Question

Change the following groups of fractions to like fractions:

(i)$\frac{1}{3},\frac{2}{5},\frac{3}{4},\frac{1}{6}$

(ii)$\frac{5}{6},\frac{7}{8},\frac{11}{12},\frac{3}{10}$

(iii) $\frac{2}{7},\frac{7}{8},\frac{5}{14},\frac{9}{16}$

Answer 1

$\left(i\right)\frac{1}{3},\frac{2}{5},\frac{3}{4},\frac{1}{6}$

LCM$(3,4,5,6)=60$

$=\frac{1\times 20}{3\times 20},\frac{2\times 12}{5\times 12},\frac{3\times 15}{4\times 15},\frac{1\times 10}{6\times 10}$

$=\frac{20}{60},\frac{24}{60},\frac{45}{60},\frac{10}{60}$

$\left(ii\right)\frac{5}{6},\frac{7}{8},\frac{11}{12},\frac{3}{10}$

LCM$(6,8,10,12)=120$

$=\frac{5\times 20}{6\times 20},\frac{7\times 15}{8\times 15},\frac{11\times 10}{12\times 10},\frac{3\times 12}{10\times 12}$

$=\frac{100}{120},\frac{105}{120},\frac{110}{120},\frac{36}{120}$

$\left(iii\right)\frac{2}{7},\frac{7}{8},\frac{5}{14},\frac{9}{16}$

LCM$(7,8,14,16)=112$

$=\frac{2\times 16}{7\times 16},\frac{7\times 14}{8\times 14},\frac{5\times 8}{14\times 8},\frac{9\times 7}{16\times 7}$

$=\frac{32}{112},\frac{98}{112},\frac{40}{112},\frac{63}{112}$