Chapter 6, Problem 3QC

To determine

To calculate: The simplified form of the fraction $\frac{30}{45}$ .

Answer to Problem 3QC

The simplified form of the fraction $\frac{2}{3}$ .

Explanation of Solution

Given information:

The fraction $\frac{30}{45}$ .

Formula used:

A natural number can be written as a product of its prime factors. Prime numbers are those who have one and the number itself as its factors.

Calculation:

Consider the provided fraction $\frac{30}{45}$ .

Factorize the numerator and denominator of the above fraction.

  $30$ is written as product of 2 and 15.

  $45$ is written as product of 3 and 15.

  $\frac{30}{45}=\frac{2\times 15}{3\times 15}$

Strike off the common terms,

  $\frac{30}{45}=\frac{2}{3}$

Observe that 2 and 3 have common factor as 1 only.

Therefore, it cannot be simplified further.

Hence, the simplified form of the fraction is $\frac{2}{3}$ .