Question

Match the equivalent fractions and write two more for each. (i) \(\frac{250}{400}\) (ii) \(\frac{180}{400}\) (iii) \(\frac{660}{990}\) (iv) \(\frac{180}{360}\) (v) \(\frac{220}{520}\) (a)\(\frac{2}{3}\) (b)\(\frac{2}{5}\) (c)\(\frac{1}{2}\) (d)\(\frac{5}{8}\) (e) \(\frac{9}{10}\)

Answer 1

(i) \(\frac{250}{400}\)

Greatest Common Factor of 250 and 400 is 50. 

\(\frac{250 }{ 400} ÷ \frac{50 }{ 50}\) = \(\frac{5 }{ 8}\)

∴ \((i)\equiv(d)\)

Two more equivalent fractions are \(\frac{5 }{ 8} × \frac{3 }{ 2} = \frac{15 }{ 16}\) and \(\frac{5 }{ 8} × \frac{3 }{3} = \frac{15 }{ 24}\).

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(ii) \(\frac{180}{400}\)

Greatest Common Factor of 180 and 200 is 20.

\(\frac{180}{400}\) ÷ \(\frac{20 }{ 20}\) = \(\frac{9 }{ 10}\)

∴ \((ii) \equiv (e)\).

Two more equivalent fractions are \(\frac{9 }{10} ×\frac{ 3}{  2} = \frac{27 }{ 20}\) and \(\frac{9 }{ 10} × \frac{3 }{3} = \frac{27 }{ 30}\).

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(iii) \(\frac{660}{990}\)

Greatest Common Factor of 660 and 990 is 330. 

\(\frac{660}{990}\) ÷ \(\frac{330 }{ 330}\) = \(\frac{2 }{3}\)

∴ \((iii) \equiv (a)\).

Two more equivalent fractions are \(\frac{2 }{ 3} × \frac{2 }{ 2}\) = 4 / 6 and 2 /3 × 3 /3 = 6 / 9.

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(iv) \(\frac{180}{360}\)

Greatest Common Factor of 180 and 360 is 18.

\(\frac{180}{360}\) ÷ \(\frac{18 }{ 18}\) = \(\frac{1 }{2}\).

∴ \((iv) \equiv (c)\).

Two more equivalent fractions are \(\frac{1}{2} ×\frac{ 2 }{ 2} = \frac{2 }{ 4}\) and \(\frac{1}{2} × \frac{3 }{3} = \frac{3 }{ 6}\).

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(v) 220 / 550

Greatest Common Factor of 220 and 550 is 110. 

\(\frac{220 }{ 550} ÷ \frac{110 }{ 110} = \frac{2 }{5}\)

∴ \((v) \equiv (b)\).

Two more equivalent fractions are \(\frac{2 }{ 5} × \frac{3} {4} = \frac{6}{20}\) and \(\frac{2}{ 5} × \frac{3 }{3} = \frac{6 }{ 15}\).