# Simplifying Fractions Worksheet

Simplifying Fractions Worksheet
• Page 1
1.
Express the fraction $\frac{48}{192}$ in lowest terms.
 a. $\frac{1}{6}$ b. $\frac{1}{5}$ c. $\frac{1}{4}$ d. None of the above

#### Solution:

48 = 2 × 2 × 2 × 2 × 3
192 = 2 × 2 × 2 × 2 × 2 × 2 × 3
[Write the prime factorizations of numerator and denominator.]

GCF = 48
[Multiply the common factors to get the GCF.]

48192 = 48÷48192÷48 = 14
[Divide 48 and 192 by their GCF, 48.]

The simplified fraction of 48 / 192 is 1 / 4.

2.
There are 70 rooms in a complex. 40 rooms have been leased out to a newspaper office. Write a fraction in its simplest form for the number of rooms leased out to the office.
 a. $\frac{40}{71}$ b. $\frac{5}{9}$ c. $\frac{4}{7}$ d. None of the above

#### Solution:

The fraction of rooms leased out to the office = 40 / 70

[Write prime factorizations of 40 and 70.]

= 47
[Cancel the common factors and simplify.]

4 / 7 of the rooms were leased out to the office.

3.
Kelsey bought 30 lb of fruits to prepare fruit salad. She used 3 lb of fruits to prepare the salad. Identify a fraction in its simplest form for the fruits Kelsey used.
 a. $\frac{4}{15}$ b. $\frac{1}{10}$ c. $\frac{7}{20}$ d. None of the above

#### Solution:

The fraction of the fruits Kelsey used in preparing fruit salad = 3 / 30

3÷330÷3 = 110
[Divide 3 and 30 by their GCF 3.]

Kelsey used 1 / 10 of the fruits to prepare the fruit salad.

4.
Simplify the fraction $\frac{36}{90}$ using the GCF of 36 and 90.
 a. $\frac{4}{11}$ b. $\frac{2}{5}$ c. $\frac{1}{2}$ d. $\frac{1}{3}$

#### Solution:

36 = 4 x 9
90 = 10 x 9
[The GCF is 9.]

36÷9 / 90÷9 = 4 / 10
[Divide numerator and denominator by the GCF.]

The fraction 36 / 90 in simplest form is 4 / 10.

5.
Simplify the fraction $\frac{55}{65}$ using prime factorization.
 a. $\frac{4}{9}$ b. $\frac{1}{2}$ c. $\frac{11}{13}$ d. None of the above

#### Solution:

5565
[Original fraction.]

[Write prime factors for numerator and denominator.]

= 1113
[Cancel the common factors and simplify.]

The fraction 55 / 65 in simplest form is 11 / 13.

6.
In a class of 20 students, 8 took the biology test. What fraction of the students took the test? Write the fraction in its simplest form.
 a. $\frac{5}{2}$ b. $\frac{2}{5}$ c. $\frac{3}{5}$ d. None of the above

#### Solution:

The fraction of students who took the test = 8 / 20

8÷420÷4 = 25
[Divide 8 and 20 by a common factor.]

The simplified fraction for the students who took the test is 2 / 5.

7.
Henry surveyed 18 students and found 8 of them to be of Spanish origin. What fraction of the total students are of Spanish origin? Simplify the fraction using GCF.
 a. $\frac{9}{4}$ b. $\frac{8}{9}$ c. $\frac{4}{9}$ d. None of the above

#### Solution:

Fraction of students who are of Spanish origin = 8 / 18

18 = 2 × 3 × 3
8 = 2 × 2 × 2
[Write the prime factors of numerator and denominator.]

GCF is 2
[Multiply the common factors.]

818 = 8÷218÷2 = 49
[Divide numerator and denominator by the GCF, 2.]

The simplified fraction for students who are of Spanish origin is 4 / 9.

8.
In a conference, 6 out of 16 delegates wore black ties. What fraction of the delegates wore black ties? Simplify the fraction using prime factorization.
 a. $\frac{3}{8}$ b. $\frac{1}{3}$ c. $\frac{4}{9}$ d. $\frac{1}{2}$

#### Solution:

The fraction of delegates who wore black ties = 6 / 16

616 = 2 × 316× 3D=2 × 2 × 2 × 2
[Write prime factors for numerator and denominator.]

= 38
[Write the fraction in simplest form.]

The fraction 6 / 16 in simplest form is 3 / 8.

9.
There are 21 students in 7th grade. Out of them, 14 students went on a picnic. What fraction of the students went on the picnic? Simplify the fraction using GCF.
 a. $\frac{2}{3}$ b. $\frac{16}{23}$ c. $\frac{14}{23}$ d. $\frac{16}{21}$

#### Solution:

The fraction of the students who went on picnic = 14 / 21

14 = 2 × 7
21 = 3 × 7
[Write Prime Factors for 14 and 21.]

14÷721÷7 = 23
[Divide numerator and denominator by the GCF.]

So, the simplest fraction for 14 / 21 is 2 / 3.

10.
A pizza was cut into 27 equal pieces. Andy and Jimmy together ate 18 pieces. What fraction of the pizza did Andy and Jimmy eat? Simplify the fraction.
 a. $\frac{3}{4}$ b. $\frac{2}{4}$ c. $\frac{2}{3}$ d. None of the above

#### Solution:

The fraction of the pizza Andy and Jimmy ate = 18 / 27

18÷327÷3 = 69
[Divide numerator and denominator by a common factor.]

6÷39÷3 = 23
[If necessary, divide again by another common factor.]

So, Andy and Jimmy together ate 2 / 3 of the pizza.