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Equivalent Fractions Worksheet - Page 9

Equivalent Fractions Worksheet
  • Page 9
 81.  
Are the fractions represented by the figures equivalent?


a.
Yes
b.
No


Solution:

In the first figure 1 out of 3 parts are shaded. So, the fraction represented by it is 1 / 3.

In the second figure 2 out of 6 parts are shaded. So, the fraction represented by it is 2 / 6 and in the third figure 3 out of 9 parts are shaded and the fraction represented by it is 3 / 9.

Simplify 2 / 6 and 3 / 9 to lowest term.

2 / 6= 2×1 / 2×3 and 3 / 9 = 3×1 / 3×3

2 / 6 = 3 / 9 = 1 / 3.

The value of the fractions in all the three situations is the same.

So, the fractions represented by the figures are equivalent.


Correct answer : (1)
 82.  
Pick the fractions equivalent to 12 15.
ABCD
4/540/508/15400/500

a.
A, B and D
b.
B, C and D
c.
A and C
d.
None of the above


Solution:

An equivalent of the fraction is obtained by multiplying or dividing the numerator and the denominator of the fraction with a common number.

A is obtained by dividing the numerator and the denominator of 12 / 15 by 3.

B is obtained by dividing the numerator and the denominator of 12 / 15 by 3 and multiplying them with 10.

Similarly, D is obtained by dividing the numerator and the denominator of 12 / 15 by 3 and multiplying them with 100.

In C the denominators are equal, but the numerators are different. So it is not an equivalent fraction of 12 / 15.

A, B and D are equivalent fractions of 12 / 15


Correct answer : (1)
 83.  
Which of the figures represent equivalent fractions?


a.
(a) A, B, C and D
b.
(a) A, and B (b) C, D and E
c.
(a) A, B and E (b) C and D
d.
(a) A, B and E (b) C, D and E


Solution:

In the picture A and B represent the fraction 2 / 4.

2 / 4 = 1 / 2
[Simplify to the lowest term.]

E represents 1 / 2.

A, B and E represent 1 / 2, and are equivalent.

In C and D, 1 out of 4 parts is shaded. So, both C and D represent 1 / 4 and are equivalent.


Correct answer : (3)
 84.  
Are the fractions represented by the figures equivalent?

a.
Yes
b.
No


Solution:

In the first figure 1 out of 2 parts are shaded. So, it represents the fraction 1 / 2.

In the second figure also 1 out of 2 parts is shaded. So, it also represent the fraction 1 / 2.


Though the figures and their sizes are different they both represent the same fraction 1 / 2.

So, the fractions represented by the figures are equivalent.


Correct answer : (1)
 85.  
Pick the fractions equivalent to 2 3.
ABCD
4/910/15


Solution:

An equivalent of the fraction is obtained by multiplying or dividing the numerator and the denominator of the fraction with a common number.

We cannot get A by multiplying the numerator and the denominator of 2 / 3 by any number.

So, A is not an equivalent fraction of the fraction.

We get B by multiplying the numerator and the denominator of 2 / 3 by 5

= 2×5 / 3×5 = 10 / 15

We cannot get C by multiplying the numerator and the denominator of 2 / 3 by any number.

So, C is not an equivalent fraction of the fraction.

We get D by multiplying the numerator and the denominator of 2 / 3 by 6

= 2×6 / 3×6 = 12 / 18

So, choice A is correct.


Correct answer : (0)
 86.  
Are 9 12and 15 20 equivalent?
a.
Yes
b.
No


Solution:

Divide the numerator and denominator of 9 / 12 by 3. The resultant fraction is 3 / 4.

Divide the numerator and denominator of 15 / 20 by 5. The resultant fraction is 3 / 4.

Both 9 / 12 and 15 / 20 result in the same lowest term when simplified. So, they are equivalent fractions.


Correct answer : (1)
 87.  
Find x in the expression.
1 = x 7
a.
7
b.
1
c.
Cannot be determined


Solution:

7 / 7 = 1. So the missing numerator, x = 7.


Correct answer : (1)
 88.  
Solve 3 4 = 9 z.
a.
4
b.
48
c.
12
d.
9


Solution:

Given, the fractions are equivalent. So, the numerator and the denominator of the first fraction are multiplied or divided by a common number to get its equivalent fraction.

The numerator in the resultant fraction is a multiple of the first fraction. 9 = 3 × 3.

As the numerator of the resultant fraction is multiplied by 3, the denominator should also be multiplied by 3.

The denominator of the resultant fraction = 4 × 3 = 12.


Correct answer : (3)
 89.  
Are 5 6 and 15 24 equivalent?
a.
Yes
b.
No


Solution:

In 5 / 6 and 15 / 24, the numerator 15 is a multiple of 5 and the denominator 24 is a multiple of 6.

But both the numerator and the denominator are not multiplied by the same number. 15 = 5 × 3 and the denominator 24 = 6 × 4.

5 / 65×3 / 6×4

5 / 615 / 24

So, the fractions are not equivalent.


Correct answer : (2)
 90.  
Can the fractions represented by the shaded parts of the two figures be called equivalent?


a.
Yes
b.
No


Solution:

The number of grids in the Figure 1 is 8.

The number of shaded grids in the Figure 1 is 4.

The fraction of the shaded part of the Figure 1 = The number of shaded gridsThe total number of grids.

= 48
[Substitute the values.]

= 12
[Divide.]

The number of grids in the Figure 2 is 12.

The number of shaded grids in the Figure 2 is 6.

The fraction of the shaded part of the Figure 2 = The number of shaded gridsThe total number of grids.

= 612
[Substitute the values.]

= 12
[Divide.]

The fractions of the shaded parts in both the Figures are equivalent.


Correct answer : (1)
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