
Area of the triangle = \(\frac{1}{2}\) × Base of the triangle × Height of the triangle
= \(\frac{1}{2}\) × 5 × 5
= \(\frac{1}{2}\) × 25
= 12.5 square cm.

Question 16.

Answer:
Area of the triangle = 9.

Explanation:
Base of the triangle = 2.
Height of the triangle = 9.
Area of the triangle = \(\frac{1}{2}\) × Base of the triangle × Height of the triangle
= \(\frac{1}{2}\) × 2 × 9
= 9.

Question 17.
A sailboat has a triangular sail with an area of 12 ft². If the height of the sail is 6 feet, how long is the base?
Answer:
Area of the triangle = 4 feet.

Explanation:
Area of the triangular sail = 12 ft².
Height of the triangular sail = 6 feet.
Base of the triangular sail = ?? feet.
Area of the triangle = \(\frac{1}{2}\) × Base of the triangle × Height of the triangle
=> 12 square feet = \(\frac{1}{2}\) × Base of the triangle × 6 feet
=> 12 square feet = Base of the triangle × 3 feet
=> 12 ÷ 3 = Base of the triangle
=> 4 feet = Base of the triangle

Question 18.
What is the area of the figure below?

Answer:
Total area of the figure = 27.

Explanation:
Length of the  rectangle = 6.
Width of the rectangle = 4.
Area of the rectangle = Length of the  rectangle × Width of the rectangle
= 6 × 4
= 24.
Base of the triangle = 6.
Height of the triangle = 1.
Area of the triangle = \(\frac{1}{2}\) × Base of the triangle × Height of the triangle
= \(\frac{1}{2}\) × 6 × 1
= 3.
Total area of the figure = Area of the rectangle + Area of the triangle
= 24 + 3
= 27.

Question 19.
Erlene needs 5 square feet of fabric to make a jacket. If she buys a square of blue fabric that is 2 feet long and 2 feet wide and a triangular piece of red fabric for the hood that measures 2 feet across the base and is 1 foot high, will she have enough fabric?
Answer:
Area of the square of blue fabric = 4 square feet.

Explanation:
Area of the fabric to make a jacket Erlene needs = 5 square feet.
Side of the square of blue fabric = 2 feet.
Area of the square of blue fabric = Side of the square of blue fabric × Side of the square of blue fabric
= 2 feet × 2 feet
= 4 square feet.

Question 20.
The total area of a square is 9 inches². If the square is cut in half diagonally, what is the area of one of the triangles?
Answer:
Area of a triangle = 4.5 Square units.

Explanation:
Total area of a square = 9 square inches.
Side of a square = √9 = 3 units.
Base of the triangle = 3 units.
Height of the triangle = 3 units.
Area of a triangle = \(\frac{1}{2}\) × Base of the triangle × Height of the triangle
= \(\frac{1}{2}\) × 3 × 3
= \(\frac{1}{2}\) × 9
= 4.5 Square units.

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 18.4 Perimeter will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 18.4 Perimeter

Exercises
SOLVE
Question 1.
What is the perimeter of a 2-inch square?
Answer:
Perimeter of the square = 8 inches.

Explanation:
Side of square = 2 inches.
Perimeter of the square = 4 × Side of square
= 4 × 2 inches
= 8 inches.

Question 2.
A right triangle with sides measuring 3, 4, and 5 feet has what perimeter?
Answer:
Perimeter of the right triangle = 12 feet.

Explanation:
Sides of the right triangle = 3, 4, and 5 feet
Perimeter of the right triangle = side of the right triangle + side of the right triangle + side of the right triangle
= 3 feet + 4 feet + 5 feet
= 7 feet + 5 feet
= 12 feet.

Question 3.
Which has a longer perimeter, a 7-foot square or a rectangle with sides of 5 feet and 8 feet?
Answer:
A 7-foot square has a longer perimeter than a rectangle with sides of 5 feet and 8 feet.

Explanation:
Side of square = 7 foot.
Perimeter of square = 4 × Side of square
= 4 × 7 foot
= 28 foot.
Length of rectangle = 8 feet.
Width of rectangle = 5 feet.
Perimeter of rectangle = 2 (Length of rectangle + Width of rectangle)
= 2(8 feet + 5feet)
= 2 × 13 feet
= 26 feet.

Question 4.
A farmer is building a fence and wants to save fencing material. So he builds a rectangular fence with sides of 30 feet and 45 feet. One of the shorter sides of the fence will be the side of the barn. How many feet of fencing material will the farmer need?
Answer:
150 feet of fencing material the farmer will need.

Explanation:
Length of the rectangular fence = 45 feet.
Width of the rectangular fence = 30 feet.
Perimeter of the rectangular fence = 2(Length of the rectangular fence + Width of the rectangular fence)
= 2 (45 feet + 30feet)
= 2 × 75 feet
= 150 feet.

Question 5.
Which has a longer perimeter, a 14-foot square or an equilateral triangle with sides of 10 feet?
Answer:
14-foot square has a longer perimeter than an equilateral triangle with sides of 10 feet.

Explanation:
Side of the square = 14 foot.
Perimeter of the square = 4 × Side of the square
= 4 × 14 foot
= 56 foot.
Length of the equilateral triangle = 10 feet.
Perimeter of the equilateral triangle = 3 × Length of the equilateral triangle
= 3 × 10 feet
= 30 feet.

Question 6.
A triangle has one side of 5 inches and two sides of 7 inches. What is its perimeter?
Answer:
Perimeter of the triangle = 19 inches.

Explanation:
Length of one side of triangle = 5 inches.
Length of other two sides of triangle = 7 inches.
Perimeter of the triangle = Length of one side of triangle + Length of other two sides of triangle
= 5 inches + 7 inches + 7 inches
= 12 inches + 7 inches
= 19 inches.

Question 7.
A triangle has 3 equal sides of 200 feet. What is its perimeter?
Answer:
Perimeter of the triangle = 600 feet.

Explanation:
Length of 3 equal sides of triangle = 200 feet.
Perimeter of the triangle = 3 × Length of 3 equal sides of triangle
= 3 × 200 feet
= 600 feet.

Question 8.
A building has a rectangular base with sides of 200 feet and 450 feet. What is its perimeter?
Answer:
Perimeter of a building has a rectangular base = 1,300 feet.

Explanation:
Length of a building has a rectangular base = 450 feet.
Width of a building has a rectangular base = 200 feet.
Perimeter of a building has a rectangular base = 2 (Length of a building has a rectangular base + Width of a building has a rectangular base)
= 2 (450 feet + 200 feet)
= 2 × 650 feet
= 1,300 feet.

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 18.3 Customary Units of Weight will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 18.3 Customary Units of Weight

Exercises
CONVERT
Question 1.
10 pounds is how many ounces?
Answer:
10 pounds is 160 ounces.

Explanation:
10 pounds = ??
1 pound = 16 ounces.
10 pounds = 16 × 10
=> 160 ounces.

Question 2.
15.2 tons is how many pounds?
Answer:
15.2 tons is 34,000 pounds.

Explanation:
15.2 tons = ?? pounds.
Conversion:
1 ton = 2000 pounds.
=> 15.2 tons = 2000 × 15.2
=> 34,000 pounds.

Question 3.
14 tons is how many ounces?
Answer:
14 tons is 4,48,000 ounces.

Explanation:
Conversion:
1 ton = 32,000 ounces.
=> 14 tons = 32000 × 14
=> 4,48,000 ounces.

Question 4.
125 ounces is how many pounds?
Answer:
125 ounces is 7.8125 pounds.

Explanation:
Conversion:
1 pound = 16 ounces.
=> 125 ounces = 125 ÷ 16
=> 7.8125 pounds.

Question 5.
.234 tons is how many pounds?
Answer:
.234 tons is 468 pounds.

Explanation:
.234 tons = ?? pounds.
Conversion:
1 ton = 2000 pounds.
=>.234 tons = 2000 × 0.234
=> 468 pounds.

Question 6.
1 pound is how many tons?
Answer:
1 pound is 0.0005 tons.

Explanation:
1 pound = ?? tons.
1 ton = 2000 pounds.
=> 1 pound = 1 ÷ 2000
=> 0.0005 tons.

Question 7.
.892 tons is how many ounces?
Answer:
.892 tons is 28,544 ounces.

Explanation:
.892 tons = ?? ounces.
Conversion:
1 ton = 32,000 ounces.
=> .892 tons = 32,000 × 0.892
=> 28,544 ounces.

Question 8.
14 ounces is how many pounds?
Answer:
14 ounces is 0.875 pounds.

Explanation:
14 ounces = ?? pounds.
Conversion:
1 pounds = 16 ounce.
=> 14 ounces = 14 ÷ 16
=>0.875 pounds.

Question 9.
32 tons is how many pounds?
Answer:
32 tons is 64,000 pounds.

Explanation:
32 tons = ?? pounds.
Conversion:
1 ton = 2000 pounds.
=> 32 tons = 2000 × 32
=> 64,000 pounds.

Question 10.
2,345 ounces is how many tons?
Answer:
2,345 ounces is 0.0733 tons.

Conversion:
2,345 ounces = ?? tons.
1 tons = 32000 ounces.
=> 2,345 ounces = 2,345 ÷ 32,000
=> 0.0733 tons.

Question 11.
45.2 lbs is how many ounces?
Answer:
45.2 lbs is 723.2 ounces.

Explanation:
45.2 lbs = ?? ounces.
Conversion:
1 pound = 16 ounces.
=> 45.2 lbs = 16 × 45.2
=> 723.2 ounces.

Question 12.
60,000 ounces is how many tons?
Answer:
60,000 ounces is 1.875 tons.

Explanation:
60,000 ounces = ?? tons
Conversion:
1 ton = 32,000 ounces
=> 60,000 ounces = 60,000 ÷ 32,000
=> 1.875 tons.

Question 13.
A 250-pound man weighs how many tons?
Answer:
A 250-pound man weighs 0.125 tons.

Explanation:
250 pounds = ?? tons.
Conversion:
1 ton = 2000 pounds.
=> 250 pounds = 250 ÷ 2000
=> 0.125 tons.

Question 14.
A 3.5-ton elephant weighs how many pounds?
Answer:
A 3.5-ton elephant weighs 7,000 pounds.

Explanation:
3.5 tons = ?? pounds.
Conversion:
1 ton = 2000 pounds.
=> 3.5 tons = 2000 × 3.5
=> 7,000 pounds.

Question 15.
A \(\frac{3}{4}\) ton truck can carry \(\frac{3}{4}\) of a ton of materials. How many pounds is that?
Answer:
Number of pounds of materials truck can carry = 2666.67 pounds.

Explanation:
Number of tons of materials truck can carry = \(\frac{3}{4}\) of a ton.
=> 1 ÷  \(\frac{3}{4}\)
=>   \(\frac{4}{3}\)
=> 1.33.
Number of tons the truck weighs = \(\frac{3}{4}\)
Conversion:
1 ton = 2,000 pounds.
Number of pounds of materials truck can carry =
1.33 tons = 1.33 × 2,000
=>2666.67 pounds.

Question 16.
If there are 850 students at school and each eats 4 ounces (\(\frac{1}{4}\) pound) of hamburger for lunch, how many pounds of hamburger, in total, do the students eat every day?
Answer:
Number of pounds of hamburger, in total, the students eat every day = 425 pounds.

Explanation:
Number of students at school = 850.
Quantity of hamburger for lunch they eat each = 4 ounces (\(\frac{1}{4}\) pound)
Conversion:
1 pound = 16 ounces.
4 ounces = 4 ÷ 16 = 0.25 pounds.
=> 4 ounces (\(\frac{1}{4}\) pound) = 0.25 + 0.25
=> 0.50 pounds.
Number of pounds of hamburger, in total, the students eat every day = Number of students at school × 0.50 pounds.
=> 850 × 0.50 pounds
=> 425 pounds.

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 18.2 Customary Units of Liquid Volume will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 18.2 Customary Units of Liquid Volume

Exercises
CONVERT
Question 1.
1 gallon is how many pints?
Answer:
1 gallon is 8 pints.

Explanation:
Conversion:
1 gallon = 8 pints.

Question 2.
A 23-gallon gas tank holds how many quarts?
Answer:
A 23-gallon gas tank holds 92 quarts.

Explanation:
Conversion:
1 gallon = 4 quart.
=> 23-gallon = 4 × 23
=> 92 quarts.

Question 3.
54 quarts is how many gallons?
Answer:
54 quarts is 13.5 gallons.

Explanation:
Conversion:
1 gallon = 4 quart.
=> 54 quart = 54 ÷ 4
=> 13.5 gallons.

Question 4.
15 pints is how many gallons?
Answer:
15 pints is 1.875 gallons.

Explanation:
Conversion:
1 gallon = 8 pints.
=> 15 pints = 15 ÷ 8
=> 1.875 gallons.

Question 5.
1,000 cups is how many quarts?
Answer:
1,000 cups = 250 quarts.

Explanation:
Conversion:
1 quarts = 4 cups.
=> 1,000 cups = 1,000 ÷ 4
=> 250 quarts.

Question 6.
250 pints is how many cups?
Answer:
250 pints is 500 cups.

Explanation:
250 pints = ?? cups.
Conversion:
1 pint = 2 cups.
=> 250 pints = 2 × 250
=> 500 cups.

Question 7.
57 gallons is how many pints?
Answer:
57 gallons is 456 pints.

Explanation:
57 gallons = ?? pints.
Conversion:
1 gallon = 8 pints.
=> 57 gallons = 8 × 57
=> 456 pints.

Question 8.
21 quarts is how many cups?
Answer:
21 quarts is 84 cups.

Explanation:
Conversion:
1 quart = 4 cups.
=> 21 quarts = 4 × 21
=> 84 cups.

Question 9.
32 pints is how many gallons?
Answer:
32 pints is 4 gallons.

Explanation:
32 pints = ?? gallons.
Conversion:
1 gallon = 8 pints.
=> 32 pints = 32 ÷ 8
=> 4 gallons.

Question 10.
88 pints is how many quarts?
Answer:
88 pints is 44 quarts.

Explanation:
88 pints = ?? quarts.
1 pint = 0.5 quarts
=> 88 pints = 0.5 × 88
=> 44 quarts.

Question 11.
125 cups is how many pints?
Answer:
125 cups is 62.5 pints.

Explanation:
125 cups = ?? pints.
Conversion:
1 pint = 2 cups.
=> 125 cups = 125 ÷ 2
=> 62.5 pints.

Question 12.
125 pints is how many cups?
Answer:
125 pints is 250 cups.

Explanation:
125 pints = ?? cups.
Conversion:
1 pint = 2 cups.
=> 125 pints = 2 × 125
=> 250 cups.

Question 13.
77 gallons is how many quarts?
Answer:
77 gallons is 308 quarts.

Explanation:
77 gallons = ?? quarts.
Conversion:
1 gallon = 4 quarts.
=> 77 gallons = 4 × 77
=> 308 quarts.

Question 14.
22 pints is how many gallons?
Answer:
22 pints is 2.75 gallons.

Explanation:
22 pints = ?? gallons.
Conversion:
1 gallon = 8 pint.
=> 22 pints = 22 ÷ 8
=> 2.75 gallons.

Question 15.
256 quarts is how many gallons?
Answer:
256 quarts is 64 gallons.

Explanation:
256 quarts = ?? gallons.
Conversion:
1 gallons = 4 quarts.
=> 256 quarts = 256 ÷ 4
=> 64 gallons.

Question 16.
256 pints is how many gallons?
Answer:
256 pints is 32 gallons.

Explanation:
256 pints = ?? gallons.
Conversion:
1 gallon = 8 pint.
=> 256 pints = 256 ÷ 8
=> 32 gallons.

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 18.1 Customary Units of Length will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 18.1 Customary Units of Length

Exercises
CONVERT
Question 1.
3.5 feet is how many inches?
Answer:
3.5 feet = 42 inches.

Explanation:
3.5 feet = ?? inches.
Conversion:
1 feet = 12 inches
=> 3.5 feet  = 12 × 3.5
=> 42 inches.

Question 2.
2 miles is how many feet?
Answer:
2 miles = 10,560 feet.

Explanation:
2 miles = ?? feet.
Conversion:
1 mile = 5,280 feet.
=> 2 miles = 2 × 5,280
=> 10,560 feet.

Question 3.
39 inches is how many yards?
Answer:
39 inches = 1.083 yards.

Explanation:
39 inches = ?? yards
Conversion:
1 yard = 36 inches.
=> 39 inches = 39 ÷ 36
=> 1.083 yards.

Question 4.
5 miles is how many feet?
Answer:
5 miles = 10,560 feet.

Explanation:
5 miles = ?? feet.
Conversion:
1 mile = 5280 feet.
=> 5 miles = 5 × 5280
=> 10,560 feet.

Question 5.
78 inches is how many feet?
Answer:
78 inches = 6.5 feet.

Explanation:
78 inches = ?? feet.
Conversion:
1 feet = 12 inches.
=> 78 inches = 78 ÷ 12
=> 6.5 feet.

Question 6.
10,000 yards is how many miles?
Answer:
10,000 yards = 5.68 miles.

Explanation:
10,000 yards = ?? miles.
Conversion:
1 miles = 1760 yards.
=> 10,000 yards = 10000 ÷ 1760
=> 5.68 miles.

Question 7.
10.5 yards is how many feet?
Answer:
10.5 yards = 31.5 feet.

Explanation:
10.5 yards = ?? feet.
Conversion:
1 yard = 3 feet.
=> 10.5 yards = 3 × 10.5
=> 31.5 feet.

Question 8.
7.25 miles is how many inches?
Answer:
7.25 miles = 4,59,360 inches.

Explanation:
7.25 miles = ?? inches.
Conversion:
1 mile = 63,360 inches.
=> 7.25 miles = 63,360 × 7.25
=> 4,59,360 inches.

Question 9.
3.75 yards is how many inches?
Answer:
3.75 yards = 135 inches.

Explanation:
3.75 yards = ?? inches.
Conversion:
1 yard = 36 inches.
=> 3.75 yards = 36 × 3.75
=> 135 inches.

Question 10.
125 miles is how many yards?
Answer:
125 miles = 2,20,000 yards.

Explanation:
125 miles = ?? yards.
Conversion:
1 mile = 1760 yard.
=> 125 miles = 125 × 1760
=> 2,20,000 yards.

Question 11.
72 feet is how many miles?
Answer:
72 feet = 3,80,160 miles.

Explanation:
Conversion:
1 feet = 5280 miles.
=> 72 feet  = 72 × 5280
=> 3,80,160 miles.

Question 12.
72 feet is how many inches?
Answer:
72 feet = 864 inches.

Explanation:
72 feet = ?? inches.
Conversion:
1 feet = 12 inches.
=> 72 feet = 12 × 72
=> 864 inches.

Question 13.
245 yards is how many feet?
Answer:
245 yards = 735 feet.

Explanation:
245 yards = ?? feet.
Conversion:
1 yard = 3 feet.
=> 245 yards = 3 × 245
=> 735 feet.

Question 14.
10,000 inches is how many miles?
Answer:
10,000 inches = 0.1578 miles.

Explanation:
10,000 inches = ?? miles.
Conversion:
1 mile= 63,360 inches.
=> 10,000 inches = 10000 ÷ 63,360
=> 0.1578 miles.

Question 15.
53 yards is how many miles?
Answer:
53 yards = 0.301 miles.

Explanation:
53 yards = ?? miles.
Conversion:
1 mile = 1760 yards.
=> 53 yards = 53 ÷ 1760
=> 0.301 miles.

Question 16.
9,000 yards is how many inches?
Answer:
9,000 yards = 3,24,000  inches.

Explanation:
Conversion:
1 yard = 36 inches.
=> 9,000 yards = 36 × 9000
=> 3,24,000  inches.

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 17.5 Solving Equations and Inequalities by Substitution will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 17.5 Solving Equations and Inequalities by Substitution

Exercises

Question 1.
Sydney has a dozen eggs. He wants to bake a cake, but his mother says she needs 9 of the 12 eggs. What equation could he write to see how many eggs he will be able to use for his cake?
Answer:
Number of eggs he will be able to use for his cake = 3.

Explanation:
Number of eggs Sydney has = 12.
Number of eggs his mom needs = 9.
Number of eggs he will be able to use for his cake = Number of eggs Sydney has – Number of eggs his mom needs
= 12 – 9
= 3.

Question 2.
If Sydney’s cake recipe calls for 4 eggs, will he have enough eggs to bake the cake?
Answer:
No, he doesn’t have enough eggs to bake the cake because number of eggs he will be able to have are less than his cake recipe.

Explanation:
Number of eggs he will be able to use for his cake = 3.
Number of eggs Sydney’s cake recipe calls = 4.

Question 3.
If Sydney decides instead to make brownies that require only 3 eggs, will he have enough eggs to make the brownies?
Answer:
Yes, he can make brownies because he has enough eggs with him.

Explanation:
Number of eggs he will be able to use for his cake = 3.
Number of eggs he needs to make brownies = 3.

Question 4.
Kai has 4 red marbles, 3 blue marbles, 3 green marbles, and 2 yellow marbles. Kai wants to play a game with his brother that requires 6 marbles that are all the same color. Kai’s brother says he can bring 2 marbles of any color. Which color should Kai bring?
Answer:
Red Marbles color his brother should get because it total matches the number of marbles he needs to play with his brother.

Explanation:
Number of red marble Kai has = 4.
Number of blue marble Kai has = 3.
Number of green marble Kai has = 3.
Number of yellow marble Kai has = 2.
Number of marbles he needs to play with his brother = 6.
Number of marbles his brother said will bring of any color = 2.
Marbles color his brother should get:
Number of marbles his brother said will bring of any color + Number of red marble Kai has
= 2 + 4
= 6.
Number of marbles his brother said will bring of any color + Number of blue marble Kai has
= 2 + 3
= 5.
Number of marbles his brother said will bring of any color + Number of green marble Kai has
= 2 + 3
= 5.
Number of marbles his brother said will bring of any color + Number of yellow marble Kai has
= 2 + 2
= 4.

Question 5.
Write an equation that describes the total number of marbles in the game in question 4, using the letter m for the number of marbles Kai should bring.
Answer:
Total number of marbles Kai should bring = m = 2 + 4 = 6.

Explanation:
Number of red marble Kai has = 4.
Number of blue marble Kai has = 3.
Number of green marble Kai has = 3.
Number of yellow marble Kai has = 2.
Total number of marbles Kai should bring = m = 6.
Number of marbles his brother said will bring of any color + Number of red marble Kai has
= 2 + 4
= 6.

Question 6.
If \(\frac{4}{k}\) = 2, which of the following could k be the value of k?
(A) 1
(B) 2
(C) 3
(D) 4
Answer:
If \(\frac{4}{k}\) = 2, then k = 2.
(B) 2

Explanation:
If \(\frac{4}{k}\) = 2
=> 4 = 2 × k
=> 4 ÷ 2 = k
=> 2 = k.

Question 7.
The Ferris wheel costs 4 tickets for each rider. Sarah and Sadie want to ride together. Sarah has only 3 tickets left. Sadie will need to have at least how many tickets for them to ride together?
Answer:
Number of tickets Sadie will need to have for them to ride together = 5.

Explanation:
Cost of tickets the Ferris wheel costs for each rider = 4.
Number of tickets Sarah has left = 3.
Number of tickets needed for two riders = 2 × Cost of tickets the Ferris wheel costs for each rider
= 2 × 4
=8.
Number of tickets Sadie will need to have for them to ride together = Number of tickets needed for two riders – Number of tickets Sarah has left
= 8 – 3
= 5.

Question 8.
Write the total number of tickets Sarah and Sadie need in question 7 as an inequality, using x for the number of tickets Sadie will need.
Answer:
Number of tickets Sadie will need to have for them to ride together = 5.

Explanation:
Let the number of tickets Sadie will need to have for them to ride together be x.
Number of tickets needed for two riders = 8.
Number of tickets Sarah has left = 3.
Number of tickets needed for two riders – Number of tickets Sarah has left = x
= > 8 – 3 = x
=> 5 = x.