Question

Change the following group of fractions to like fractions:
i. $\frac{1}{3},\frac{2}{5},\frac{3}{4},\frac{1}{6}$

Answer 1

$\text{Step 1: Finding L.C.M of denominators of all the fractions}$

Given, group of fractions are $\frac{1}{3},\frac{2}{5},\frac{3}{4},\frac{1}{6}$.

$\text{Step 2: Dividing obtained L.C.M by denominators of each fraction.}$

$\therefore$ L.C.M of 3, 5, 4 ,6 $=2\times 2\times 3\times 5$

$=4\times 15$

$=60$

$\Rightarrow \frac{60}{3}=20$ (i) [denominator of $\frac{1}{3}$ ]

$\Rightarrow \frac{60}{5}=12$ (ii) [denominator of $\frac{2}{5}$ ]

$\Rightarrow \frac{60}{4}=15$ (iii) [denominator of $\frac{3}{4}$ ]

$\Rightarrow \frac{60}{6}=10$ (i) [denominator of $\frac{1}{6}$ ]

$\text{Step 3: Multiplying each fraction by their respective quotients to both numerators and denominators}$

$\Rightarrow \frac{1}{3}=\frac{1\times 20}{3\times 20}$ ….. [From (i)] = $\frac{20}{60}$

$\Rightarrow \frac{2}{5}=\frac{2\times 12}{(5\times 12}$….. [From (ii)] $=\frac{24}{60}$

$\Rightarrow \frac{3}{4}=\frac{3\times 15}{4\times 15}$….. [From (iii)] $=\frac{45}{60}$

$\Rightarrow \frac{1}{6}=\frac{1\times 10}{6\times 10}$….. [From (iv)] $\frac{10}{60}$

Hence, $\frac{20}{60}$, $\frac{24}{60}$, $\frac{45}{60}$, $\frac{10}{60}$ are required like fractions.