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Equivalent Fractions Worksheet - Page 5

Equivalent Fractions Worksheet
  • Page 5
 41.  
Express the fraction 30 70 in its simplest form.
a.
- 37
b.
7 3
c.
3 7
d.
None of the above


Solution:

Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30.
[Write factors for numerator.]

Factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70.
[Write factors for denominator.]

GCF of 30 and 70 is 10.
[Select the greatest common factor.]

30 / 70 = 30 ÷ 1070 ÷ 10 = 3 / 7
[Divide numerator and denominator by GCF 10.]

The simplest form of the fraction 30 / 70 is 3 / 7.


Correct answer : (3)
 42.  
With what number would you multiply the numerator and the denominator of the fraction 7 13 to get 77 143 ?
a.
12
b.
11
c.
10
d.
None of the above


Solution:

77 = 7 × 11 and 143 = 13 × 11
[Express 77 as a multiple of 7 and 143 as a multiple of 13.]

The numerator and denominator of 7 / 13 must be multiplied by 11 to get 77 / 143 .


Correct answer : (2)
 43.  
Using common factors, find two fractions equivalent to 16 24.
a.
12 4 , 8 6
b.
8 4 , 12 6
c.
8 12 , 4 6
d.
None of the above


Solution:

Factors of 16 are 1, 2, 4, 8, 16.
[Write the factors for 16.]

Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.
[Write the factors for 24.]

The common factors for 16 and 24 are 1, 2, 4, 8.

1624 = 16÷224÷2 = 812
[Divide numerator and denominator by the common factors and then simplify.]

1624 = 16÷424÷4 = 46
[Divide numerator and denominator by the common factors and then simplify.]

The two fractions equivalent to 16 / 24 are 8 / 12 and 4 / 6 .


Correct answer : (3)
 44.  
Find two equivalent fractions of 10 40.
a.
1 4 and 2 8
b.
none of these
c.
1 4 and 1 8
d.
1 4 and 12 8


Solution:

10 / 40 = 10÷1040÷10 = 1 / 4
[Divide numerator and denominator by their GCF 10.]

1 / 4 = 1×24×2 = 2 / 8
[Multiply numerator and denominator of 1 / 4 by same non-zero number.]

The two equivalent fractions of 10 / 40 are 1 / 4 and 2 / 8.


Correct answer : (1)
 45.  
Josh has 16 chocolates and he gave 7 of them to Ashley. Choose a fraction that is equivalent to the fraction of the chocolates left with Josh.
a.
19 33
b.
32 18
c.
18 32
d.
None of the above


Solution:

The number of chocolates left with Josh = 16 - 7 = 9

The fraction of the chocolates left with Josh = Remaining chocolatesTotal chocolates = 9 / 16

The equivalent fraction for this is, 9×216×2 = 18 / 32
[Multiply numerator and denominator by same non-zero number.]

The equivalent fraction is 18 / 32.


Correct answer : (3)
 46.  
Find two equivalent fractions of 3 4.
a.
9 12, 15 20
b.
9 13, 16 20
c.
10 12, 15 21
d.
None of the above


Solution:

Multiples of 3 are 3 , 6, 9, 12, 15, 18, 21, 24, 27.
[List a few multiples of 3.]

Multiples of 4 are 4 , 8, 12, 16, 20, 24, 28, 32, 36.
[List a few multiples of 4.]

3x34x3 = 912
[Multiply numerator and denominator by the same number and simplify.]

3x54x5= 1520
[Multiply numerator and denominator by the same number and simplify.]

The two equivalent fractions of 3 / 4 are 9 / 12 and 15 / 20.


Correct answer : (1)
 47.  
In a college election the number of votes polled were 500. Francis got 200 votes. Express the votes that Francis got as a fraction in the simplest form.
a.
3 5
b.
1 2
c.
2 5
d.
None of the above


Solution:

The fraction of votes Francis got = Number of votes Francis got Total number of votes = 200 / 500

200 = 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200
500 = 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500
[Write factors for numerator and denominator.]

G.C.F of 200 and 500 is 100
[Select the greatest common factor.]

200÷100 / 500÷100 = 2 / 5
[Divide numerator and denominator by GCF,100.]

Francis got 2 / 5of the total number of votes polled.


Correct answer : (3)
 48.  
Find the value of x, if x 49and 3 7 are equivalent fractions.
a.
10
b.
49
c.
1
d.
21


Solution:

x49 = 37
[Given expression.]

x49 = (3x7)(7x7)
[Multiply numerator and denominator of 3 / 7 by 7 to make the denominators of the two fractions equal.]

x = 3 x 7
[Take the numerators of the two fractions.]

= 21
[Multiply.]

So, the value of x is 21.


Correct answer : (4)
 49.  
In a game of 35 matches, Josh won 21 matches. What fraction of the matches did Josh win? Choose two equivalent fractions of this fraction.
a.
21 35, 3570 and 542
b.
21 35, 4270 and 35
c.
21 35, 370 and 542
d.
None of the above


Solution:

The fraction of matches Josh won = Number of matches wonTotal number of matches = 21 / 35

The equivalent fractions for this is, 21 × 235 × 2 = 42 / 70
[Multiply numerator and denominator by the same nonzero number.]

21÷7 / 35÷7 = 3 / 5
[Divide numerator and denominator by GCF 7.]

The two equivalent fractions of 21 / 35 are 42 / 70 and 3 / 5


Correct answer : (2)
 50.  
Write an equivalent fraction for the model.

a.
3 9
b.
6 4
c.
8 16
d.
None of the above


Solution:

In the model, 4 divisions are shaded out of 8 divisions.

The model represents the fraction 4 / 8.

Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36. . .

Multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72. . .

The equivalent fractions for 4 / 8 are 8 / 16, 12 / 24, 16 / 32, . . . .

So, the equivalent fraction for the model is 8 / 16.


Correct answer : (3)

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