Question

Check whether the given fractions are equivalent : (a) $\frac{5}{9}$, $\frac{30}{54}$ , (b) $\frac{3}{10}$, $\frac{12}{50}$ , (c) $\frac{7}{13}$, $\frac{5}{11}$

Answer 1

(a) $\frac{5}{9}$, $\frac{30}{54}$

Dividing the fraction $\frac{30}{54}$ by $\frac{6 }{ 6}$, we get $\frac{30 }{ 54} ÷ \frac{6 }{ 6}$

= $\frac{5 }{ 9}$.

∴ Dividing both the numerator and denominator of $\frac{30}{54}$ by $6$ simplifies it to $\frac{5}{9}$, demonstrating their equal representation.

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(b) $\frac{3}{10}$, $\frac{12}{50}$

Dividing the fraction $\frac{12}{50}$ by $\frac{ 2 }{ 2}$, we get

$\frac{12}{50}$ ÷ $\frac{ 2 }{ 2}$ = $\frac{6 }{ 25}$.

∴ Simplifying both $\frac{3}{10}$ and $\frac{12}{50}$ reveals their true identities: $\frac{3}{10}$ remains itself, while $\frac{12}{50}$ transforms into$\frac{6 }{ 25}$.
This proves they aren't equal "fractions of wholes".

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(c) $\frac{7}{13}$ , $\frac{5}{11}$

The above fractions are already in their lowest terms.
∴ Analyzing their ratios through simplification, we discover that $\frac{7}{13}$ and $\frac{5}{11}$ hold distinct proportions.
Even when reduced to their irreducible forms, they represent different shares.