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.