Go Math Answer Key

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Pretest existing for free of cost

Complete the following test items on pages 4-8.

Question 1.
Restate the number 4,587,902.453.
Expanded form: ________________
Written form: _________________
Answer:
Expanded form: (4 x 1,000,000) + (5 x 100,000) + (8 x 10,000) + (7 x 1,000) + (9 x 100) + (2 x 1) + (4 x 0.1) +
(5 x 0.01) + (3 x 0.001)
Written form: For million five hundred eighty seven thousand nine hundred two and four hundred and fifty three thousandths.
Explanation:
Numbers can be written in 3 ways like,
Standard form; Expanded form and Written form.
In Expanded form each number is multiplied with their place value, as shown above.
In written form each number is written in word form according to their place values.
Numbers can be written according to their place values as shown above.

Question 2.
Cheryl’s Department Store is having a sale. They have 145 coats in stock and are adding 55 more. If at the end of the sale they still have 25 coats in stock, how many coats did they sell?
Answer:
175 coats
Explanation:
Cheryl’s Department Store have 145 coats in stock and are adding 55 more.
145 + 55 = 200
If at the end of the sale they still have 25 coats in stock,
Number of coats sold = 200 – 25 = 175 coats.

Question 3.
Tracey pedals 16 miles a day on a stationary bicycle. How many miles does she pedal in the month of March? (Remember, March has 31 days.) _______
How many yards does she pedal? ___________
Answer:
496 miles;
872,960 yards.
Explanation:
Tracey pedals 16 miles a day on a stationary bicycle.
How many miles does she pedal in the month of March,
March has 31 days = 31 x 16 = 496 miles,
Number of yards she pedal,
1 mile = 1760
496 miles = 1760 x 496
= 872,960 yards.

Calculate.

Question 4.

Answer:
792
Explanation:
Multiply the entire number by ones place and then by tens place.

Question 5.

Answer:
-649
Explanation:
As we are multiplying -11 with 59,
we get the product as -649 as shown below.

Question 6.

Answer:
2812
Explanation:
Multiply the entire number by ones place and then by tens place.

Question 7.

Answer:
1917
Explanation:
Multiply the entire number by ones place and then by tens place.

Question 8.

Answer:
83
Explanation:

Question 9.

Answer:
21
Explanation:

Question 10.

Answer:
107.118
Explanation:

Question 11.

Answer:
6.2
Explanation:

Question 12.
Bailey bought 11\(\frac{1}{4}\) kilograms of bird feed. On the way home, he spilled 3\(\frac{5}{8}\) kilograms. How much bird feed does he still have left? _____________________________
Answer:
7\(\frac{5}{8}\) kilograms
Explanation:
11\(\frac{1}{4}\)– 3\(\frac{5}{8}\)
= \(\frac{(11 X 4) +1}{4}\)– \(\frac{(3 X 8)+5}{8}\)
= \(\frac{45}{4}\)– \(\frac{29}{8}\)
= \(\frac{90}{8}\)– \(\frac{29}{8}\)
= \(\frac{90 – 29}{8}\)
= \(\frac{61}{8}\)
=7\(\frac{5}{8}\) kilograms

Question 13.
Margaret mixes 1,400 centiliters of grape juice with 5\(\frac{2}{3}\) liters of seltzer and \(\frac{2}{5}\) liters of orange juice: How many liters of punch will this make?
Answer:
7\(\frac{7}{15}\) L
Explanation:
Margaret mixes 1,400 centiliters of grape juice with 5\(\frac{2}{3}\) liters of seltzer and,
\(\frac{2}{5}\) liters of orange juice,
Total liters of punch will this make,
1.4 + 5\(\frac{2}{3}\) + \(\frac{2}{5}\)
= 1.4 +\(\frac{15 + 2}{3}\)+\(\frac{2}{5}\)
= 1.4 + \(\frac{17}{3}\) + \(\frac{2}{5}\)
= \(\frac{1.4 X 15}{15}\) + \(\frac{17 X 5}{15}\)+ \(\frac{2 X 3}{15}\)
= \(\frac{21 + 85 + 6}{15}\)
= \(\frac{112}{15}\)
= 7\(\frac{7}{15}\)

Question 14.
1\(\frac{4}{15}\) + 7\(\frac{2}{5}\) + \(\frac{1}{3}\) = ___________
Answer:
9
Explanation:
1\(\frac{4}{15}\) + 7\(\frac{2}{5}\) + \(\frac{1}{3}\)
= \(\frac{(15 X 1) + 4}{15}\) + \(\frac{(7 X 5) + 2}{5}\) + \(\frac{1}{3}\)
= \(\frac{19}{15}\) + \(\frac{37}{5}\) + \(\frac{1}{3}\)
= \(\frac{19}{15}\) + \(\frac{37 X 3}{5 X 3}\) + \(\frac{1 X 5}{3 X 5}\)
= \(\frac{19}{15}\) + \(\frac{111}{15}\) + \(\frac{5}{15}\)
= \(\frac{19 + 111 + 5}{15}\)
= \(\frac{135}{15}\)
= 9

Question 15.
-9 + 10 – (-8) + 6(-2) + \(\frac{6}{-2}\) =
Answer:
-6
Explanation:
-9 + 10 – (-8) + 6(-2) + \(\frac{6}{-2}\)
= 1 + 8 – 12 + \(\frac{6}{-2}\)
= – 3 – 3
= -6

Question 16.
Solve for x: x — 9 = 18 ______________
Answer:
x = 27
Explanation:
x — 9 = 18
x = 18 + 9
x = 27

Question 17.
Solve for x: 2x + 5 < 15 _____
Answer:
x < 5
Explanation:
2x + 5 < 15
= 2x  < 15 – 5
2x <10
x < 5

Question 18.
What property is represented by the following equation?
4(5 + 6) = 4 × 5 + 4 × 6
______________
Answer:
Distributive Property of Multiplication over Addition.
Explanation:
Distributive Property of Multiplication over Addition.
a x (b x c) = a x b + a x c
4(5 + 6)
= 4 × 5 + 4 × 6
= 20 + 24
= 44

Question 19.
What property is represented by the following equation?
(3 + 6) + 6 = 3 + (6 + 6)
Answer:
Associative Property of Addition.
Explanation:
Associative Property of Addition.
(x + y) + z = x + (y + z)
(3 + 6) + 6 = 3 + (6 + 6)
15 = 15

Question 20.
|—9| + (2 + 3)² — (6 ÷ 3) + 4(8 × 3) + 4(5 — 3) = ___________
Answer:
136
Explanation:
|—9| + (2 + 3)² — (6 ÷ 3) + 4(8 × 3) + 4(5 — 3)
= 9 + 5² — 2 + 96 + 8
= 9 + 25 — 2 + 96 + 8
= 9 + 23 + 96 + 8
= 136

Question 21.
Give the coordinates for the points.
A ___________
B ___________
C ___________
D __________

Answer:
A(2,3); B(-3,5); C(1,-5); D(-3,-3)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical lines.

Question 22.
Restate in exponent form, then solve:
4 × 4 × 4 + 2 × 2 =
_________________
Answer:
= 68
Explanation:
= 4 × 4 × 4 + 2 × 2
= 4³ + 2²  
= 68

Question 23.
What is the area of the rectangle?
__________________

What is the perimeter of the rectangle?
______________
Answer:
Area = 120 sq cm;
Perimeter = 44 cm.
Explanation:
Area of a rectangle = length x width
A = l x w
A = 12 x 10
A = 120 sq cm
Perimeter of  a rectangle P = 2(length + width)
P = 2(L+W)
P = 2(12 + 10)
P = 44 cm

Question 24.
What is the area of the circle? (Use 3.14 for π.)
______________

What is the circumference of the circle?
_______________
Answer:
Area = 19.625 sq cm;
Circumference = 15.75 cm.
Explanation:
Area of circle A = π.r²
A = 3.14 x 2.5²
A = 19.625 sq cm
Circumference = 2 πr
= 2 x 3.14 x 2.5
= 15.75 cm.

Question 25.
Identify the following angles as obtuse, acute, or right.



Answer:



Explanation:
Any angle that is greater than 90° but less than 180° is known as obtuse angle.
If the angle formed between two rays is exactly 90° then it is called a right angle.
If two rays intersect at a vertex, forming an angle that is less than 90° is known as acute.

Question 26.
Identify the triangles as scalene, isosceles, or equilateral.

_______

_____

__________
Answer:



Explanation:
All angles of a scalene triangle are unequal, all are of different size.
An equilateral triangle is a triangle with all three sides of equal length.
An isosceles triangle is a triangle with two equal sides.

Question 27.
Ramon spends $28.94 a month having pictures developed. He is working on a project that will take 19 months to finish. How much should he plan to spend on developing pictures for the project?
Answer:
$549.86
Explanation:
Ramon spends $28.94 a month having pictures developed.
He is working on a project that will take 19 months to finish.
Total amount he plan to spend on developing pictures for the project,
$28.94 a month x 19 months
28.94 x 19 = 549.86

Question 28.
Restate 3.6 as an improper fraction and a mixed number. ____________
Answer:
3\(\frac{3}{5}\) or \(\frac{18}{5}\)
Explanation:
3\(\frac{3}{5}\) or \(\frac{18}{5}\)
= \(\frac{15 + 3}{5}\)
= \(\frac{18}{5}\)

Question 29.
Restate 4\(\frac{5}{8}\) as a decimal. __________________ ________________
Answer:
4.625
Explanation:
4\(\frac{5}{8}\)
= \(\frac{(4 X 8) +5}{8}\)
= \(\frac{37}{8}\)
= 4.625

Question 30.
Is the following true or false? \(\frac{5}{16}\) = \(\frac{60}{192}\) _______ _______________
Answer:
True
Explanation:
\(\frac{5}{16}\) = \(\frac{60}{192}\)
\(\frac{5 X 12}{16 X 12}\) = \(\frac{60}{192}\)
Thus, equation is TRUE.

Question 31.
\(\sqrt{73}\) is between ____________ and _______________
Answer:
8 and 9
Explanation:
Given, \(\sqrt{73}\)
\( sqrt {64} \) = 8
\( sqrt {81} \) = 9
\( sqrt {73} \) lies between 8 and 9

Question 32.
Drayson deposits $125 in a bank account that earns 4% simple interest. How much money will he have in the account after 1 year? ______
After 2 years ? _____
Answer:
$130 after 1year,
$135.20 after 2 years.
Explanation:
SI = (PTR)/100
SI = 125 x 4 x 1 / 100
SI = 5
Amount after 1 year = 125 + 5 = $130
SI = (PTR)/100
SI = 130 x 4 x 1 / 100
SI = 5.2
Amount after 1 year = 130 + 5.2 = $135.2

Question 33.
What is the mode of the data distribution?

What is the median?
___________
Answer:
Mode = 38
Median = 38
Explanation:
values with respect to the stem leaf data plot is,
{13, 15, 23, 26, 29, 33, 38, 38, 38, 44, 44, 45, 46, 46, 43, 54, 56}
Median is the mid point in the given data.
Mode : frequently occurring or observed value

Question 34.
\(\frac{4}{7}\) × 5\(\frac{4}{9}\) = ______
Answer:
3\(\frac{1}{9}\)
Explanation:
\(\frac{4}{7}\) × 5\(\frac{4}{9}\)
= \(\frac{4}{7}\) × 5\(\frac{9 x 5 + 4}{9}\)
= \(\frac{4}{7}\) × \(\frac{45}{9}\)
= \(\frac{4 X 45}{63}\)
= \(\frac{180}{63}\)
= 3\(\frac{1}{9}\)

Question 35.
What is \(\frac{3}{8}\) of 88%?
Answer:
33%
Explanation:
\(\frac{3}{8}\) of 88%
= \(\frac{3}{8}\) x 88%
= 3 x 11%
= 33%

Question 36.
What is 30% of .675? _______________
Answer:
0.2025
Explanation:
30% x 0.675
(30 x 0.675)/100 = 0.2025

Question 37.

Answer:
1.5667
Explanation:
0.15 x 100 = 15
0.235 x 100 = 23.5

0.235 / 0.15 = 1.5667

Question 38.
latex]\frac{4}{3}[/latex] + latex]\frac{2}{3}[/latex] + latex]\frac{5}{3}[/latex] – latex]\frac{1}{3}[/latex] – latex]\frac{7}{3}[/latex] = _____
Answer:
1
Explanation:
latex]\frac{4}{3}[/latex] + latex]\frac{2}{3}[/latex] + latex]\frac{5}{3}[/latex] – latex]\frac{1}{3}[/latex] – latex]\frac{7}{3}[/latex]
= latex]\frac{4 + 2 + 5 – 1 – 7}{3}[/latex]
= latex]\frac{11 – 8}{3}[/latex]
= latex]\frac{3}{3}[/latex]
=1

Question 39.
Identify each quadrilateral as a square, rectangle, kite, rhombus, or trapezoid.

_____

_____

_____

_____

_____
Answer:





Explanation:
A trapezoid is a flat closed shape having 4 straight sides,
with one pair of parallel sides.
A square is closed, two-dimensional shape with 4 equal sides.
Rhombus is a quadrilateral with all equal sides.
Since opposite sides of a parallelogram are equal.
So, Rhombus is a special type of a parallelogram whose all sides are equal.
A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees.
The two sides at each corner or vertex meet at the right angles.
The opposite sides of the rectangle are equal in length which makes it different from a square.
A Kite is a flat shape with 4 straight sides that has two pairs of sides,
which are two adjacent sides that are equal in length.

Question 40.
Identify the following figures.

_____

_____

_____
Answer:



Explanation:
Hexa means six and gona means angles.
A hexagon is a closed two-dimensional polygon with six sides.
Hexagon has 6 vertices and 6 angles.
Penta denotes five and gon denotes angle.
A pentagon is a simple polygon, which has five sides and five angles.
Hepta means seven and gon means sides.
A Heptagon is a polygon with seven sides and seven angles.
It has seven straight sides and seven corners or vertices.

Question 41.
Restate 5\(\frac{6}{13}\) as an improper fraction.
Answer:
\(\frac{71}{13}\)
Explanation:
5\(\frac{6}{13}\)
= 5\(\frac{(5 X 13) + 6}{13}\)
= \(\frac{65 + 6}{13}\)
= \(\frac{71}{13}\)

Question 42.
Restate \(\frac{43}{16}\) as a mixed number.
Answer:
2\(\frac{11}{16}\)
Explanation:
\(\frac{43}{16}\)

2\(\frac{11}{16}\)

Question 43.
What are the chances of choosing a black marker out of a bag containing 3 red markers, 5 blue markers, 3 yellow markers, and 4 black markers? What is the probability of choosing two black markers if the first marker is put back before the second is drawn?
Answer:
\(\frac{4}{15}\); \(\frac{16}{225}\)
Explanation :
Total number of markers = 3 + 5 + 3 + 4 = 15
Probability of choosing black markers
Number of black markers = 4
Probability = black markers ÷ total no of markers
4 ÷ 15 = \(\frac{4}{15}\)
Probability of choosing a black markers again
Number of black markers = 4
remaining number of marbles after choosing a black markers = 4 – 1 + 1 = 4
[the black marker is put back ]
Probability of choosing black markers= black markers ÷ total markers x remaining markers
= 4 ÷ 15 x 15
= \(\frac{4}{225}\)

Question 44.
According to the graph, how many videos did Jamie watch in July?

Answer:
15
Explanation:
According to the graph of Jamie’s Summer Video List
he watched 15 videos July.

Question 45.
During which week did Kelly and Heather swim the same distance?

Answer:
Week 2
Explanation:
According to the graph of Kelly and Heather’s Workout Schedule,
second week they swim the same distance.

Question 46.
What fruit is most preferred by the students?

Answer:
Apples
Explanation:
From the above pie chart of Favorite Fruits,
most preferred fruit by the students are Apples.

Question 47.
Peggy’s score was about 30 pins higher than whose score?

Answer:
Kathy
Explanation:
From the above chart of Bowling Scores,
Peggy’s score was about 30 pins higher than Kathy score.

Question 48.
What is the range of the data in the box-and-whisker plot below?
What is the average (mean) of the data points shown?
________________

Answer:
15; 11.9; 4.12
Explanation:
The range of the data in the box-and-whisker plot is,
R = max – min
R = 20 – 5 = 15
mean average = sum of event / total number of events.
mean average = 5 + 8.5 + 12 + 14 + 20 / 5
mean average = 59.5/5 = 11.9
11.9 – 5 = 6.9
11.9 – 8.5 = 3.4
12 – 11.9 = 0.1
14 – 11.9 = 2.1
20. – 11.9 = 8.1
6.9 + 3.4 + 0.1 + 2.1 + 8.1 = 20.6
average mean = 20.6/5 = 4.12

Question 49.
How much plastic wrap would you need to cover this rectangular solid?

Answer:
94 sq in.
Explanation:
TSA – Total Surface Area to be calculated
the surface area of a cuboid, add the areas of all 6 faces.
We can also label the length (l), width (w), and height (h) of the prism and use the formula,
SA=2lw+2lh+2hw, to find the surface area
TSA = 2(4 x 5 + 5 x 3 + 3 x 4)
TSA = 2(20 + 15 + 12)
TSA = 2 x 47
TSA = 94 sq in

Question 50.
Name two line segments. _____________
Name four rays. ________
Name a line. _________________

Answer:
Line segments:\(\overline{BD}\), \(\overline{DB}\), \(\overline{CA}\), \(\overline{AC}\),\(\overline{HG}\), \(\overline{GH}\), \(\overline{BE}\), \(\overline{EB}\),\(\overline{AB}\), \(\overline{AF}\), \(\overline{FA}\);
Rays: \(\overline{AC}\), \(\overline{BD}\), \(\overline{BE}\),
\(\overline{AF}\), \(\overline{BA}\), \(\overline{AB}\);
Line: \(\overline{AB}\)
Explanation:
A line segment is part of a line that has two endpoints and is finite in length.
A ray is a line segment that extends indefinitely in one direction.
A line has no end points.

Question 51.
Fill in a Venn Diagram that displays the following data: There are two groups of students, 30 who take the bus to school and 25 who have a younger sibling in the school. There are 10 students who take the bus and who also have a younger sibling in the school.

Answer:

Explanation:
There are two groups of students,
30 who take the bus to school and,
25 who have a younger sibling in the school.
There are 10 students who take the bus and who also have a younger sibling in the school.
who take bus to school 30 – 10 = 20,
who have younger siblings 25 – 10 = 15.

Question 52.
Are the rates in the table below proportional?

Answer:
No,
Explanation:
Car A is going 45 miles per hour and Car b is going 48 miles per hour.
So, they are not proportional to each other.

Question 53.
What is the unit rate for the price of grapes as shown on the graph below?

Answer:
1.50
Explanation :
By observing the graph we can conclude that,
for 6 dollars we get 9 pounds of grapes.
for 1 dollar we get,
9 ÷ 6 = 1.50 pounds of grapes
Hence, 1.5 is the unit rate for the price of grapes.

Question 54.
What is the best way to get a representative sample of the people at a baseball game for a survey about parking at the stadium?
(a) Choose one of the luxury boxes at random and survey all the people in that box.
(b) Survey the first 50 people to walk into the stadium.
(c) Choose 50 seat numbers at random and survey the people in those seats.
Answer:
Option(C)
Explanation :
A representative survey must be done at random.
If we choose to survey the people in luxury boxes,
we can not get a perfect result as they might get a better parking space.
If we choose to survey the first 50 people that walk in,
we can’t get a perfect result,
as the first 50 people are likely to find more empty spots that the people that come in later.

Question No 55.
Complete the probability table below.

Answer:

Explanation:
By looking at the A probability we can say that
Number of wins = 23
Total matches = 90
Line-wise By looking at the C probability we can say that,
probability of a match being a draw = \(\frac{53}{90}\) = 0.59
Number of draws = 53
Therefore number of loses = 90 – 23 + 53
= 13
Probability of losing a match = 13 ÷ 90
= \(\frac{13}{90}\)
= 0.16

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Posttest existing for free of cost.

McGraw-Hill Math Grade 7 Posttest Answer Key

Complete the following test items on pages 156-160.

Question 1.
Restate the number 5,176,802.4539.
Expanded form: ____________________
Written form: ____________________
Answer:
Expanded form:
(5 x 1,000,000) +(1 x 100,000) + (7 x 10,000) + (6 x 1,000) + (5 x 0.01) + (3 x 0.001) + (9 x 0.0001)
Written form :
Five million one hundred seventy-six thousand eight hundred two and four thousand five hundred thirty-nine ten thousandths.
Explanation:
In Expanded form each number is multiplied with their place value, as shown above.
In written form each number is written in word form according to their place values.

Question 2.
Brian’s Bakery is having a sale on cakes. They have 95 cakes and will be baking 23 more before the start of the sale. If at the end of the sale they still have 7 cakes, how many cakes did they sell?
Answer:
111 cakes
Explanation:
Initially they have 95 cakes,
By adding 23 more before the start of the sale ,
the number of cakes are 95 + 23 = 118
They left with 7 cakes at the end of the sale,

Question 3.
Stuart pedals 19 miles a day on his bicycle. How many miles does he pedal in the month of February? (Remember, February has 28 days.)
Answer:
532 miles
Explanation:
pedals 19 miles a day on his bicycle,
He pedal in the month of February which has 28 days.
By multiplying 19 x 28, we get the total number of miles he pedaled in the month of February.

Question 4.

Answer:
-2010
Explanation:

As we are multiplying 134 with -15 which is negative number,
we get the product as -2010 as shown below.

Question 5.

Answer:
5320
Explanation:
As we are multiplying 133 with 40, the product is 5320

Question 6.

Answer:
22032
Explanation:
As we are multiplying -432 with -51, the product is 22032.
Both of the given numbers are negative integers,
So, we get product as positive after multiplication.

Question 7.

Answer:
17617
Explanation:
As we are multiplying 223 with 79, the product is 17,617.

Question 8.

Answer:
28
Explanation:

Question 9.

Answer:
-21
Explanation:
As divisor is negative number, the answer is also with negative sign.

Question 10.

Answer:
19.4166
Explanation:

Question 11.

Answer:
24
Explanation:

Question 12.
Danetta bought 19 \(\frac{3}{8}\) kilograms of gerbil food. On the way home, she spilled 3 \(\frac{4}{5}\) kilograms. How much gerbil food does she still have?
Answer:
15 \(\frac{23}{40}\) kilograms of gerbil food.
Explanation:
19 \(\frac{3}{8}\) – 3\(\frac{4}{5}\)
= \(\frac{155}{8}\) – \(\frac{19}{5}\)
= \(\frac{155 X 5}{8 X 5}\) – \(\frac{19 X 8}{5 X 8}\)
= \(\frac{155 X 5}{8 X 5}\) – \(\frac{19 X 8}{5 X 8}\)
= \(\frac{775 – 152}{40}\)
= \(\frac{623}{40}\)
= 15 \(\frac{23}{40}\)

Question 13.
To make his favorite fruit punch, Ezekiel mixes 1,950 centiliters of juice with 1 \(\frac{4}{9}\) liters of seltzer and \(\frac{3}{8}\) liters of orange juice. How many liters of punch will this make?
Answer:
21 \(\frac{23}{72}\) L
Explanation:
19.50 + 1 \(\frac{4}{9}\) + \(\frac{3}{8}\)
= 19.50 + \(\frac{13}{9}\) + \(\frac{3}{8}\)
= \(\frac{19.50 X 72}{72}\) + \(\frac{13 X 8}{9 X 8}\) + \(\frac{3 X 9}{8 X 9}\)
= \(\frac{1404}{72}\) + \(\frac{104}{72}\) + \(\frac{27}{72}\)
= \(\frac{1404 + 104 + 27}{72}\)
= \(\frac{2714}{72}\)
= \(\frac{1535}{72}\)
= 21 \(\frac{23}{72}\)

Question 14.
3 \(\frac{7}{12}\) + 5 \(\frac{1}{5}\) + \(\frac{1}{4}\) = _____________
Answer:
9 \(\frac{1}{30}\)
Explanation:
3 \(\frac{7}{12}\) + 5 \(\frac{1}{5}\) + \(\frac{1}{4}\)
= \(\frac{43}{12}\) + \(\frac{26}{5}\) + \(\frac{1}{4}\)
= \(\frac{43 x 5}{12 X 5}\) + \(\frac{26 X 12}{5 X 12}\) + \(\frac{1 X 15}{4 X 15}\)
= \(\frac{215}{60}\) + \(\frac{312}{60}\) + \(\frac{15}{60}\)
= \(\frac{216 + 312 + 15}{60}\)
= \(\frac{542}{60}\)
=9 \(\frac{2}{60}\)
=9 \(\frac{1}{30}\)

Question 15.
-5 + |-17| – (-6) + 7(-5) – \(\frac{9}{3}\) = _____________
Answer:
-20
Explanation:
-5 + |-17| – (-6) + 7(-5) – \(\frac{9}{3}\)
= -5 + 17 + 6 + 7(-5) – \(\frac{9}{3}\)
= -5 + 17 + 6 – 35 – \(\frac{9}{3}\)
= 23 – 40 –\(\frac{9}{3}\)
= -17 –\(\frac{9}{3}\)
= -17 x 3 –\(\frac{9}{3}\)
= –\(\frac{51}{3}\) – \(\frac{9}{3}\)
=- \(\frac{51 + 9}{3}\)
= –\(\frac{60}{3}\)
= -20

Question 16.
Solve for x: x – 91 ≥ 13 ___________
Answer:
x ≥ 104
Explanation:
x – 91 ≥ 13
x  ≥ 13 + 91
x  ≥ 104

Question 17.
Solve for x: 4x + 11 = 15 _____________
Answer:
x = 1
Explanation:
4x + 11 = 15
4x = 15 – 11
4x = 4
x = 4/4
x = 1

Question 18.
What property is represented by the following equation?
2(6 + 9) = 2 × 6 + 2 × 9
Answer:
Distributive property of Multiplication over Addition.
Explanation:
a x (b + c) = a x b + a x c
let a = 2, b =6 and c = 9
2(6 + 9) = 2 × 6 + 2 × 9

Question 19.
What property is represented by the following equation?
(4 + 8) + 8 = 4 + (8 + 8)
Answer:
Associative property of Addition
Explanation:
a+ (b + c) = (a + b) + c
let a=4, b=8 c = 8
(4 + 8) + 8 = 4 + (8 + 8)

Question 20.
|-7| + (1 + 3)² – (9 ÷ 3) + 5(8 × 3) + 2(10 – 7) = ______________
Answer:
146
Explanation:
|-7| + (1 + 3)² – (9 ÷ 3) + 5(8 × 3) + 2(10 – 7)
7 + 16 – 3 + 5(24) + 2(3)
= 7 + 13 + 120 + 6
= 20 + 120 + 6
= 146

Question 21.
Give the coordinates for the points.

A _________________
B _________________
C _________________
D _________________
Answer:
A(3,6);
B(-5,2);
C(2,-4);
D(-1,1)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical lines.

Question 22.
Restate in exponent form, then solve:
5 × 5 × 5 + 3 × 3 = _______________
Answer:
134
Explanation:
5 × 5 × 5 + 3 × 3
= 5³ + 3²
= 5³ + 3²
= 125 + 9
= 134

Question 23.
What is the area of the rectangle?

What is the perimeter of the rectangle?
Answer:
Area = 306 sq cm;
Perimeter = 70 cm
Explanation:
The area of the rectangle,
A = length x width
A = 18 x 17 = 306 cm²
the perimeter of the rectangle
P = 2(Length + Width)
P = 2(17 + 18)
= 2 x 35
= 70 cm

Question 24.
What is the area of the circle? (Use 3.14 for π)

What is the circumference of the circle?
Answer:
Area = 63.585 sq cm;
Circumference = 28.26 cm
Explanation:
The area of the circle (Use 3.14 for π)
A = π r²
r = 4.5 cm
A = 3.14 x 4.5 x 4.5
A = 63.585 sq cm
the circumference of the circle,
C = 2πr
C = 2 x 3.14 x 4.5
C = 28.26 cm

Question 25.
Identify the following angles as obtuse, acute, or right.

Answer:
Obtuse Angle; Right Angle; Acute Angle.

Explanation:
Any angle that is greater than 90° but less than 180° is known as obtuse angle.
If the angle formed between two rays is exactly 90° then it is called a right angle.
If two rays intersect at a vertex, forming an angle that is less than 90° is known as acute.

Question 26.
Identify the triangles as scalene, isosceles, or equilateral.

Answer:
Equilateral; Scalene; Isosceles Triangles.

Explanation:
An equilateral triangle is a triangle with all three sides of equal length.
All angles of a scalene triangle are unequal, all are of different size.
An isosceles triangle is a triangle with two equal sides.

Question 27.
Jackie spends $37.95 a month on art supplies. She is working on a project that will take 19 months to finish. How much should she plan to spend on art supplies for the project?
Answer:
$721.05
Explanation:
Jackie spends $37.95 a month on art supplies.
She is working on a project that will take 19 months to finish.
Total amount she plan to spend on art supplies for the project,
$37.95 x 19 = $721.05

Question 28.
Restate 7.6 as an improper fraction and a mixed number.
Answer:
\(\frac{38}{5}\) or 7 \(\frac{3}{5}\)
Explanation:
\(\frac{76}{10}\)
=\(\frac{38}{5}\)
=7\(\frac{3}{5}\)

Question 29.
\(\sqrt{21}\) is between ___________ and _____________.
Answer:
4 and 5
Explanation:
as we know values of
square of 4 is 16 :: sqrt 16 = 4
square of 5 is 25 :: sqrt 25 = 5
sqrt 21 lies between 4 and 5
sqrt 16 < sqrt 21 < sqrt 25

Question 30.
Is the following true or false? \(\frac{4}{11}\) = \(\frac{68}{187}\) _________________
Answer:
True
Explanation:
\(\frac{4}{11}\) = \(\frac{68}{187}\)
\(\frac{4 X 17}{11 X 17}\) = \(\frac{68}{187}\)

Question 31.
Put the following numbers in order from least to greatest:
1.141, 1.014, 1.044, 1.004, 1.9, 1.996, 1.89, .9 ______________
Answer:
0.9; 1.004, 1.014; 1.044; 1.141; 1.89; 1.9; 1.996
Explanation:
Arrange all the given numbers in ascending order by placing whole numbers first,
then decimals number with the least digit according to their place values.

Question 32.
Juliette deposits $295 in a bank account that earns 6% simple interest. How much money will she have in the account after 1 year?
______________ After 2 years? ________________
Answer:
$312.70; $330.40
Explanation:
Juliette deposits $295 in a bank account that earns 6% simple interest
SI = PRT/100
SI = (295 x 6 x 1)/100
SI = $17.7
Amount = $ 295 +$ 17.7 = $ 312.70 after one year
Amount = $ 312.70 + $ 17.7 = $ 330.40 after two years

Question 33.
What is the mode of the data distribution?

What is the median?
Answer:
Mode = 36
Median = 36
Explanation:
The mode is the number or numbers that occur the most frequently.
Given numbers [14, 16, 22, 25, 27, 31, 36, 36, 36, 43, 43, 45, 47, 47, 52, 55, 56]
Put the numbers in numerical order from smallest to largest.
Mode = 36
 First, arrange the given data in ascending order.
Median = Given data [14, 16, 22, 25, 27, 31, 36, 36, 36, 43, 43, 45, 47, 47, 52, 55, 56]
Next, we need to pick the middlemost data.
For the odd number of data points, there is only one middle data point,
we can take it as the median of the data as 36

Question 34.
\(\frac{2}{7}\) × 2 \(\frac{5}{22}\) = _____________
Answer:
\(\frac{7}{11}\)
Explanation:
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
\(\frac{2}{7}\) × 2\(\frac{5}{22}\)
= \(\frac{2}{7}\) × \(\frac{220}{22}\)
= \(\frac{2 X 220}{7 X 22}\)
= \(\frac{440}{154}\)
= \(\frac{2}{11}\)
= 4\(\frac{2}{3}\)

Question 35.
What is \(\frac{5}{8}\) of 75%? _____________
Answer:
46.875%
Explanation:
\(\frac{5}{8}\) of 75%
\(\frac{5 X 75}{8}\) %
46.875 %

Question 36.
What is 25% of .525?
Answer:
0.13125
Explanation:
25% of .525
\(\frac{25}{100}\) x 0.525
= \(\frac{25 X 0.525}{100}\)
= \(\frac{13.125}{100}\)
= 0.13125

Question 37.

Answer:
2350
Explanation:
While dividing the divisor with the decimal dividend,
multiply the divisor and divided with 100.

Question 38.
\(\frac{5}{4}\) + \(\frac{7}{4}\) + \(\frac{15}{4}\) – \(\frac{9}{4}\) – \(\frac{17}{4}\) = ____________
Answer:
\(\frac{1}{4}\)
Explanation:
\(\frac{5}{4}\) + \(\frac{7}{4}\) + \(\frac{15}{4}\) – \(\frac{9}{4}\) – \(\frac{17}{4}\) =
= \(\frac{5 + 7 + 15 – 9 – 17}{4}\)
= \(\frac{27 – 26}{4}\)
= \(\frac{1}{4}\)

Question 39.
Identify each quadrilateral as a square, rectangle, kite, rhombus, or trapezoid.

Answer:
Trapezoid; Square; Rhombus; Rectangle and Kite.

Explanation:
A trapezoid is a flat closed shape having 4 straight sides,
with one pair of parallel sides.
A square is closed, two-dimensional shape with 4 equal sides.
Rhombus is a quadrilateral with all equal sides.
Since opposite sides of a parallelogram are equal.
So, Rhombus is a special type of a parallelogram whose all sides are equal.
A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees.
The two sides at each corner or vertex meet at the right angles.
The opposite sides of the rectangle are equal in length which makes it different from a square.
A kite is a flat shape with 4 straight sides that has two pairs of sides,
which are two adjacent sides that are equal in length.

Question 40.
Identify the following figures.

Answer:
Hexagon; Pentagon; Heptagon.

Explanation:
Hexa means six and gona means angles.
A hexagon is a closed two-dimensional polygon with six sides.
Hexagon has 6 vertices and 6 angles.
Penta denotes five and gon denotes angle.
A pentagon is a simple polygon, which has five sides and five angles.
Hepta means seven and gon means sides.
A Heptagon is a polygon with seven sides and seven angles.
It has seven straight sides and seven corners or vertices.

Question 41.
Restate 9 \(\frac{11}{13}\) as an improper fraction.
Answer:
\(\frac{128}{13}\)
Explanation:
9 \(\frac{11}{13}\)
= \(\frac{9 x 13 + 11}{13}\)
=  \(\frac{117 + 11}{13}\)
=  \(\frac{128}{13}\)

Question 42.
Restate \(\frac{72}{13}\) as a mixed number.
Answer:
5\(\frac{7}{13}\)
Explanation:
=  \(\frac{72}{13}\)
= \(\frac{5 x 13 + 7}{13}\)
=  \(\frac{72}{13}\)

Question 43.
What are the chances of choosing a blue marble out of a bag containing 7 red marbles, 6 green marbles, 11 yellow marbles, and 4 blue marbles?
What is the probability of choosing a blue marble, not replacing it, and then choosing a green marble?
Answer:
\(\frac{1}{7}\) and \(\frac{6}{189}\)
Explanation:
Total number of marbles = 7 + 6 + 11 + 4 = 28
Probability of choosing blue marbles
Number of blue marbles = 4
Probability = marbles ÷ total no of marbles
4 ÷ 28 = \(\frac{1}{7}\)
Probability of choosing a green marble
Number of green marbles = 6
remaining number of marbles after choosing a blue marble = 28 – 1 = 27
Probability of choosing green marbles = marbles ÷ total marbles x remaining marbles
= 6 ÷ 27 x 28
= \(\frac{6}{189}\)

Question 44.
According to the graph, how many miles did Janice swim in September?

Answer:
10 miles
Explanation:
From the above graph of Janice’s Swimming Chart,
he swims 10 miles in september.

Question 45.
During which week did Brian and Ray run the same distance?

Answer:
week 2
Explanation:
From the given chart of Brain nd Ray’s Running Schedule,
they both run same distance in second week.

Question 46.
Which vegetable is most preferred by the students?

Answer:
Cauliflower
Explanation:
From the above pie chart of Favorite vegetables Of The Students,
Cauliflower is preferred by many of the students.

Question 47.
Dean’s score was about 20 points higher than whose score?

Answer:
Joe’s
Explanation:
From the above Dart Scores,
Dean scored the highest and also 20 points more than Joe.

Question 48.
What is the range of the data in the box-and-whisker plot below?

What is the average (mean) of the data points shown? ____________
What is the mean absolute deviation of the data points shown? ___________
Answer:
15; 12.4; 4.72
Explanation:
Range of the data is the difference between max – min
Range = 20 – 5 = 15
mean = \(\frac{5 + 8 + 13 + 16 + 20}{5}\)
mean =\(\frac{62}{5}\)
mean  =12.4
the mean absolute deviation of the data points
I 12.4 – 5 I = 7.4
I 12.4 – 8 I = 4.4
I 12.4 – 13 I = 0.6
I 12.4 – 16 I = 3.6
I 12.4 – 20 I = 7.6
mean absolute deviation( MAD )= \(\frac{7.4 + 4.4 + 0.6 + 3.6 + 7.6}{5}\)
MAD=\(\frac{23.6}{5}\)
MAD  = 4.72

Question 49.
How much plastic wrap would you need to cover this rectangular solid?

Answer:
318 sq in.
Explanation:
TSA – Total Surface Area to be calculated
the surface area of a cuboid, add the areas of all 6 faces.
We can also label the length (l), width (w), and height (h) of the prism and use the formula,
SA=2lw+2lh+2hw, to find the surface area
TSA = 2(7 x 6 + 6 x 9 + 9 x 7)
TSA = 2(42 + 54 + 63)
TSA = 2 x 159
TSA = 318 sq in

Question 50.
Name two line segments.

Name 4 rays. _______________
Name a line. ___________
Answer:
Line segments:
\(\overline{YS}\), \(\overline{XT}\), \(\overline{XR}\), \(\overline{YZ}\),\(\overline{LM}\), \(\overline{ML}\), \(\overline{XY}\), \(\overline{TX}\),\(\overline{RX}\), \(\overline{SY}\), \(\overline{ZY}\);
Rays:
\(\overline{XR}\), \(\overline{XT}\), \(\overline{YS}\), \(\overline{YZ}\),
\(\overline{XY}\), \(\overline{YX}\);
Line:
\(\overline{XY}\)
Explanation:
A line segment is part of a line that has two endpoints and is finite in length.
A ray is a line segment that extends indefinitely in one direction.
A line has no end points.

Question 51.
Fill in a Venn Diagram that displays the following data:

There are two groups of students, 25 who are in the drama club and 15 who enjoy math. There are 8 students who are in the drama club who also enjoy math.
Answer:

Explanation:
There are two groups of students,
25 who are in the drama club and 15 who enjoy math.
There are 8 students who are in the drama club who also enjoy math.
Number of students in Drama Club = 25 – 8 = 17
Number of students enjoy Math = 15 – 8 = 7

Question 52.
Are the rates in the table below proportional?

Answer:
Yes, Both are $2.50 per pound.
Explanation:
Lets write them in the form of ratio
$5.00 : 2 pounds
$1.25 : 0.5 pounds
according to proportion,
product of means = product of extremes
5 : 2 = 1.25 : 0.5
product of means :
= 2 x 1.25 = 2.5
product of extremes :
= 2 x 0.5 = 2.5
product of means = product of extremes = 2.5
Hence ; both of them are proportioanal

Question 53.
What is the unit rate for the speed of the car shown on the graph below?

Answer:
\(\frac{1}{2}\)
Explanation :
By observing the graph we can see that
it took 6 seconds to travel 4 miles
that means the distance traveled in 1 second = \(\frac{1}{2}\)

Question 54.
Ebony asked four of her female friends if they liked wearing sandals better than wearing boots. All four said yes. Ebony concluded that none of the girls her age like boots. Is her conclusion valid? Did she use a representative sample for her survey?
Answer:
No
Explanation:
The Conclusion is based on too small a sample,
A representative sample is a sample from a larger group,
that accurately represents the characteristics of a larger population.
It’s known as a representative sample because the answers obtained from it,
accurately reflect the results you would achieve by interviewing the entire population.
The sample is not representative since she only asked her friends.

Question 55.
Create a probability table for choosing a marble out of a bag of 14 white, 18 black, and 6 red marbles.

Answer:

Explanation:
Total number of marbles = 14+ 18 + 6 = 38
Probability of choosing white marble,
number of white marbles = 14
probability = no of marbles ÷ total number of marbles
= 14 ÷ 38
= \(\frac{14}{38}\)
= 0.37
Probability of choosing black marble,
number of black marbles = 18
probability = no of marbles ÷ total number of marbles
= 18 ÷ 38
= \(\frac{18}{38}\)
= 0.47
Probability of choosing red marble,
number of red marbles = 6
probability = no of marbles ÷ total number of marbles
= 6 ÷ 38
= \(\frac{6}{38}\)
= 0.16

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 9.4 Comparing and Ordering Decimals existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 9.4 Comparing and Ordering Decimals

Exercises Compare

Each problem will have three numbers: a lowest, middle, and largest number.
You will be told which of the three to select: lowest, middle or largest.

Question 1.
4, 5, and 10 Lowest
_______________
Answer:
4
Explanation:
Line up the given numbers according to their place values.
Each digit is one place value higher than the digit to its right.
4, 5 and 10 Lowest,
4 is the lowest number in the given numbers above.

Question 2.
10.01, 10.10, and 10.11 Middle
____________
Answer:
10.10
Explanation:
Line up the given numbers according to their place values.
Each digit is one place value higher than the digit to its right.
10.01, 10.10 and 10.11 Middle,
10.10 is middle among the numbers given above.

Question 3.
.567, .5677, and .56 Largest
____________
Answer:
0.5677
Explanation:
Line up the given numbers according to their place values.
Each digit is one place value higher than the digit to its right.
0.56, 0.567 and 0.5677 Largest,
0.5677 is the largest among the numbers given above.

Question 4.
45.45, 45.449, and 45.4449 Middle
____________
Answer:
45.449
Explanation:
Line up the given numbers according to their place values.
Each digit is one place value higher than the digit to its right.
45.4449, 45.449, and 45.45 Middle,
45.449 is the middle among the numbers given above.

Question 5.
14.125, 14.0126, and 14.00126 Lowest
Answer:
14.00126
Explanation:
Line up the given numbers according to their place values.
Each digit is one place value higher than the digit to its right.
14.00126, 14.0126 and 14.125 Lowest,
14.00126 is the lowest among the numbers given above.

Question 6.
21.21, 21.211, and 21.2121 Lowest
Answer:
21.21
Explanation:
Line up the given numbers according to their place values.
Each digit is one place value higher than the digit to its right.
21.21, 21.211 and 21.2121 Lowest,
21.21 is the lowest among the numbers given above.

Question 7.
11.1, 11.11, and 11.111 Largest
Answer:
11.111
Explanation:
Line up the given numbers according to their place values.
Each digit is one place value higher than the digit to its right.
11.1, 11.11 and 11.111 largest,
11.111 is the largest among the numbers given above.

Question 8.
12.12, 12.102, and 12.1023 Middle
Answer:
12.1023
Explanation:
Line up the given numbers according to their place values.
Each digit is one place value higher than the digit to its right.
12.102, 12.1023 and 12.12 Middle,
12.1023 is the middle among the numbers given above.

Question 9.
166.66, 166.60, and 166.6607 Middle
Answer:
166.66
Explanation:
Line up the given numbers according to their place values.
Each digit is one place value higher than the digit to its right.
166.60, 166.66 and 166.6607 Middle,
166.66 is the middle among the numbers given above.

Question 10.
144.32, 14.432, and 1.4432 Largest
Answer:
144.32
Explanation:
Line up the given numbers according to their place values.
Each digit is one place value higher than the digit to its right.
1.4432, 14.432 and 144.32 Largest,
144.32 is the largest among the numbers given above.

Question 11.
25.025, 25.205, and 25.502 Middle
Answer:
25.205
Explanation:
Line up the given numbers according to their place values.
Each digit is one place value higher than the digit to its right.
25.025, 25.205, and 25.502 Middle,
25.205 is the middle among the numbers given above.

Question 12.
156.12, 157.01, and 158.32 Lowest
Answer:
156.12
Explanation:
Line up the given numbers according to their place values.
Each digit is one place value higher than the digit to its right.
156.12, 157.01, and 158.32 Lowest,
156.12 is the lowest among the numbers given above.

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 9.3 Changing Decimals to Fractions existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 9.3 Changing Decimals to Fractions

Exercises Change Decimals To Fractions

Question 1.
.85
Answer:
\(\frac{17}{20}\)
Explanation:
Given, .85
\(\frac{85}{100}\)
dividing both the numerator and denominator with 5
17 x 5 = 85
20 x 5 = 100
\(\frac{17}{20}\)

Question 2.
.77
Answer:
\(\frac{77}{100}\)
Explanation:
Given, 0.77
multiplying both the numerator and denominator with 100
\(\frac{77}{100}\)

Question 3.
.888
Answer:
\(\frac{111}{125}\)
Explanation:
Given, 0.888
\(\frac{888}{1000}\)
dividing both the numerator and denominator with 8
111 x 8 = 888
125 x 8 = 1000
\(\frac{111}{125}\)

Question 4.
.0125
Answer:
\(\frac{1}{80}\)
Explanation:
Given, 0.125
\(\frac{125}{10000}\)
dividing both the numerator and denominator with 125
1 x 125 = 125
80 x 125 = 10000
\(\frac{1}{80}\)

Question 5.
.678
Answer:
\(\frac{339}{500}\)
Explanation:
Given, 0.678
\(\frac{678}{1000}\)
dividing both the numerator and denominator with 2
339 x 2 = 678
500 x 2 = 1000
\(\frac{339}{500}\)

Question 6.
.6255
Answer:
\(\frac{1251}{2000}\)
Explanation:
Given, 0.6255
\(\frac{6255}{10000}\)
dividing both the numerator and denominator with 5
1251 x 5 = 6255
2000 x 5 = 10000
\(\frac{1251}{2000}\)

Question 7.
.331
Answer:
\(\frac{331}{1000}\)
Explanation:
Given, 0.331
multiplying both the numerator and denominator with 1000
\(\frac{331}{1000}\)

Question 8.
.4545
Answer:
\(\frac{909}{2000}\)
Explanation:
Given, 0.4545
\(\frac{4545}{10000}\)
dividing both the numerator and denominator with 5
909 x 5 = 4545
2000 x 5 = 10000
\(\frac{909}{2000}\)

Question 9.
.876
Answer:
\(\frac{219}{250}\)
Explanation:
Given, 0.87
\(\frac{876}{1000}\)
dividing both the numerator and denominator with 4
219 x 4 = 876
250 x 4 = 1000
\(\frac{219}{250}\)

Question 10.
.3125
Answer:
\(\frac{5}{16}\)
Explanation:
Given, 0.3125
\(\frac{3125}{10000}\)
dividing both the numerator and denominator with 625
5 x 625 = 3125
16 x 625 = 10000
\(\frac{5}{16}\)

Question 11.
.3435
Answer:
\(\frac{687}{2000}\)
Explanation:
\(\frac{3435}{10000}\)
dividing both the numerator and denominator with 5
687 x 5 = 3435
2000 x 5 = 10000
\(\frac{687}{2000}\)

Question 12.
.7007
Answer:
\(\frac{7007}{10000}\)
Explanation:
Given 0.7007
multiplying both the numerator and denominator with 10000
\(\frac{7007}{10000}\)

Question 13.
.336
Answer:
\(\frac{42}{125}\)
Explanation:
Given, 0.336
\(\frac{336}{1000}\)
dividing both the numerator and denominator with 8
42 x 8 = 336
125 x 8 = 1000
\(\frac{42}{125}\)

Question 14.
.2141
Answer:
\(\frac{2141}{10000}\)
Explanation:
Given, 0.2141
multiplying both the numerator and denominator with 10000
\(\frac{2141}{10000}\)

Question 15.
.56
Answer:
\(\frac{14}{25}\)
Explanation:
Given, 0.56
\(\frac{56}{100}\)
dividing both the numerator and denominator with 4
14 x 4 = 56
25 x 4 = 100
\(\frac{14}{25}\)

Question 16.
.0055
Answer:
Given, 0.0055
\(\frac{11}{2000}\)
Explanation:
\(\frac{55}{10000}\)
dividing both the numerator and denominator with 5
11 x 5 = 55
2000 x 5 = 10000
\(\frac{11}{2000}\)

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 9.2 Changing Fractions to Decimals existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 9.2 Changing Fractions to Decimals

Exercises Change Fractions To Decimals
Round to the nearest ten-thousandth.

Question 1.
\(\frac{5}{16}\)
Answer:
0.3125
Explanation:
Every fraction represents its numerator divided by its denominator.
So, \(\frac{5}{16}\) = 5 ÷ 16 to set up a division problem,
Add a decimal point and as many placeholder zeros as you need in your dividend, as shown below.

Question 2.
\(\frac{4}{7}\)
Answer:
0.5714
Explanation:
Every fraction represents its numerator divided by its denominator.
So, \(\frac{4}{7}\) = 4 ÷ 7 to set up a division problem,
Add a decimal point and as many placeholder zeros as you need in your dividend, as shown below.

Question 3.
\(\frac{15}{31}\)
Answer:
0.4839
Explanation:
Every fraction represents its numerator divided by its denominator.
So, \(\frac{15}{31}\) = 15 ÷ 31 to set up a division problem,
Add a decimal point and as many placeholder zeros as you need in your dividend, as shown below.

Question 4.
\(\frac{3}{5}\)
Answer:
0.6000
Explanation:
Every fraction represents its numerator divided by its denominator.
So, \(\frac{3}{5}\) = 3 ÷ 5 to set up a division problem,
Add a decimal point and as many placeholder zeros as you need in your dividend, as shown below.

Question 5.
\(\frac{5}{212}\)
Answer:
0.0236
Explanation:
Every fraction represents its numerator divided by its denominator.
So, \(\frac{5}{212}\) = 5 ÷ 212 to set up a division problem,
Add a decimal point and as many placeholder zeros as you need in your dividend, as shown below.

Question 6.
\(\frac{31}{33}\)
Answer:
0.9394
Explanation:
Every fraction represents its numerator divided by its denominator.
So, \(\frac{31}{33}\) = 31 ÷ 33 to set up a division problem,
Add a decimal point and as many placeholder zeros as you need in your dividend, as shown below.

Question 7.
\(\frac{45}{157}\)
Answer:
0.2866
Explanation:
Every fraction represents its numerator divided by its denominator.
So, \(\frac{45}{157}\) = 45 ÷ 157 to set up a division problem,
Add a decimal point and as many placeholder zeros as you need in your dividend, as shown below.

Question 8.
\(\frac{12}{13}\)
Answer:
0.9231
Explanation:
Every fraction represents its numerator divided by its denominator.
So, \(\frac{12}{13}\) = 12 ÷ 13 to set up a division problem,
Add a decimal point and as many placeholder zeros as you need in your dividend, as shown below.

Question 9.
\(\frac{1}{2001}\)
Answer:
0.0005
Explanation:
Every fraction represents its numerator divided by its denominator.
So, \(\frac{5}{16}\) = 1 ÷ 2001 to set up a division problem,
Add a decimal point and as many placeholder zeros as you need in your dividend, as shown below.

Question 10.
\(\frac{23}{76}\)
Answer:
0.3026
Explanation:
Every fraction represents its numerator divided by its denominator.
So, \(\frac{23}{76}\) = 23 ÷ 76 to set up a division problem,
Add a decimal point and as many placeholder zeros as you need in your dividend, as shown below.

Question 11.
\(\frac{3}{32}\)
Answer:
0.0938
Explanation:
Every fraction represents its numerator divided by its denominator.
So, \(\frac{3}{32}\) = 3 ÷ 32 to set up a division problem,
Add a decimal point and as many placeholder zeros as you need in your dividend, as shown below.

Question 12.
\(\frac{55}{66}\)
Answer:
0.8333
Explanation:
Every fraction represents its numerator divided by its denominator.
So, \(\frac{55}{66}\) = 55 ÷ 66 to set up a division problem,
Add a decimal point and as many placeholder zeros as you need in your dividend, as shown below.

Question 13.
\(\frac{12}{47}\)
Answer:
0.2553
Explanation:
Every fraction represents its numerator divided by its denominator.
So, \(\frac{12}{47}\) = 12 ÷ 47 to set up a division problem,
Add a decimal point and as many placeholder zeros as you need in your dividend, as shown below.

Question 14.
\(\frac{7}{8}\)
Answer:
0.8750
Explanation:
Every fraction represents its numerator divided by its denominator.
So, \(\frac{7}{8}\) = 7 ÷ 8 to set up a division problem,
Add a decimal point and as many placeholder zeros as you need in your dividend, as shown below.

Question 15.
\(\frac{13}{15}\)
Answer:
0.8667
Explanation:
Every fraction represents its numerator divided by its denominator.
So, \(\frac{13}{15}\) = 13 ÷ 15 to set up a division problem,
Add a decimal point and as many placeholder zeros as you need in your dividend, as shown below.

Question 16.
\(\frac{13}{17}\)
Answer:
0.7647
Explanation:
Every fraction represents its numerator divided by its denominator.
So, \(\frac{13}{17}\) = 13 ÷ 17 to set up a division problem,
Add a decimal point and as many placeholder zeros as you need in your dividend, as shown below.

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 9.1 Place Value and Rounding existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 9.1 Place Value and Rounding

Exercises Round

Round to the nearest whole number.

Question 1.
14.37
Answer:
14
Explanation:
Observe the digit in the tenth place which is less than 5,
Round to the whole number given.
So, 14.37 is round to the nearest whole number as 14.

Question 2.
77.4
Answer:
77
Explanation:
Observe the digit in the tenth place  which is less than 5,
Round to the whole number given.
So, 77.4 is round to the nearest whole number as 77.

Question 3.
145.6
Answer:
146
Explanation:
Observe the digit in the tenth place  which is greater than 5,
Add one to the given whole number.
So, 145.6 is round to the nearest whole number as 146.

Question 4.
1000.9
Answer:
1001
Explanation:
Observe the digit in the tenth place  which is greater than 5,
Add one to the given whole number.
So, 1000.9 is round to the nearest whole number as 1001.

Question 5.
89.4
Answer:
89
Explanation:
Observe the digit in the tenth place  which is less than 5,
Round to the whole number given.
So, 89.4 is round to the nearest whole number as 89.

Question 6.
1501.1
Answer:
1501
Explanation:
Observe the digit in the tenth place  which is less than 5,
Round to the whole number given.
So, 1501.1 is round to the nearest whole number as 1501.

Round to the nearest tenth.

Question 7.
14.37
Answer:
14.4
Explanation:
Observe the digit to the right of the rounding place,
if the digit is greater than 5 add 1 to the digit in the rounding place.
So, 14.37 is round to the nearest tenth place is 14.4

Question 8.
125.51
Answer:
125.5
Explanation:
Observe the digit to the right of the rounding place,
if the digit is less than 5 keep the digit in the rounding place.
So, 125 is round to the nearest tenth as 125.51.

Question 9.
149.49
Answer:
149.5
Explanation:
Observe the digit to the right of the rounding place,
if the digit is greater than 5 add 1 to the digit in the rounding place.
So, 149.49 is round to the nearest tenth as 149.5.

Question 10.
33.35
Answer:
33.4
Explanation:
Observe the digit to the right of the rounding place,
if the digit is greater than 5 add 1 to the digit in the rounding place.
So, 33.35 is round to the nearest tenth as 33.4.

Question 11.
275.77
Answer:
275.8
Explanation:
Observe the digit to the right of the rounding place,
if the digit is greater than 5 add 1 to the digit in the rounding place.
So, 275.77 is round to the nearest tenth as 275.8.

Question 12.
212.99
Answer:
213
Explanation:
Observe the digit to the right of the rounding place,
if the digit is greater than 5 add 1 to the digit in the rounding place.
So, 212.99 is round to the nearest tenth as 213.

Round to the nearest hundredth.

Question 13.
1435.344
Answer:
1435.34
Explanation:
Observe the digit to the right of the rounding place,
if the digit is less than 5 keep the digit in the rounding place.
So, 1435.344 is round to the nearest hundredth as 1435.34.

Question 14.
3.555
Answer:
3.56
Explanation:
Observe the digit to the right of the rounding place,
if the digit is greater than 5 add 1 to the digit in the rounding place.
So, 3.555 is round to the nearest hundredth as 3.56.

Question 15.
111.119
Answer:
111.12
Explanation:
Observe the digit to the right of the rounding place,
if the digit is greater than 5 add 1 to the digit in the rounding place.
So, 111.119 is round to the nearest hundredth as 111.12.

Question 16.
32.756
Answer:
32.76
Explanation:
Observe the digit to the right of the rounding place,
if the digit is greater than 5 add 1 to the digit in the rounding place.
So, 32.756 is round to the nearest hundredth as 32.76.

Question 17.
999.989
Answer:
999.99
Explanation:
Observe the digit to the right of the rounding place,
if the digit is greater than 5 add 1 to the digit in the rounding place.
So, 999.989 is round to the nearest hundredth as 999.99.

Question 18.
954.376
Answer:
954.38
Explanation:
Observe the digit to the right of the rounding place,
if the digit is greater than 5 add 1 to the digit in the rounding place.
So, 954.376 is round to the nearest hundredth as 954.38.

Round to the nearest thousandth.

Question 19.
3.2378
Answer:
3.238
Explanation:
Observe the digit to the right of the rounding place,
if the digit is greater than 5 add 1 to the digit in the rounding place.
So, 3.2378 is round to the nearest thousandth as 3.238.

Question 20.
329.3297
Answer:
329.330
Explanation:
Observe the digit to the right of the rounding place,
if the digit is greater than 5 add 1 to the digit in the rounding place.
So, 329.3297 is round to the nearest thousandth as 329.330.

Question 21.
109.1090
Answer:
109.109
Explanation:
Observe the digit to the right of the rounding place,
if the digit is less than 5 keep to the digit in the rounding place.
So, 109.1090 is round to the nearest thousandth as 109.109.

Question 22.
8256.7835
Answer:
8256.784
Explanation:
Observe the digit to the right of the rounding place,
if the digit is greater than 5 add 1 to the digit in the rounding place.
So, 8256.7835 is round to the nearest thousandth as 8256.784.

Question 23.
49.4949
Answer:
49.495
Explanation:
Observe the digit to the right of the rounding place,
if the digit is greater than 5 add 1 to the digit in the rounding place.
So, 49.4949 is round to the nearest thousandth as 49.495.

Question 24.
0.1138
Answer:
0.114
Explanation:
Observe the digit to the right of the rounding place,
if the digit is greater than 5 add 1 to the digit in the rounding place.
So, 0.114 is round to the nearest thousandth as 0.114.

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 8.4 Dividing Mixed Numbers existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 8.4 Dividing Mixed Numbers

Exercises Divide

Question 1.
1\(\frac{1}{3}\) ÷ -2\(\frac{1}{2}\)
Answer:
–\(\frac{8}{15}\)
Explanation:
1\(\frac{1}{3}\) ÷ -2\(\frac{1}{2}\)
Convert mixed fraction into improper fraction.
\(\frac{4}{3}\) ÷ –\(\frac{5}{2}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{4}{3}\) x –\(\frac{2}{5}\)
Multiply the numerators and denominators,
4 x 2= 8
3 x 5 = 15
place the numerator over denominator,
–\(\frac{8}{15}\)

Question 2.
3\(\frac{3}{5}\) ÷ 1\(\frac{1}{8}\)
Answer:
3\(\frac{1}{5}\)
Explanation:
3\(\frac{3}{5}\) ÷ 1\(\frac{1}{8}\)
Convert mixed fraction into improper fraction.
\(\frac{18}{5}\) ÷ \(\frac{9}{8}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{18}{5}\) x \(\frac{8}{9}\)
Multiply the numerators and denominators,
18 x 8 = 2 x 8 = 16
5 x 9 = 5 = 5
place the numerator over denominator,
\(\frac{16}{5}\)
Reduce to the simplest form,
3\(\frac{1}{5}\)

Question 3.
7\(\frac{1}{7}\) ÷ 3\(\frac{1}{3}\)
Answer:
2\(\frac{1}{7}\)
Explanation:
7\(\frac{1}{7}\) ÷ 3\(\frac{1}{3}\)
Convert mixed fraction into improper fraction.
\(\frac{50}{7}\) ÷ \(\frac{10}{3}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{50}{7}\) x \(\frac{3}{10}\)
Multiply the numerators and denominators,
50 x 3 = 5 x 3 = 15
7 x 10 = 7 = 7
place the numerator over denominator,
\(\frac{15}{7}\)
Reduce to the simplest form,
2\(\frac{1}{7}\)

Question 4.
3\(\frac{4}{7}\) ÷ 2\(\frac{2}{5}\)
Answer:
1\(\frac{41}{84}\)
Explanation:
3\(\frac{4}{7}\) ÷ 2\(\frac{2}{5}\)
Convert mixed fraction into improper fraction.
\(\frac{25}{7}\) ÷ \(\frac{12}{5}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{25}{7}\) x \(\frac{5}{12}\)
Multiply the numerators and denominators,
25 x 5 = 125
7 x 12 = 84
place the numerator over denominator,
\(\frac{125}{84}\)
Reduce to the simplest form,
1\(\frac{41}{84}\)

Question 5.
6\(\frac{4}{5}\) ÷ 3\(\frac{2}{5}\)
Answer:
2
Explanation:
6\(\frac{4}{5}\) ÷ 3\(\frac{2}{5}\)
Convert mixed fraction into improper fraction.
\(\frac{34}{5}\) ÷ \(\frac{17}{5}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{34}{5}\) x \(\frac{5}{17}\)
Multiply the numerators and denominators,
34 x 5 = 2
5 x 17 = 1
place the numerator over denominator,
= \(\frac{2}{1}\) = 2

Question 6.
5\(\frac{1}{2}\) ÷ 3\(\frac{3}{4}\)
Answer:
1\(\frac{7}{15}\)
Explanation:
5\(\frac{1}{2}\) ÷ 3\(\frac{3}{4}\)
Convert mixed fraction into improper fraction.
\(\frac{11}{2}\) ÷ \(\frac{15}{4}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{11}{2}\) x \(\frac{4}{15}\)
Multiply the numerators and denominators,
11 x 4 = 11 x 2 = 22
2 x 15 = 15
place the numerator over denominator,
\(\frac{22}{15}\)
Reduce to the simplest form,
1\(\frac{7}{15}\)

Question 7.
4\(\frac{2}{9}\) ÷ 2\(\frac{4}{9}\)
Answer:
1\(\frac{8}{11}\)
Explanation:
4\(\frac{2}{9}\) ÷ 2\(\frac{4}{9}\)
Convert mixed fraction into improper fraction.
\(\frac{38}{9}\) ÷ \(\frac{22}{9}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{38}{9}\) x \(\frac{9}{22}\)
Multiply the numerators and denominators,
38 x 9 = 19
9 x 22 = 11
place the numerator over denominator,
\(\frac{19}{11}\)
Reduce to the simplest form,
1\(\frac{8}{11}\)

Question 8.
-9\(\frac{2}{7}\) ÷ -2\(\frac{1}{2}\)
Answer:
3\(\frac{5}{7}\)
Explanation:
-9\(\frac{2}{7}\) ÷ -2\(\frac{1}{2}\)
let – in numerator and – inn denominator get cancelled
Convert mixed fraction into improper fraction.
\(\frac{65}{7}\) ÷ \(\frac{5}{2}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{65}{7}\) x \(\frac{2}{5}\)
Multiply the numerators and denominators,
65 x 2 = 13 x 2 = 26
7 x 5 = 7
place the numerator over denominator,
\(\frac{26}{7}\)
Reduce to the simplest form,
3\(\frac{5}{7}\)

Question 9.
5\(\frac{6}{17}\) ÷ 2\(\frac{2}{3}\)
Answer:
2\(\frac{1}{136}\)
Explanation:
5\(\frac{6}{17}\) ÷ 2\(\frac{2}{3}\)
Convert mixed fraction into improper fraction.
\(\frac{91}{17}\) ÷ \(\frac{8}{3}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{91}{17}\) x \(\frac{3}{8}\)
Multiply the numerators and denominators,
91 x 3 = 273
17 x 8 = 136
place the numerator over denominator,
\(\frac{273}{136}\)
Reduce to the simplest form,
2\(\frac{1}{136}\)

Question 10.
5\(\frac{3}{13}\) ÷ 2\(\frac{3}{4}\)
Answer:
1\(\frac{129}{143}\)
Explanation:
5\(\frac{3}{13}\) ÷ 2\(\frac{3}{4}\)
Convert mixed fraction into improper fraction.
\(\frac{68}{13}\) ÷ \(\frac{11}{4}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{68}{13}\) x \(\frac{4}{11}\)
Multiply the numerators and denominators,
68 x 4 = 272
13 x 11 = 143
place the numerator over denominator,
\(\frac{272}{143}\)
Reduce to the simplest form,
1\(\frac{129}{143}\)

Question 11.
1\(\frac{3}{4}\) ÷ -4\(\frac{3}{5}\)
Answer:
–\(\frac{35}{92}\)
Explanation:
1\(\frac{3}{4}\) ÷ -4\(\frac{3}{5}\)
Convert mixed fraction into improper fraction.
\(\frac{7}{4}\) ÷ \(\frac{23}{5}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{7}{4}\) x \(\frac{5}{23}\)
Multiply the numerators and denominators,
7 x 5 = 35
4 x 23 = 92
place the numerator over denominator,
– \(\frac{35}{92}\)

Question 12.
9\(\frac{3}{8}\) ÷ 1\(\frac{1}{4}\)
Answer:
7\(\frac{1}{2}\)
Explanation:
9\(\frac{3}{8}\) ÷ 1\(\frac{1}{4}\)
Convert mixed fraction into improper fraction.
\(\frac{75}{8}\) ÷ \(\frac{5}{4}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{75}{8}\) x \(\frac{4}{5}\)
Multiply the numerators and denominators,
75 x 4 = 15
8 x 5 = 2
place the numerator over denominator,
\(\frac{15}{2}\)
Reduce to the simplest form,
7\(\frac{1}{2}\)

Question 13.
-44\(\frac{4}{5}\) ÷ -4\(\frac{1}{2}\)
Answer:
9\(\frac{43}{45}\)
Explanation:
-44\(\frac{4}{5}\) ÷ -4\(\frac{1}{2}\)
Convert mixed fraction into improper fraction.
\(\frac{224}{5}\) ÷ \(\frac{9}{2}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{224}{5}\) x \(\frac{2}{9}\)
Multiply the numerators and denominators,
224 x 2 = 448
5 x 9 = 45
place the numerator over denominator,
\(\frac{448}{45}\)
Reduce to the simplest form,
9\(\frac{43}{45}\)

Question 14.
1\(\frac{1}{2}\) ÷ 3\(\frac{1}{2}\)
Answer:
1\(\frac{129}{143}\)
Explanation:
1\(\frac{1}{2}\) ÷ 3\(\frac{1}{2}\)
Convert mixed fraction into improper fraction.
\(\frac{3}{2}\) ÷ \(\frac{7}{2}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{3}{2}\) x \(\frac{2}{7}\)
Multiply the numerators and denominators,
3 x 2 = 3
2 x 7 = 7
place the numerator over denominator,
\(\frac{3}{7}\)

Question 15.
5\(\frac{3}{5}\) ÷ 1\(\frac{1}{3}\)
Answer:
4\(\frac{1}{5}\)
Explanation:
5\(\frac{3}{5}\) ÷ 1\(\frac{1}{3}\)
Convert mixed fraction into improper fraction.
\(\frac{28}{5}\) ÷ \(\frac{4}{3}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{28}{5}\) x \(\frac{3}{4}\)
Multiply the numerators and denominators,
28 x 3 = 7 x 3 = 21
5 x 4 = 5
place the numerator over denominator,
\(\frac{21}{5}\)
Reduce to the simplest form,
4\(\frac{1}{5}\)

Question 16.
1\(\frac{2}{11}\) ÷ 3\(\frac{1}{3}\)
Answer:
\(\frac{39}{110}\)
Explanation:
1\(\frac{2}{11}\) ÷ 3\(\frac{1}{3}\)
Convert mixed fraction into improper fraction.
\(\frac{13}{11}\) ÷ \(\frac{10}{3}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{13}{11}\) x \(\frac{3}{10}\)
Multiply the numerators and denominators,
13 x 3 = 39
11 x 10 = 110
place the numerator over denominator,
\(\frac{39}{110}\)

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 8.3 Dividing Fractions by Fractions existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 8.3 Dividing Fractions by Fractions

Exercises Divide

Question 1.
\(\frac{5}{7}\) ÷ \(\frac{3}{4}\)
Answer:
\(\frac{20}{21}\)
Explanation:
\(\frac{5}{7}\) ÷ \(\frac{3}{4}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{5}{7}\) x \(\frac{4}{3}\)
Multiply the numerators and denominators,
4 x 5 = 20
3 x 7 = 21
place the numerator over denominator,
\(\frac{20}{21}\)

Question 2.
\(\frac{2}{3}\) ÷ \(\frac{2}{7}\)
Answer:
2\(\frac{1}{3}\)
Explanation:
\(\frac{2}{3}\) ÷ \(\frac{2}{7}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{2}{3}\) x \(\frac{7}{2}\)
Multiply the numerators and denominators,
2 x 7 = 14
3 x 2 = 6
place the numerator over denominator,
\(\frac{14}{6}\)
Reduce to the simplest form,
\(\frac{7}{3}\) = 2\(\frac{1}{3}\)

Question 3.
\(\frac{1}{9}\) ÷ –\(\frac{3}{7}\)
Answer:-
–\(\frac{7}{27}\)
Explanation:
\(\frac{1}{9}\) ÷ –\(\frac{3}{7}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{1}{9}\) x –\(\frac{7}{3}\)
Multiply the numerators and denominators,
1 x 7 = 7
3 x 9 = 27
place the numerator over denominator,
–\(\frac{7}{27}\)

Question 4.
\(\frac{3}{4}\) ÷ \(\frac{1}{9}\)
Answer:
6\(\frac{3}{4}\)
Explanation:
\(\frac{3}{4}\) ÷ \(\frac{1}{9}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{3 X 9}{4}\)
\(\frac{27}{4}\)
Reduce to the simplest form,
6\(\frac{3}{4}\)

Question 5.
–\(\frac{3}{13}\) ÷ –\(\frac{2}{9}\)
Answer:
1\(\frac{1}{26}\)
Explanation:
–\(\frac{3}{13}\) ÷ –\(\frac{2}{9}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{3}{13}\) x \(\frac{9}{2}\)
Multiply the numerators and denominators,
3 x 9 = 27
13 x 2 = 26
place the numerator over denominator,
\(\frac{27}{26}\)
Reduce to the simplest form,
1\(\frac{1}{26}\)

Question 6.
\(\frac{1}{9}\) ÷ \(\frac{1}{3}\)
Answer:
\(\frac{1}{3}\)
Explanation:
\(\frac{1}{9}\) ÷ \(\frac{1}{3}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{1 X 3}{9}\)
\(\frac{1}{3}\)

Question 7.
\(\frac{2}{13}\) ÷ \(\frac{1}{5}\)
Answer:
\(\frac{10}{13}\)
Explanation:
\(\frac{2}{13}\) ÷ \(\frac{1}{5}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{2 X 5}{13}\)
\(\frac{10}{13}\)

Question 8.
\(\frac{3}{13}\) ÷ \(\frac{2}{13}\)
Answer:
1\(\frac{1}{2}\)
Explanation:
\(\frac{3}{13}\) ÷ \(\frac{2}{13}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{3}{13}\) x \(\frac{13}{2}\)
Multiply the numerators and denominators,
3 x 13 = 39
13 x 2 = 26
place the numerator over denominator,
\(\frac{39}{26}\)
Reduce to the simplest form,
\(\frac{3}{2}\) = 1\(\frac{1}{2}\)

Question 9.
\(\frac{4}{3}\) ÷ \(\frac{1}{4}\)
Answer:
5\(\frac{1}{3}\)
Explanation:
\(\frac{4}{3}\) ÷ \(\frac{1}{4}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{4 X 4}{3}\)
\(\frac{16}{3}\)
Reduce to the simplest form,
5\(\frac{1}{3}\)

Question 10.
\(\frac{15}{4}\) ÷ \(\frac{4}{3}\)
Answer:
2\(\frac{13}{16}\)
Explanation:
\(\frac{15}{4}\) ÷ \(\frac{4}{3}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{15}{4}\) x \(\frac{3}{4}\)
Multiply the numerators and denominators,
15 x 3 = 45
4 x 4 = 16
place the numerator over denominator,
\(\frac{45}{16}\)
Reduce to the simplest form,
2\(\frac{13}{16}\)

Question 11.
\(\frac{6}{7}\) ÷ \(\frac{1}{7}\)
Answer:
6
Explanation:
\(\frac{6}{7}\) ÷ \(\frac{1}{7}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{6 X 7}{7}\)
\(\frac{42}{7}\) = 6

Question 12.
\(\frac{3}{17}\) ÷ –\(\frac{4}{17}\)
Answer:
–\(\frac{3}{4}\)
Explanation:
\(\frac{3}{17}\) ÷ –\(\frac{4}{17}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{3}{17}\) x –\(\frac{17}{4}\)
Multiply the numerators and denominators,
3 x 17 = 51
17 x 4 = 68
place the numerator over denominator,
–\(\frac{51}{68}\)
Reduce to the simplest form,
–\(\frac{3}{4}\)

Question 13.
\(\frac{1}{11}\) ÷ \(\frac{22}{3}\)
Answer:
\(\frac{3}{242}\)
Explanation:
\(\frac{1}{11}\) ÷ \(\frac{22}{3}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{3}{22 X11}\)
\(\frac{3}{242}\)

Question 14.
–\(\frac{3}{7}\) ÷ –\(\frac{1}{21}\)
Answer:
9
Explanation:
–\(\frac{3}{7}\) ÷ –\(\frac{1}{21}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{3 X 21}{7}\)
\(\frac{63}{7}\) = 9

Question 15.
\(\frac{5}{14}\) ÷ \(\frac{1}{7}\)
Answer:
2\(\frac{1}{2}\)
Explanation:
\(\frac{5}{14}\) ÷ \(\frac{1}{7}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{5 X 7}{14}\)
\(\frac{35}{14}\)
Reduce to the simplest form,
\(\frac{5}{2}\) = 2\(\frac{1}{2}\)

Question 16.
\(\frac{3}{4}\) ÷ \(\frac{8}{3}\)
Answer:
\(\frac{9}{32}\)
Explanation:
\(\frac{3}{4}\) ÷ \(\frac{8}{3}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{3}{4}\) x \(\frac{3}{8}\)
Multiply the numerators and denominators,
3 x 3 = 9
4 x 8 = 32
place the numerator over denominator,
\(\frac{9}{32}\)

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 8.2 Dividing Whole Numbers by Fractions existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 8.2 Dividing Whole Numbers by Fractions

Exercises Multiply

Question 1.
5 ÷ \(\frac{1}{4}\)
Answer:
20
Explanation:
5 ÷ \(\frac{1}{4}\)
Multiply the whole number by reciprocal of fraction,
5 x 4 = 20

Question 2.
3 ÷ –\(\frac{4}{5}\)
Answer:
-3\(\frac{3}{4}\)
Explanation:
3 ÷ –\(\frac{4}{5}\)
Multiply the whole number by reciprocal of fraction,
5 x 3 = 15
–\(\frac{15}{4}\)
Reduce to the simplest form,
-3\(\frac{3}{4}\)

Question 3.
7 ÷ \(\frac{1}{7}\)
Answer:
49
Explanation:
7 ÷ \(\frac{1}{7}\)
Multiply the whole number by reciprocal of fraction,
7 x 7 = 49

Question 4.
9 ÷ \(\frac{4}{7}\)
Answer:
15\(\frac{3}{4}\)
Explanation:
9 ÷ \(\frac{4}{7}\)
Multiply the whole number by reciprocal of fraction,
9 x 7 = 63
\(\frac{63}{4}\)
Reduce to the simplest form,
15\(\frac{3}{4}\)

Question 5.
2 ÷ \(\frac{1}{2}\)
Answer:
4
Explanation:
2 ÷ \(\frac{1}{2}\)
Multiply the whole number by reciprocal of fraction,
2 x 2 = 4

Question 6.
4 ÷ \(\frac{2}{7}\)
Answer:
14
Explanation:
4 ÷ \(\frac{2}{7}\)
Multiply the whole number by reciprocal of fraction,
4 x 7 = 28
\(\frac{28}{2}\) = 14

Question 7.
15 ÷ \(\frac{5}{7}\)
Answer:
21
Explanation:
15 ÷ \(\frac{5}{7}\)
Multiply the whole number by reciprocal of fraction,
15 x 7 = 105
\(\frac{105}{5}\) = 21

Question 8.
4 ÷ –\(\frac{2}{9}\)
Answer:
-18
Explanation:
4 ÷ –\(\frac{2}{9}\)
Multiply the whole number by reciprocal of fraction,
9 x 4 = 36
–\(\frac{36}{2}\) = -18

Question 9.
17 ÷ –\(\frac{2}{3}\)
Answer:
-25\(\frac{1}{3}\)
Explanation:
17 ÷ –\(\frac{1}{3}\)
Multiply the whole number by reciprocal of fraction,
3 x 17 = 51
–\(\frac{51}{3}\)
Reduce to the simplest form,
-25\(\frac{1}{3}\)

Question 10.
5 ÷ \(\frac{3}{5}\)
Answer:
8\(\frac{1}{3}\)
Explanation:
5 ÷ \(\frac{3}{5}\)
Multiply the whole number by reciprocal of fraction,
5 x 5 = 25
\(\frac{25}{3}\)
Reduce to the simplest form,
8\(\frac{1}{3}\)

Question 11.
6 ÷ \(\frac{2}{3}\)
Answer:
9
Explanation:
6 ÷ \(\frac{2}{3}\)
Multiply the whole number by reciprocal of fraction,
6 x 3 = 18
\(\frac{18}{2}\) = 9

Question 12.
9 ÷ \(\frac{2}{3}\)
Answer:
13\(\frac{1}{2}\)
Explanation:
9 ÷ \(\frac{2}{3}\)
Multiply the whole number by reciprocal of fraction,
9 x 3 = 27
\(\frac{27}{2}\)
Reduce to the simplest form,
13\(\frac{1}{2}\)

Question 13.
5 ÷ \(\frac{1}{11}\)
Answer:
55
Explanation:
5 ÷ \(\frac{1}{11}\)
Multiply the whole number by reciprocal of fraction,
5 x 11 = 55

Question 14.
14 ÷ \(\frac{7}{2}\)
Answer:
4
Explanation:
14 ÷ \(\frac{7}{2}\)
Multiply the whole number by reciprocal of fraction,
14 x 2 = 28
\(\frac{28}{7}\) = 4

Question 15.
3 ÷ –\(\frac{1}{9}\)
Answer:
-27
Explanation:
3 ÷ –\(\frac{1}{9}\)
Multiply the whole number by reciprocal of fraction,
9 x 3 = 27

Question 16.
3 ÷ \(\frac{7}{2}\)
Answer:
\(\frac{6}{7}\)
Explanation:
3 ÷ \(\frac{7}{2}\)
Multiply the whole number by reciprocal of fraction,
3 x 2 = 6
\(\frac{6}{7}\)

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 8.1 Dividing Fractions by Whole Numbers existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 8.1 Dividing Fractions by Whole Numbers

Exercises Multiply

Question 1.
–\(\frac{1}{2}\) ÷ 4
Answer:
–\(\frac{1}{8}\)
Explanation:
–\(\frac{1}{2}\) ÷ 4
Multiply the whole number by denominator,
4 x 2 = 8
place the numerator over denominator,
–\(\frac{1}{8}\)

Question 2.
\(\frac{3}{5}\) ÷ 4
Answer:
\(\frac{3}{20}\)
Explanation:
\(\frac{3}{5}\) ÷ 4
Multiply the whole number by denominator,
4 x 5 = 20
place the numerator over denominator,
\(\frac{3}{20}\)

Question 3.
\(\frac{6}{7}\) ÷ 3
Answer:
\(\frac{2}{7}\)
Explanation:
\(\frac{6}{7}\) ÷ 3
Multiply the whole number by denominator,
7 x 3 = 21
place the numerator over denominator,
\(\frac{6}{21}\)
= \(\frac{2}{7}\)

Question 4.
\(\frac{1}{5}\) ÷ 11
Answer:
\(\frac{1}{55}\)
Explanation:
\(\frac{1}{5}\) ÷ 11
Multiply the whole number by denominator,
5 x 11 = 55
place the numerator over denominator,
\(\frac{1}{55}\)

Question 5.
\(\frac{5}{19}\) ÷ 2
Answer:
\(\frac{5}{38}\)
Explanation:
\(\frac{5}{19}\) ÷ 2
Multiply the whole number by denominator,
19 x 2 = 38
place the numerator over denominator,
\(\frac{5}{38}\)

Question 6.
–\(\frac{4}{5}\) ÷ 7
Answer:
–\(\frac{4}{35}\)
Explanation:
–\(\frac{4}{5}\) ÷ 7
Multiply the whole number by denominator,
7 x 5 = 35
place the numerator over denominator,
–\(\frac{4}{35}\)

Question 7.
\(\frac{1}{9}\) ÷ 9
Answer:
\(\frac{1}{81}\)
Explanation:
\(\frac{1}{8}\) ÷ 9
Multiply the whole number by denominator,
8 x 9 = 81
place the numerator over denominator,
\(\frac{1}{81}\)

Question 8.
\(\frac{3}{11}\) ÷ 12
Answer:
\(\frac{1}{44}\)
Explanation:
\(\frac{3}{11}\) ÷ 12
Multiply the whole number by denominator,
11 x 12 = 132
place the numerator over denominator,
\(\frac{3}{132}\)
= \(\frac{1}{44}\)

Question 9.
\(\frac{17}{18}\) ÷ 4
Answer:
\(\frac{17}{72}\)
Explanation:
\(\frac{17}{18}\) ÷ 4
Multiply the whole number by denominator,
18 x 4 = 72
place the numerator over denominator,
\(\frac{17}{72}\)

Question 10.
\(\frac{12}{13}\) ÷ 3
Answer:
\(\frac{4}{13}\)
Explanation:
\(\frac{12}{13}\) ÷ 3
Multiply the whole number by denominator,
13 x 3 = 39
place the numerator over denominator,
\(\frac{12}{39}\)
= \(\frac{4}{13}\)

Question 11.
\(\frac{2}{3}\) ÷ 6
Answer:
\(\frac{1}{9}\)
Explanation:
\(\frac{2}{3}\) ÷ 6
Multiply the whole number by denominator,
6 x 3 = 18
place the numerator over denominator,
\(\frac{2}{18}\)
= \(\frac{1}{9}\)

Question 12.
–\(\frac{5}{11}\) ÷ 20
Answer:
–\(\frac{1}{44}\)
Explanation:
–\(\frac{5}{11}\) ÷ 20
Multiply the whole number by denominator,
11 x 20 = 220
place the numerator over denominator,
–\(\frac{5}{220}\)
= –\(\frac{1}{44}\)

Question 13.
\(\frac{3}{7}\) ÷ 11
Answer:
\(\frac{3}{77}\)
Explanation:
\(\frac{3}{7}\) ÷ 11
Multiply the whole number by denominator,
7 x 11 = 77
place the numerator over denominator,
\(\frac{3}{77}\)

Question 14.
–\(\frac{1}{3}\) ÷ 9
Answer:
–\(\frac{1}{27}\)
Explanation:
–\(\frac{1}{3}\) ÷ 9
Multiply the whole number by denominator,
9 x 3 = 27
place the numerator over denominator,
–\(\frac{1}{27}\)

Question 15.
\(\frac{10}{11}\) ÷ 5
Answer:
\(\frac{2}{11}\)
Explanation:
\(\frac{10}{11}\) ÷ 5
Multiply the whole number by denominator,
11 x 5 = 55
place the numerator over denominator,
\(\frac{10}{55}\)
= \(\frac{2}{11}\)

Question 16.
\(\frac{10}{13}\) ÷ 4
Answer:
\(\frac{5}{26}\)
Explanation:
\(\frac{10}{13}\) ÷ 4
Multiply the whole number by denominator,
4 x 13 = 52
place the numerator over denominator,
\(\frac{10}{52}\)
= \(\frac{5}{26}\)

Question 17.
\(\frac{4}{5}\) ÷ 4
Answer:
\(\frac{1}{5}\)
Explanation:
\(\frac{4}{5}\) ÷ 4
Multiply the whole number by denominator,
5 x 4 = 20
place the numerator over denominator,
\(\frac{4}{20}\)
= \(\frac{1}{5}\)

Question 18.
\(\frac{12}{13}\) ÷ 5
Answer:
\(\frac{12}{65}\)
Explanation:
\(\frac{12}{13}\) ÷ 5
Multiply the whole number by denominator,
5 x 13 = 65
place the numerator over denominator,
\(\frac{12}{65}\)

Question 19.
–\(\frac{2}{11}\) ÷ 4
Answer:
–\(\frac{1}{22}\)
Explanation:
–\(\frac{2}{11}\) ÷ 4
Multiply the whole number by denominator,
11 x 4 = 44
place the numerator over denominator,
–\(\frac{2}{44}\)
= –\(\frac{1}{22}\)

Question 20.
\(\frac{3}{4}\) ÷ 7
Answer:
\(\frac{3}{28}\)
Explanation:
\(\frac{3}{4}\) ÷ 7
Multiply the whole number by denominator,
7 x 4 = 28
place the numerator over denominator,
\(\frac{3}{28}\)