Question

Look at the figures and write ‘<’ or ‘>’, ‘=’ between the given pairs of fractions.

1. \(\frac{1}{6} [  ]\frac{1}{3}\)
2. \(\frac{3}{4} [  ]\frac{ 2}{6}\)
3. \(\frac{2}{3} [  ] \frac{2}{4}\)
4. \(\frac{6}{6} [  ] \frac{3}{3}\)
5. \(\frac{5}{6} [  ] \frac{5}{5}\)
   Make five more such problems yourself and solve them with your friends.

Answer 1

(a) \(\frac{1}{6} [ < ]\frac{1}{3}\) - The numerators of two given fractions are the same. So, the fraction that has the lesser denominator is the largest.

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(b) \(\frac{3}{4} [ > ]\frac{ 2}{6}\) - Cross multiplying the denominators and the numerators, we have 3/4 =9/12 and 2/6=4/12. Here, for 9/12 and 4/12, 9 >. The denominators of the two fractions are the same. So, the fraction that has the greater numerator is the largest.

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(c) \(\frac{2}{3} [ > ] \frac{2}{4}\) - The numerators of two given fractions are the same. So, the fraction that has the lesser denominator is the largest.

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(d) \(\frac{6}{6} [ = ] \frac{3}{3}\) - \(\frac{6}{6}\) and \(\frac{3}{3}\) can be both simplified to \(1\) and hence they are equal.

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(e) \(\frac{5}{6} [ < ] \frac{5}{5}\) - The numerators of two given fractions are the same. So, the fraction that has the lesser denominator is the largest.

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Five more such problems are:

(a) \(\frac{1}{7} [<] \frac{1}{4}\)

(b) \(\frac{5}{8} [>] \frac{4}{12}\)

(c) \(\frac{4}{6} [>] \frac{4}{8}\)

(d) \(\frac{4}{4} (=)\frac{ 2}{2}\)

(e) \(\frac{10}{12} [<] \frac{10}{10}\)