Question

How do you simplify $\dfrac{60}{75}$ to lowest terms?

Answer 1

Hint: In this problem we need to simplify the given fraction to lowest terms. We know that a fraction contains a numerator as well as a denominator. So, we will consider the both numerator and denominator in the given fraction separately. Now we will write all the factors of both the numerator and denominator. After that we will write them in the given fraction and cancel the possible factors which are in both numerator and denominator to get the required result.

Complete step by step solution:
Given fraction, $\dfrac{60}{75}$.
Numerator in the above given fraction is $60$.
Denominator in the above given fraction is $75$.
We know that the factors of the numerator $60$ is $1$, $2$, $3$, $4$, $5$, $6$, $10$, $12$, $15$, $20$, $30$, $60$.
We know that the factors if the denominator $75$ is $1$, $3$, $5$, $15$, $25$, $75$.
From the above values we can write the numerator $60$ as $60=15\times 4$.
From the above values we can write the denominator $75$ as $75=15\times 5$.
Substituting these values in the given fraction, then we will get
$\dfrac{60}{75}=\dfrac{15\times 4}{15\times 5}$
Cancelling the term $15$ which is in both numerator and denominator, then we will get
$\Rightarrow \dfrac{60}{75}=\dfrac{4}{5}$

Hence the simplified form of the fraction $\dfrac{60}{75}$ is $\dfrac{4}{5}$.

Note: In the problem they have only asked to simplify the fraction into lowest terms, so we have cancelled the common terms in their factors. You may also write the decimal value of the given fraction. We know that the value of $\dfrac{4}{5}$ is $0.8$. So, we can write the given fraction $\dfrac{60}{75}$ as $0.8$ in decimal value.