Question

Check whether the given fractions are equivalent:
$\dfrac{5}{9},\dfrac{30}{54}$

Answer 1

Hint: 1. Find the common factor for the numerator and denominator for the fraction $\dfrac{30}{54}$ to convert it in simplest form.
2. Another approach is to do the cross multiplication of a given fraction and check if L.H.S is equal to the R.H.S, the given fractions are equivalent.
Complete step-by-step answer:
Approach 1:
Given fraction are:
$\dfrac{5}{9},\dfrac{30}{54}$
The highest common factor of fraction $\dfrac{30}{54}$ is 6.
Hence on simplification(By dividing numerator and denominator by 6), we get
$\dfrac{30}{54}=\dfrac{5}{9}$
Hence given fractions are equivalent fractions.
Approach 2:
To check we make both fraction equal and cross multiply
$\dfrac{5}{9}=\dfrac{30}{54}$
$\Rightarrow 5\times 54=30\times 9$
$\Rightarrow 270=270$
Since this is true
$\therefore \dfrac{5}{9},\dfrac{30}{54}$ are the equivalent fractions.
Note: 1. Equivalent fractions are the fractions with different numerators and denominators that represent the same value.
2. The highest common factor is the highest number that divides exactly two or more numbers. It is the greatest number for simplifying fractions.