Comparing Fractions
Comparing like fractions Fractions with the same denominator are called like fractions. In like fractions, the fraction with the greater numerator is greater. e.g. In fractions $\frac{\text{5}}{\text{7}}$ and $\frac{\text{3}}{\text{7}}$. $\frac{\text{5}}{\text{7}}$ > $\frac{\text{3}}{\text{7}}$ as 5 is greater than 3. Three or more like fractions can be arranged in ascending or descending order by arranging their numerators in ascending or descending order respectively. Comparing unlike fractions Fractions with different denominators are called unlike fractions. If two fractions with the same numerator but different denominators are to be compared, then the fraction with the smaller denominator is greater of the two. To compare unlike fractions, we first convert them into like fractions.  e.g. Compare the fractions $\frac{\text{6}}{\text{8}}$ and $\frac{\text{4}}{\text{6}}$. least common multiple (LCM) of 6 and 8 = 24  $\frac{\text{(6 x 3)}}{\text{(8 x 3)}}$ = $\frac{\text{18}}{\text{24}}$  $\frac{\text{(4 x 4)}}{\text{(6 x 4)}}$ = $\frac{\text{16}}{\text{24}}$ $\frac{\text{18}}{\text{24}}$ > $\frac{\text{16}}{\text{24}}$ ⇒ $\frac{\text{6}}{\text{8}}$ > $\frac{\text{4}}{\text{6}}$ Hence, we can say that $\frac{\text{6}}{\text{8}}$ is greater than $\frac{\text{4}}{\text{6}}$.

Summary

Comparing like fractions Fractions with the same denominator are called like fractions. In like fractions, the fraction with the greater numerator is greater. e.g. In fractions $\frac{\text{5}}{\text{7}}$ and $\frac{\text{3}}{\text{7}}$. $\frac{\text{5}}{\text{7}}$ > $\frac{\text{3}}{\text{7}}$ as 5 is greater than 3. Three or more like fractions can be arranged in ascending or descending order by arranging their numerators in ascending or descending order respectively. Comparing unlike fractions Fractions with different denominators are called unlike fractions. If two fractions with the same numerator but different denominators are to be compared, then the fraction with the smaller denominator is greater of the two. To compare unlike fractions, we first convert them into like fractions.  e.g. Compare the fractions $\frac{\text{6}}{\text{8}}$ and $\frac{\text{4}}{\text{6}}$. least common multiple (LCM) of 6 and 8 = 24  $\frac{\text{(6 x 3)}}{\text{(8 x 3)}}$ = $\frac{\text{18}}{\text{24}}$  $\frac{\text{(4 x 4)}}{\text{(6 x 4)}}$ = $\frac{\text{16}}{\text{24}}$ $\frac{\text{18}}{\text{24}}$ > $\frac{\text{16}}{\text{24}}$ ⇒ $\frac{\text{6}}{\text{8}}$ > $\frac{\text{4}}{\text{6}}$ Hence, we can say that $\frac{\text{6}}{\text{8}}$ is greater than $\frac{\text{4}}{\text{6}}$.

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