7th

proportions Grade

8
5 and 3 –2
5
40 7
15 9 –10
25
35

45 x
=
27 3
Identifying
Proportions

28
24
20
16
12
8
4 Proportional
-14 -12 -10 -8 -6 -4 -2 2 4 6
-4
-8
-12

Workbook 3
MathWorksheets4Kids.com Answer key
 Answer key

Proportion - Ratio

Write whether each pair of ratios forms a proportion.

13 and 26 12 and 4
1) 2)
19 48 8 5

Not a Proportion Not a Proportion

9 and 27 8 and 72
3) 4)
15 60 9 81

Not a Proportion Proportion

6 and 2 1 and 22
5) 6)
12 4 45 3

Proportion Not a Proportion

32 and 8 5 and 10
7) 8)
44 11 19 38

Proportion Proportion

68 and 19 15 and 75
9) 10)
7 3 4 20

Not a Proportion Proportion

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 Answer key

Proportion - Table
Determine whether the and values in each table are proportional.

1) 2)
–35 20 55 –15 21 70 49 15

7 –4 –11 3

3 10 7 5

Proportional Non-Proportional

3) 4)
–24 3 9 27 81 22 14 6

8 6 –3 –9

27 66 42 18

Non-Proportional Non-Proportional

5) 6)
2 9 –11 10 –3 6 –4 8

–16 –72 88 –80

27 –54 36 –72

Proportional Proportional

7) 8)
18 15 14 12 4 19 22 18

90 75 70 60

32 76 88 72

Proportional Non-Proportional

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 Answer key

Form a Proportion

Create a proportion using the given set of numbers.

1) 36, 6, 42, 7 2) 45, 5, 6, 54

6 : 7 = 36 : 42 45 : 5 = 54 : 6

3) 9, 24, 27, 8 4) 19, 57, 3, 9

8 : 9 = 24 : 27 3 : 19 = 9 : 57

5) 72, 4, 18, 16 6) 64, 15, 60, 16

4 : 18 = 16 : 72 16 : 15 = 64 : 60

7) 28, 21, 12, 49 8) 5, 20, 56, 14

12 : 28 = 21 : 49 5 : 14 = 20 : 56

9) 1, 4, 4, 16 10) 3, 42, 2, 63

1 : 4 = 4 : 16 42 : 2 = 63 : 3

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 Answer key

Form a Proportion

Create a proportion from each set of numbers. Only use 4 numbers from each set.

1) 13, 45, 76, 19, 52 2) 27, 45, 81, 7, 15

19 : 13 = 76 : 52 27 : 15 = 81 : 45

3) 8, 4, 18, 1, 72 4) 46, 11, 20, 23, 10

4 : 1 = 72 : 18 10 : 23 = 20 : 46

5) 3, 21, 5, 8, 35 6) 5, 3, 30, 90, 1

3 : 5 = 21 : 35 1 : 3 = 30 : 90

7) 36, 27, 6, 12, 2 8) 6, 56, 21, 24, 14

2 : 6 = 12 : 36 14 : 6 = 56 : 24

9) 3, 78, 99, 2, 52 10) 11, 55, 19, 95, 16

3 : 2 = 78 : 52 19 : 11 = 95 : 55

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 Answer key

Form a Proportion

Create a proportion from each set of numbers. Only use 4 numbers from each set.

1) 7, 9, 8, 49, 3, 56 2) 91, 6, 12, 84, 4, 13

7 : 8 = 49 : 56 12 : 84 = 13 : 91

3) 15, 24, 30, 5, 48, 6 4) 2, 10, 15, 21, 14, 5

15 : 30 = 24 : 48 14 : 10 = 21 : 15

5) 1, 18, 3, 15, 6, 12 6) 81, 3, 3, 5, 9, 45

1 : 3 = 6 : 18 5 : 45 = 9 : 81

7) 12, 22, 96, 9, 32, 4 8) 3, 34, 8, 2, 6, 51

32 : 4 = 96 : 12 3 : 2 = 51 : 34

9) 36, 30, 2, 60, 7, 72 10) 55, 15, 32, 11, 20, 88

30 : 60 = 36 : 72 32 : 20 = 88 : 55

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 Answer key

Check whether the coordinates of the points on the graph represents a proportional
relationship. Justify your answer.

1) 5
4
3
2
1

-30 -24 -18 -12 -6 6 12 18 24 30

The line passes through the origin - Proportion
-1
-2
-3
-4
-5

2) 5
4
3
2
1

-5 -4 -3 -2 -1 1 2 3 4 5
The line does not pass through the origin - Not a Proportion
-1
-2
-3
-4
-5

3) 35
28
21
14
7

-2 -1 1 2 3 4 5 6 7 8
The line passes through the origin - Proportion
-7
-14
-21
-28
-35

4) 1
-36 -32 -28 -24 -20-16 -12 -8 -4 4
-1
-2
-3
-4 The line passes through the origin - Proportion
-5
-6
-7
-8
-9

5) 5
4
3
2
1

-5 -4 -3 -2 -1 1 2 3 4 5
The graph is not a line - Not a Proportion
-1
-2
-3
-4
-5

© mathworksheets4kids.com –6–
 Answer key

Proportional Relationship
Use the graph to tell whether and are in proportional relationship.



1) 

–10 –8 –4 2 6 2) 

–21 –15 –12 –9 –6

–40 –32 –16 8 24 –6 0 3 6 9
 

32 9
24 6
16 3
8
-21 -18 -15 -12 -9 -6 -3 3 6 9
-3
-12 -10 -8 -6 -4 -2 2 4 6 8
-8 -6
-16 -9
-24 -12
-32 -15
-40 -18
-48 -21

Proportional Non-Proportional

3) 

–36 –18 18 9 –27 4) 

–5 –1 1 2 3
–7 –14 –28 –21 7 50 10 –10 –20 –30
 

28 60
21 50
14 40
7 30
20
-36 -27 -18 -9 9 18 27 36 45 54
-7 10
-14
-7 -6 -5 -4 -3 -2 -1 1 2 3
-21 -10
-28 -20
-35 -30
-42 -40

Non-Proportional Proportional

5) 

–12 –12 –12 –12 –12 6) 

–6 –4 –2 2 4
36 18 0 –18 –27 –24 –16 –8 8 16
 

45 16
36 12
27 8
18 4
9
-12 -10 -8 -6 -4 -2 2 4 6 8
-4
-15 -12 -9 -6 -3 3 6 9 12 15
-9 -8
-18 -12
-27 -16
-36 -20
-45 -24

Non-Proportional Proportional

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 Answer key

Constant of Proportionality - Graph

Identify the constant of proportionality(k) for each graph and write the proportional
relationship ( = k ).

1)

2)

9 9
8 6
7 3
6
-14 -7 7 14 21 28 35 42 49 56
5 -3
4 -6
3 -9
2 -12
1 -15
-18
-45 -36 -27 -18 -9 9 18 27 36 45
-1 -21

2 = 2
k= ; k= 3 ; = 3


9 9 7 7
 

3) 4)

70 40
60 32
50 24
40 16
30 8
20
-10 -8 -6 -4 -2 2 4 6 8 10
10 -8
-16
-35 -30 -25 -20 -15 -10 -5 5 10 15
-10 -24
-20 -32
-30 -40

k=1 ; 

= 
k=8 ; 

=8 

5)

6)

14 30
12 24
10 18
8 12
6 6
4
-15 -12 -9 -6 -3 3 6 9 12 15
2 -6
-12
-35 -28 -21 -14 -7 7 14 21 28 35
-2 -18
-4 -24
-6 -30

k= 4 ; 

= 4
7 7 k=2 ; =2


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 Answer key

Constant of Proportionality
Find the constant of proportionality(k) for each linear relationship.
2
= 44 2) 20 = 90

1)

k= 2
k = 22 9

3) 56 = 32


4) 2 – 62 = 0

k= 4
7 k = 31
9 35
–1=0 = 25

5) 6)
108

k= 5
k = 12 7
7
=1

7) –144 + 3 = 0 8)
42

k = 48 k=6

9) 110 = 11

10) 65 = 13

1
k=
k = 10 5

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 Answer key

Constant of Proportionality - Table

Determine the constant of proportionality(k) for each table and write the proportional
relationship between and .

1) 2)
6 18 36 16 14 21 28 42

3 9 18 8 6 9 12 18

1 1 3 3
k= ; =

k= ; =

2 2 7 7

3) 4)
7 4 5 8 12 7 6 5

63 36 45 72 60 35 30 25

k=9 ; =9

k=5 ; =5

5) 6)
16 24 32 40 35 30 20 45

10 15 20 25 28 24 16 36

5 5 4 4
k= ; =

k= ; =

8 8 5 5

7) 8)
3 5 7 9 4 9 13 17

18 30 42 54 8 18 26 34

k=6 ; =6

k=2 ; =2

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 Answer key

Constant of Proportionality - Table

The values of and are proportional. Determine the constant of proportionality(k)
and find the missing values.

1) 2)
4 2 3 6 40 20 5 35

40 20 30 60 24 12 3 21

k= 3
k = 10 5

3) 4)
8 7 3 13 56 21 14 28

32 28 12 52 8 3 2 4

k= 1
k=4 7

5) 6)
9 6 12 18 14 12 10 13

6 4 8 12 98 84 70 91

k= 2
3 k=7

7) 8)
20 15 25 50 21 19 18 24

16 12 20 40 63 57 54 72

k= 4
5 k=3

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 Answer key

Solving Proportions

Solve each proportion.

25 10 90 w
1) = 2) =
y 6 80 72

y = 15 w = 81

h 4 6 12
3) = 4) =
6 24 5 2z

h=1 z=5

72 r u 16
5) = 6) =
56 7 21 84

r=9 u=4

12 36 5 8
7) = 8) =
24 8k b 48

k=9 b = 30

100 75 7 x
9) v = 6 10) =
5 20

v=8 x = 28

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 Answer key

Solving Proportions

Solve each proportion.

84 22 u 49
1) = 2) =
7 5w 5 65

11 49 10
w= u= or 3
30 13 13

3 35 29 r
3) = 4) =
a 16 18 2

48 13 29 2
a= or 1 r= or 3
35 35 9 9

h 4 71 96
5) = 6) =
8 9 v 3

32 5 71 7
h= or 3 v= or 2
9 9 32 32

1 t 86 5
7) = 8) =
12 31 9 c

31 7 45
t= or 2 c=
12 12 86

51 8 4d 7
9) = 10) =
27 s 6 48

72 4 7
s= or 4 d=
17 17 32

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 Answer key

Solve each proportion.

1.8 0.9 64.8 w

1) = 2) =
b 41.4 5.4 6.3

b = 82.8 w = 75.6

9.1 8.4 y 77.5

3) = 4) =
54.6 v 1.2 2.5

v = 50.4 y = 37.2

h 46.5 0.8 1.3

5) = 6) =
3.7 9.3 48.8 m

h = 18.5 m = 79.3

94.6 u 8.3 7.2

7) = 8) =
8.6 7.7 d 14.4

u = 84.7 d = 16.6

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 Answer key

Solving Proportions - Algebraic Expressions

Solve each proportion.

54 u – 13 8 + 5x 6
1) = 2) =
18 2 21 42

u = 19 x = –1

9r – 38 20 65 13
3) = 4) =
4 5 7 + 2v 3

r=6 v=4

4 7c + 45 9 2
5) = 6) =
2 26 72 h – 19

c=1 h = 35

7 63 5 11
7) = 8) =
6 4z + 6 10 – g 88

z = 12 g = –30

© mathworksheets4kids.com –15–
 Answer key

Solving Proportions - Algebraic Expressions

Solve each proportion.

3t + 9 12 2q + 4 12q
1) = 2) =
2t + 3 7 5 15

t=9 q=2

6 2 2h 8
3) = 4) =
7s + 2 2s + 3 h–1 3

s=7 h=4

9 7 m – 10 m
5) = 6) =
9b 8b – 3 4 3

b=3 m = –30

7 6 13 26
7) = 8) =
8–u 11 – u 2x 3x + 12

u = 29 x = 12

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 Answer key

Solving Proportions
1) A team of nine artists created wall murals in 18 classrooms at a constant rate.
How many classrooms can a team of 15 artists paint?

30 classrooms

2) Joe spent $35.40 to fill 15 gallons of gas in his minivan. How much does 6
gallons of gas cost?

$14.16

3) A pitcher of mocktail contains 8 cups of pineapple juice and 2 cups of orange

juice. How many cups of orange juice will be required to make a mocktail with
12 cups of pineapple juice?

3 cups of orange juice

4) Laura buys a pack of 24 blueberry muffins that has a total of 1,536 calories.
What is her calorie intake, if she ate 3 muffins for breakfast?

192 calories

5) Yvonne buys 6 cans of diced tomatoes that weigh a total of 87 oz. Find the
weight of 5 cans of diced tomatoes.

72.5 oz of diced tomatoes

6) Ed spends 21 hours practicing drums over a fortnight. At that rate, how much
time will he spend on practicing drums over a 7 week period?

73.5 hours

© mathworksheets4kids.com –17–
 Answer key

Write the rate and unit rate for each phrase given below.
1) 600 fl.oz orange juice in 6 bottles
600 fl.oz of orange juice
Rate : 6 bottles

Unit Rate : 100 fl.oz of orange juice per bottle

2) 8 umbrellas cost $96

$96
Rate : 8 umbrellas

Unit Rate : $12 per umbrella

3) Mow 4 backyards in 2 days

4 backyards
Rate : 2 days

Unit Rate : 2 backyards mowed per day

4) 45 mozzarella sticks in 9 serving plates

45 mozzarella sticks
Rate : 9 serving plates

Unit Rate : 5 mozzarella sticks per serving plate

5) 48 seashells in 3 bags
48 seashells
Rate : 3 bags

Unit Rate : 16 seashells per bag

6) 75 muffins in 5 batches
75 muffins
Rate : 5 batches

Unit Rate : 15 muffins per batch

© mathworksheets4kids.com –18–
 Answer key

1) Dennis bought 24 tennis balls packed equally in 8 sets. How many tennis balls
does each set contain?

3 tennis balls/set

2) Katrina and her friends ordered for 4 pizzas at a local bistro. What is the cost
of one pizza, if they were charged $48?

$12/pizza

3) Lucy, a caricaturist drew 28 sketches of kids at a birthday event in a total of

224 minutes. Find the time spent to sketch one caricature.

8 minutes/caricature

4) Elizabeth took up an online typing test. She managed to type in 585 words in
9 minutes. How many words did she type per minute?

65 words/minute

5) Helen clocked in 150 hours of work over a period of 25 days in November. How
many hours of work did she put in per day?

6 hours/day

6) Emma poured 40 fl.oz of grape juice equally into 5 cups. How much grape
juice does each cup contain?

8 fl.oz of grape juice/cup

© mathworksheets4kids.com –19–
 Answer key

1) A retailer manages to sell 120 food processors in 6 days. If they were sold at a
constant rate, how many of them were purchased in 4 days ?

20 food processors/day ; 80 food processors

2) Vanessa, a dressmaker requires 49 yards of fabric to stitch 7 evening gowns.

If she needs to stitch up 13 such gowns, how many yards of fabric will Vanessa
need?

7 yards of fabric/gown ; 91 yards of fabric

3) Deal-o-deals offers a pack of 4 solar-powered lights for $16. What amount will
a customer pay on the purchase of 24 such lights?

$4/light ; $96

4) Diana completes 205 jumping jacks in 5 minutes at a constant rate. How many
jumping jacks did she accomplish in 2 minutes?

41 jumping jacks/minute ; 82 jumping jacks

5) Ben and his friend, Jack went to catch the latest flick at the nearest movie
theater. They spent $12 for 2 buckets of popcorn. Find the cost for 7 buckets
of popcorn.

$6/bucket of popcorn ; $42

6) A publishing company managed to sell 196 copies of a new book in one week.
If they were sold a constant rate, how many books did they sell in 5 days?

28 books/day ; 140 books

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