Question

Reduce the following fractions to their lowest term

45
54​

Answer 1

Step-by-step explanation:

The below workout with step by step calculation shows how to simplify the fraction 45/54 to its lowest term or simplest form. The below are the two methods used to convert the fraction to its lowest terms.

1. GCD or HCF method .

2. Prime factorization method.

GCD Method :

step 1 Address the formula, input parameters & values.

Input parameters & values:

The given fraction = 45/54

step 2 Find GCD (Greatest Common Factor) for both numerator & denominator.

The GCF for 45 & 54 is 9

step 3 divide the numerator & denominator by GCD 9 and rewrite the fraction

= (45/9) / (54/9)

= 5/6

Thus, 5/6 is the simplified fraction for 45/54 by using the GCD or HCF method.

Prime Factorization Method :

step 1 Address input parameters & values.

Input parameters & values:

The given fraction = 45/54

step 2 Find prime factors for both numerator & denominator and rewrite the fraction in the form of prime factors

Prime factors for 45 = 3 x 3 x 5

Prime factors for 54 = 2 x 3 x 3 x 3

= (3 x 3 x 5) / (2 x 3 x 3 x 3)

step 3 solve & rewrite the fraction

= ( 5)/(2 x 3)

= 5/6

Thus, 5/6 is the simplified fraction for 45/54 by using the prime factorization method.

Answer 2

Given: Given expression is 45/54.

To find: We have to reduce the following fractions to their lowest term.

Solution:

The fraction is 45/54.

To reduce the following fractions to their lowest term we have to determine the HCF of the numerator and denominator.

So, HCF of 45 and 54 will be-

$45 = 5 \times 3 \times 3 \\ 54 = 3 \times 2 \times 3 \times 3$

So, HCF is 9.

Thus dividing the fraction by 9 we get-

$\frac{ \frac{45}{9} }{ \frac{54}{9} } = \frac{5}{6}$

The lowest term of the fraction is 5/6.