﻿ Equivalent Fractions Worksheet - Page 4 | Problems & Solutions

# Equivalent Fractions Worksheet - Page 4

Equivalent Fractions Worksheet
• Page 4
31.
Find two fractions equivalent to $\frac{12}{48}$using common factors.
 a. $\frac{5}{16}$ , $\frac{3}{12}$ b. $\frac{4}{16}$ , $\frac{3}{12}$ c. $\frac{4}{16}$ , $\frac{4}{12}$ d. $\frac{5}{16}$ , $\frac{4}{12}$

#### Solution:

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

Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
[Write the factors for 48.]

The common factors of 12 and 48 are 3 and 4.

12 / 48 = 12÷3 / 48÷3 = 4 / 16
[Divide the numerator and the denominator by 3.]

12 / 48 = 12÷4 / 48÷4 = 3 / 12
[Divide the numerator and the denominator by 4.]

The two fractions equivalent to 12 / 48 are 4 / 16 and 3 / 12.

32.
Name the fraction equivalent to $\frac{9}{19}$.
 a. $\frac{38}{18}$ b. $\frac{17}{38}$ c. $\frac{18}{38}$ d. $\frac{18}{39}$

#### Solution:

= 1838
9×219×2
[Multiply the numerator and denominator by the same non-zero number.]

The equivalent fraction of 9 / 19 is 18 / 38

33.
Simplify the fraction $\frac{12}{24}$ and choose an equivalent fraction of the simplified fraction.
 a. $\frac{26}{13}$ b. $\frac{13}{26}$ c. $\frac{14}{26}$ d. $\frac{13}{27}$

#### Solution:

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

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

GCF of 12 and 24 is 12.
[Select the greatest common factor.]

12 / 24 = 12÷12 / 24÷12 = 1 / 2
[Divide numerator and denominator by their GCF 12.]

1 / 2 = 1×132×13 = 13 / 26
[Multiply numerator and denominator by the same nonzero number.]

The equivalent fraction of simplified 12 / 24 is 13 / 26.

34.
In a class of 80 students, 30 students went on a picnic. What fraction of students went on picnic?
 a. $\frac{3}{8}$ b. $\frac{5}{10}$ c. $\frac{4}{9}$ d. None of the above

#### Solution:

The fraction of students on the picnic = 30 / 80 .

30 = 1, 2, 3, 5, 6, 10, 15, 30 and
80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
[Write factors of the numerator and the denominator.]

GCF of 30 and 80 is 10.
[Select the greatest common factor.]

30 ÷ 1080 ÷ 10 = 38
[Divide the numerator and the denominator by their GCF, 10.]

3 / 8 th of the class went on picnic.

35.
A manufacturing company produces 152 cars per month. If 40 of them are red in color and 20 of them are blue, then what fraction of cars are blue when compared to red ones?
 a. $\frac{1}{2}$ b. $\frac{2}{3}$ c. $\frac{4}{5}$ d. $\frac{3}{4}$

#### Solution:

The fraction of blue colored cars to the red colored cars = 20 / 40

20 = 1, 2, 4, 5, 10, 20 and
40 = 1, 2, 4, 5, 8, 10, 20, 40
[Write factors of the numerator and the denominator.]

GCF of 20 and 40 is 20
[Select the greatest common factor.]

20÷2040÷20 = 12
[Divide numerator and denominator by GCF 20.]

The fraction of blue colored cars to the red colored cars is 1 / 2 .

36.
Find a number that divides the numerator and the denominator of the fraction $\frac{10}{30}$ to get $\frac{1}{3}$.
 a. 5 b. 10 c. 20 d. 15

#### Solution:

10 = 1 × 10
[Write 10 as a multiple of 1.]

30 = 3 × 10
[Write 30 as a multiple of 3.]

The number that divides the numerator and denominator of 10 / 30 to get 1 / 3 is 10.

37.
Identify an equivalent fraction for the model.

 a. $\frac{5}{3}$ b. $\frac{3}{5}$ c. $\frac{18}{10}$ d. $\frac{10}{18}$

#### Solution:

The fraction modeled by given figure is 5 / 9.
[5 out of 9 squares are shaded.]

5 / 9 = 5×29×2 = 10 / 18
[Multiply numerator and denominator by the same non-zero number.]

The equivalent fraction of the model is 10 / 18.

38.
Which among the following choices has the two equivalent fractions of $\frac{3}{4}$?
 a. $\frac{7}{8}$, $\frac{10}{12}$ b. $\frac{8}{9}$, $\frac{11}{12}$ c. $\frac{6}{8}$, $\frac{9}{12}$ d. None of the above

#### Solution:

34 = 3x24x2 = 68
34 = 3x34x3 = 912
[Multiply the numerator and the denominator by a same number.]

The two equivalent fractions of 3 / 4 are 6 / 8 and 9 / 12.

39.
The profit Tommy got last year from his shop was $298 million. He spent$18 million out of the profit for the interior decoration of his shop. Find the fraction of profit spent on decorating the shop.
 a. $\frac{149}{9}$ b. $\frac{10}{149}$ c. $\frac{9}{149}$ d. $\frac{8}{149}$

#### Solution:

The fraction of profit money spent on decorating the shop = 18 / 298

Factors of 18 are 1, 2, 3, 6, 9, 18 and the factors of 298 are 1, 2, 149, 298.
[Write the factors for numerator and denominator.]

GCF of 18 and 298 is 2.
[Select the greatest common factor.]

18÷2 / 298÷2 = 9 / 149
[Divide numerator and denominator by GCF 2.]

So, the fraction of profit spent on decorating the shop is 9 / 149 .

40.
Find two fractions equivalent to the fraction $\frac{12}{18}$.
 a. $\frac{6}{9}$, $\frac{4}{6}$ b. $\frac{6}{4}$, $\frac{9}{6}$ c. $\frac{6}{6}$, $\frac{4}{9}$ d. None of the above

#### Solution:

Factors of 12: 1, 2, 3, 4, 6, 12.

Factors of 18: 1, 2, 3, 6, 9, 18.

The common factors of 12 and 18 are 1, 2, 3, 6.

12÷218÷2 = 69
[Divide the numerator and the denominator by the common factors and simplify.]

12÷318÷3 = 46
[Divide the numerator and the denominator by the common factors and simplify.]

The two fractions equivalent to 12 / 18 are 6 / 9 and 4 / 6.