Question

Change the following group of fractions to like fractions:
$\frac{5}{6},\frac{7}{8},\frac{11}{12},\frac{3}{10}$

Answer 1

$\text{Step 1: Finding L.C.M of denominators of all the fractions}$
Given, group of fractions are $\frac{5}{6},\frac{7}{8},\frac{11}{12},\frac{3}{10}$.

$\text{Step 2: Dividing obtained L.C.M by denominators of each fraction.}$
$\therefore$ L.C.M of 6, 18, 12, 10

$=2\times 2\times 2\times 3\times 5=120$

$\Rightarrow \frac{120}{6}=20$ (i) [denominator of $\frac{5}{6}$]

$\Rightarrow \frac{120}{8}=15$ (ii) [denominator of $\frac{7}{18}$]

$\Rightarrow \frac{120}{12}=10$ (iii) [denominator of $\frac{11}{12}$]

$\Rightarrow \frac{120}{10}=12$ (iv) [denominator of $\frac{3}{10}$]
$\text{Step 3: Multiplying each fraction by their respective quotients to both numerators and denominators}$

$\Rightarrow \frac{5}{6}=\frac{5\times 20}{6\times 20}$….. [From (i)] $=\frac{100}{120}$

$\Rightarrow \frac{7}{8}=\frac{7\times 15}{8\times 15}$….. [From (ii)] $=\frac{105}{120}$

$\Rightarrow \frac{11}{12}=\frac{11\times 10}{12\times 10}$….. [From (iii)] $=\frac{110}{120}$

$\Rightarrow \frac{3}{10}=\frac{3\times 12}{10\times 12}$….. [From (iv)] $=\frac{36}{120}$

Hence, $\frac{100}{120},\frac{105}{120},\frac{110}{120},\frac{36}{120}$ are required like fractions.