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 |

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.]

[Divide 48 and 192 by their GCF, 48.]

The simplified fraction of

Correct answer : (3)

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 |

[Write prime factorizations of 40 and 70.]

=

[Cancel the common factors and simplify.]

Correct answer : (3)

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 |

[Divide 3 and 30 by their GCF 3.]

Kelsey used

Correct answer : (2)

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. | $\frac{1}{3}$ |

90 = 10 x 9

[The GCF is 9.]

[Divide numerator and denominator by the GCF.]

The fraction

Correct answer : (2)

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 |

[Original fraction.]

[Write prime factors for numerator and denominator.]

=

[Cancel the common factors and simplify.]

The fraction

Correct answer : (3)

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 |

[Divide 8 and 20 by a common factor.]

The simplified fraction for the students who took the test is

Correct answer : (2)

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 |

18 = 2 × 3 × 3

8 = 2 × 2 × 2

[Write the prime factors of numerator and denominator.]

GCF is 2

[Multiply the common factors.]

[Divide numerator and denominator by the GCF, 2.]

The simplified fraction for students who are of Spanish origin is

Correct answer : (3)

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. | $\frac{1}{2}$ |

[Write prime factors for numerator and denominator.]

=

[Write the fraction in simplest form.]

The fraction

Correct answer : (1)

9.

There are 21 students in 7^{th} 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. | $\frac{16}{21}$ |

14 = 2 × 7

21 = 3 × 7

[Write Prime Factors for 14 and 21.]

[Divide numerator and denominator by the GCF.]

So, the simplest fraction for

Correct answer : (1)

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 |

[Divide numerator and denominator by a common factor.]

[If necessary, divide again by another common factor.]

So, Andy and Jimmy together ate

Correct answer : (3)