Sample Test

Concept 45: Simplify Fractions

Instructions:

A fraction that is reducible can be reduced by dividing both the numerator and denominator by a common factor.
To reduce a fraction to its lowest terms quickly, divide the numerator and the denominator by their Greatest Common Factor, GCF
Use divisibility rules to help you find factors.
Example: Using GCF
48 ÷ 12 = 4

180 ÷ 12 15
If you need to calculate the GCF use prime factorization.
Perform a prime factorization on each number using a factor tree.
Write the prime numbers in ascending order on top of each other.
Cross out the numbers that are the same for the numerator and the denominator.
Multiply across any numbers that are left.
Example: Using prime factorization

48	=	2	⋅	2	⋅	2	⋅	2	⋅	3	=	4
180	=	2	⋅	2	⋅	3	⋅	3	⋅	5	=	15

Q1

Complete the factor trees.
Write the prime factorization of the numerator and the denominator.
Cancel the like terms
Write the fraction in simplest terms.

20

/ \

25

/ \

20	=		=
25	=		=

Q2

Complete the factor trees.
Write the prime factorization of the numerator and the denominator.
Cancel the like terms
Write the fraction in simplest terms.

54

/ \

75

/ \

54	=		=
75	=		=

Q3

Write the prime factorization of the numerator and the denominator. Cancel the like terms and finally, write the fraction in simplest terms.

60	=		=
75	=		=

Q4

Write the prime factorization of the numerator and the denominator. Cancel the like terms and finally, write the fraction in simplest terms.

9	=		=
15	=		=

Q5

Write the prime factorization of the numerator and the denominator. Cancel the like terms and finally, write the fraction in simplest terms.

4	=		=
10	=		=

Q6

Write the prime factorization of the numerator and the denominator. Cancel the like terms and finally, write the fraction in simplest terms.

9	=		=
27	=		=

Q7

Write the prime factorization of the numerator and the denominator. Cancel the like terms and finally, write the fraction in simplest terms.

30	=		=
45	=		=

Q8

Write the prime factorization of the numerator and the denominator. Cancel the like terms and finally, write the fraction in simplest terms.

10	=		=
15	=		=

Q9

Write the fraction in lowest terms

	9
	30

Q10

Reduce the fraction

	20
	30

[END OF QUESTIONS]

Answers:

[Q1] 4/5 [Q2] 18/25 [Q3] 4/5 [Q4] 3/5 [Q5] 2/5 [Q6] 1/3 [Q7] 2/3 [Q8] 2/3 [Q9] 3/10 [Q10] 2/3