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) $\frac{10}{12} [<] \frac{10}{10}$