Name: Date: Lesson 4.2 Equivalent Ratios
Express each fraction as two equivalent fractions using multiplication.
1.
4
5
2.
7
12
Express each fraction as two equivalent fractions using division.
3.
16
24
4.
27
135
Find the unknown numerator or denominator in each pair of equivalent
fractions.
3
5
8
7.
7
12
5
6.
7
49
2
5
9
8
8.
Express each fraction in simplest form.
9.
92
26
91
10.
51
85
54
5
32
36
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5.
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Name: Date: Complete.
Example
a)
The ratio of the number of cups to the number of teaspoons is
4
:
8
2
groups of cups
.
b)
4
groups of teaspoons
The ratio of the number of groups of cups to the number of groups
2
of teaspoons is
:
4
.
c)
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1
2
group of cups
groups of teaspoons
The ratio of the number of groups of cups to the number of groups of teaspoons
is
1
:
4
The ratios
:
are equivalent ratios.
2
.
8
,
2
:
4
, and
1
:
2
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Name: Date: 11. a)
The ratio of the number of stones to the number of sticks is
:
.
b)
groups of stones
groups of sticks
The ratio of the number of groups of stones to the number of groups
of sticks is
:
.
groups of stones
groups of sticks
The ratio of the number of groups of stones to the number of groups
of sticks is
The ratios
:
are equivalent ratios.
94
:
.
,
:
, and
:
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c)
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Name: 12. a)
Date: 42 stones : 18 sticks
Divide into groups of 2.
groups of 2 :
b)
groups of 2
42 stones : 18 sticks
Divide into groups of 3.
groups of 3 :
c)
groups of 3
42 stones : 18 sticks
Divide into groups of 6.
groups of 6 :
The ratios
:
and
groups of 6
,
:
:
,
:
,
are equivalent ratios.
Express each ratio in simplest form.
Example
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16 : 24
4
8
5
4
2
:
3
8
To express a ratio in simplest
form, divide each term by
their greatest common
factor. In this example, 8 is
the greatest common factor
of 16 and 24.
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Name: 13.
14.
15 : 39
4
4
60 : 36
4
4
:
5
Date: 5
:
15. 12 : 30 5
:
16. 78 : 52 5
:
17. 81 : 45 5
:
18. 56 : 98 5
:
Express each ratio in simplest form.
Example
9 L : 300 mL
9, 000
mL :
5
9, 000
:
300
5
9, 000
4
300
5
30
:
mL
Write the ratio without units.
Then simplify.
:
5
4
5
:
4
300
1
g:
5
300
:
g
:
4
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19. 400 g : 2 kg 5
96
300
9 L : 300 mL 5
Express the quantities in the
same unit. Think:
1 L 5 1,000 mL
9 L 5 9,000 mL
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Name: 20. 60 cm : 12 m 5
:
22. 5 lb : 48 oz 5
:
Date: 21. 27 in. : 3 ft 5
23. 100 s : 7 min 5
:
:
State whether each pair of ratios are equivalent.
Example
6 : 7 and 18 : 21
5 : 20 and 4 : 1
Yes
No
6 : 7 and 18 : 21 are equivalent
ratios as both can be expressed
in simplest form as 6 : 7.
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5 : 20 is 1 : 4 in simplest form.
1 : 4 is not the same ratio as
4 : 1. So 5 : 20 and 4 : 1 are not
equivalent ratios.
24. 5 : 10 and 13 : 26
25. 2 : 3 and 3 : 9
26. 36 : 60 and 6 : 10
27. 81 : 27 and 15 : 5
28. 12 : 17 and 17 : 12
29. 2 : 5 and 50 : 20
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Name: Date: Use multiplication to find three ratios equivalent to each given ratio.
Example
5:6
5:6
3
5:6
2
5
2
3
10
:
3
12
3
4
5
4
3
20
:
18
:
Multiply each term of a ratio
by the same number to find
equivalent ratios.
5:6
3
15
5
3
3
24
10 : 12
5 : 6,
are equivalent ratios.
,
15
:
18
, and
20
24
:
30. 3 : 8
3:8
3:8
5
3
3
:
5
:
3:8
3
3
5
:
3 : 8,
:
are equivalent ratios.
98
,
:
, and
:
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3
3
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Name: Date: 31. 11 : 9
32. 12 : 7
Use division to find all the whole number ratios equivalent to each given ratio.
Example
18 : 24
18 : 24
18 : 24
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4
2
5
2
4
9
:
3
4
12
5
18 : 24
4
6
5
3
:
9
18 : 24,
:
are equivalent ratios.
6
:
8
Divide the terms of a ratio
by their common factors to
find equivalent ratios.
6
4
3
4
4
12
,
6
:
8
, and
3
:
4
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Name: Date: 33. 30 : 36
30 : 36
30 : 36
4
4
5
4
4
:
:
5
30 : 36
4
4
5
:
30 : 36,
:
equivalent ratios.
,
:
, and
:
are
35. 60 : 32
100
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34. 48 : 54
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Name: Date: Find the missing term in each pair of equivalent ratios.
Example
3 : 10 5
: 20
3 : 10
3
2
5
3
6
2
To find the missing term, first find
the multiplying factor. In this case,
it is 20 4 10 5 2. Then multiply
the first term by the multiplying
factor. 3 3 2 5 6.
: 20
28 : 16 5 7 :
28 : 16
4
4
4
57:
4
To find the missing term, first
find the common factor. In this
case, it is 28 4 7 5 4. Then divide
the second term by the common
factor. 16 4 4 5 4.
4
36. 36 : 72 5 9 :
37. 5 : 2 5
: 16
36 : 72
4
4
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5:2
59:
38. 8 : 9 5
40. 2 : 5 5 18 :
: 27
3
3
: 16
5
39. 42 : 24 5 7:
41. 48 : 90 5
: 15
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Name: Date: Solve.
Example
A fruit seller packs apples and oranges into baskets. The number of apples
and the number of oranges is the same for all the baskets. The table shows the
number of fruits in the baskets. Complete the table.
Number of Baskets
Number of Apples
Number of Oranges
1
5
2
2
10
4
3
15
6
…
…
…
10
50
20
How many oranges are packed into 1 basket?
b)
Express the ratio of the number of apples to the number of oranges
oranges
5:2
10
c)
How many apples are packed into 2 baskets?
d)
How many oranges are packed into 3 baskets?
e)
How many apples and oranges are packed into 10 baskets?
50
apples and
20
oranges
6
apples
oranges
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in simplest form.
102
2
a)
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Name: Date: 42. Sam used beads to make bracelets. Each bracelet has the same number of red
beads and yellow beads. The table below shows the number of beads used to
make the bracelets. Complete the table.
Number of
Bracelets
Number of
Red Beads
Number of
Yellow Beads
16
30
…
…
1
2
3
…
12
a)
How many red beads are used in 1 bracelet?
red beads
b)
How many yellow beads are used in 1 bracelet?
yellow beads
c)
Express the ratio of the number of red beads to the number of yellow beads
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in simplest form.
d)
How many red beads are used in 3 bracelets?
red beads
e)
How many yellow beads are used in 3 bracelets?
yellow beads
f)
How many red beads are used in 12 bracelets?
red beads
g)
How many yellow beads are used in 12 bracelets?
yellow beads
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Name: Date: 43. The table below shows the number of hours Alex spends on two activities each
day. The number of hours he spends on each activity each day is the same.
Complete the table.
Number of Days
Number of Hours
Spent on Reading
Number of Hours
Spent on Exercising
1
3
2
2
3
9
…
…
…
14
a)
How many hours does Alex spend on reading in two days?
hours
b)
How many hours does Alex spend on exercising in three days?
c)
Express the ratio of the number of hours Alex spends on reading to the
number of hours he spends on exercising in simplest form.
d)
How many hours does Alex spend on reading in 14 days?
hours
e)
How many hours does Alex spend on exercising in 14 days?
hours
104
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hours
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