Question

Change the following group of fractions to like fractions:
$\frac{2}{7},\frac{7}{8},\frac{5}{14},\frac{9}{16}$

Answer 1

$\text{Step 1: Finding L.C.M of denominators of all the fractions}$
Given group of fractions are $\frac{2}{7},\frac{7}{8},\frac{5}{14},\frac{9}{16}$

$\therefore$ L.C.M of 7, 8, 14, 16
$=2\times 2\times 2\times 2\times 7$
$=112$
$\text{Step 2: Dividing obtained L.C.M by denominators of each fraction.}$

$\Rightarrow \frac{112}{7}=16$ (i) [denominator of $\frac{2}{7}$ ]

$\Rightarrow \frac{112}{8}=14$ (ii) [denominator of $\frac{7}{8}$ ]

$\Rightarrow \frac{112}{14}=8$ (iii) [denominator of $\frac{5}{14}$ ]$\Rightarrow \frac{112}{16}=7$ (i) [denominator of $\frac{9}{16}$ ]

$\text{Step 3: Multiplying each fraction by their respective quotients to both numerators and denominators}$
$\frac{2}{7}=\frac{2\times 16}{7\times 16}$….. [From (i)] =$\frac{32}{112}$

$\frac{7}{8}=\frac{7\times 14}{8\times 14}$….. [From (ii)] =$\frac{98}{112}$

$\Rightarrow \frac{5}{14}=\frac{5\times 8}{14\times 8}$….. [From (iii)] =$\frac{40}{112}$

$\Rightarrow \frac{9}{16}=\frac{9\times 7}{16\times 7}$….. [From (iv)] =$\frac{63}{112}$

Hence, $\frac{32}{112},\frac{98}{112},\frac{40}{112}and\frac{63}{112}$ are required like fractions.