﻿ Equivalent Fractions Worksheet - Page 7 | Problems & Solutions

Equivalent Fractions Worksheet - Page 7

Equivalent Fractions Worksheet
• Page 7
61.
Find the value of $n$, if $\frac{n}{4}$ = $\frac{5}{10.}$
 a. 2 b. 1 c. 4 d. 3

Solution:

Factors of 5 are 1, 5.

Factors of 10 are 1, 2, 5, 10.

The common factors are 1, 5.

n4 = 510
[Given expression.]

n4 = 5÷510÷5
[Since it is an equivalent fraction, numerator and denominator are divided by the same number and common factor, 5.]

n4 = 14
[Simplify.]

The value of n is 1.

62.
Ed had 5 toys. He gave 2 toys to his friends. Write the two equivalent fractions for the fraction of the toys left with Ed.
 a. $\frac{3}{15}$and $\frac{4}{20}$ b. $\frac{2}{10}$and $\frac{3}{15}$ c. $\frac{6}{10}$and $\frac{9}{15}$ d. None of the above

Solution:

Number of toys left with Ed = 5 - 2 = 3

The fraction of the toys left with Ed = Number of toys left / Total number of toys

= 35
[Substitute.]

3x25x2 = 610
[Multiply both numerator and denominator by the same non zero number, 2.]

3x35x3 = 915
[Multiply both numerator and denominator by the same non zero number, 3.]

The two equivalent fractions are 6 / 10 and 9 / 15.

63.
Write an equivalent fraction for the model.

 a. $\frac{1}{8}$ b. $\frac{2}{8}$ c. $\frac{6}{8}$ d. None of the above

Solution:

In the model, 3 divisions are shaded out of 4 divisions.

The model represents a fraction of 3 / 4.

The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27.
[Write the first few multiples of 3.]

The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36.
[Write the first few multiples of 4.]

So, the equivalent fractions of 3 / 4 are 6 / 8 , 9 / 12 , 12 / 16 , 15 / 20 , . . . . .

The equivalent fraction for the model is 6 / 8.

64.
Write two equivalent fractions for the model.

 a. $\frac{10}{18}$, $\frac{15}{20}$ b. $\frac{20}{32}$, $\frac{25}{30}$ c. $\frac{20}{32}$, $\frac{25}{40}$ d. None of the above

Solution:

In the model, 5 divisions are shaded out of 8 divisions.

The model represents a fraction of 5 / 8.

Multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45.
[Write the first few multiples of 5.]

Multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72.
[Write the first few multiples of 8.]

The equivalent fractions of 5 / 8 are 10 / 16 , 15 / 24 , 20 / 32 , 25 / 40 , . . . . .

The two equivalent fractions for the model are 20 / 32 and 25 / 40 .

65.
Which of the following fractions represents the simplest form of the fraction $\frac{12}{15}$?
 a. $\frac{1}{5}$ b. $\frac{1}{4}$ c. $\frac{5}{6}$ d. $\frac{4}{5}$

Solution:

A fraction is in simplest form when the greatest common factor of the numerator and the denominator is 1.

1215= 2 × 2 × 315× 2 × 3D=3 × 5
[Write the factors of 12 and 15.]

= 45
[Divide out the common factors.]

The fraction 4 / 5 is in the simplest form. So, the simplest form of the fraction 12 / 15 is 4 / 5.

66.
Find the simplest form of the fraction $\frac{20}{25}$.
 a. $\frac{1}{5}$ b. $\frac{5}{6}$ c. $\frac{1}{4}$ d. $\frac{4}{5}$

Solution:

A fraction is in simplest form when the greatest common factor of the numerator and the denominator is 1.

2025 = 2 × 2 × 525× 2 × 5D=5 × 5
[Write the factors of 20 and 25.]

= 45
[Divide out the common factors.]

The fraction 4 / 5 is in the simplest form. So, the simplest form of the fraction 20 / 25 is 4 / 5.

67.
Reduce the fraction to its simplest form.
$\frac{4}{30}$
 a. $\frac{2}{15}$ b. $\frac{1}{15}$ c. $\frac{3}{16}$ d. $\frac{2}{29}$

Solution:

430 = 2 × 22 × 3 × 5
[Write the factors for the numerator and the denominator.]

= 2 / 15
[Cancel the common factors in the numerator and the denominator.]

2 / 15 is the reduced form of 4 / 30 .

68.
Find the equivalent fraction of $\frac{3}{4}$ with the denominator as 28.
 a. $\frac{21}{28}$ b. $\frac{1}{28}$ c. $\frac{29}{28}$ d. $\frac{27}{28}$

Solution:

Equivalent fraction of a number is obtained by performing the same operation on both the numerator and denominator.

3×74×7 = 2128
To get the number 28 on denominator multiply the numerator and the denominator with 7.

So, the equivalent fraction of 3 / 4 with the denominator as 28 is 21 / 28.

69.
Which of the figures in the picture represent equivalent fractions?

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

Solution:

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

24= 12
[Simplify to the lowest term.]

E represents 1 / 2.

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

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

70.
Pick fractions equivalent to $\frac{4}{5}$.
$f$1$f$2$f$3$f$4
8/158/10

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 f1 by multiplying the numerator and the denominator of 4 / 5 by any number.

So, f1 is not an equivalent fraction of the given fraction.

= 4×25×2 = 810
We get f2 by multiplying the numerator and the denominator of 4 / 5 by 2.

We cannot get f3 by multiplying the numerator and the denominator of 4 / 5 by any number.

So, f3 is not an equivalent fraction of the given fraction.

= 4×35×3 = 1215
We get f4 by multiplying the numerator and the denominator of 4 / 5 by 3.

So, f2 and f4 are the fractions equivalent to the fraction 4 / 5 .

So, choice A is correct.

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