Question

Subtract ${\displaystyle \frac{1}{6}}$ from ${\displaystyle \frac{1}{2}}$.

Answer 1

Converting the given fractions into like fractions.

LCM of the denominators of ${\displaystyle \frac{1}{6}}$ and ${\displaystyle \frac{1}{2}}$

2	6, 2
3	3, 1
	1, 1

∴ LCM of 6 and 2 = ${\displaystyle 2\times 3}$ = 6

Now, we convert the given fractions into equivalent fractions with denominators 6.

So, ${\displaystyle \frac{1\times 1}{6\times 1}=\frac{1}{6}}$ and ${\displaystyle \frac{1}{2}=\frac{1\times 3}{2\times 3}=\frac{3}{6}}$

∴ ${\displaystyle \frac{1}{2}-\frac{1}{6}=\frac{3}{6}-\frac{1}{6}=\frac{3-1}{6}=\frac{3÷2}{6÷2}=\frac{1}{3}}$  ....${\displaystyle \left[\begin{array}{c}\because \text{For reducing a fraction to its lowest terms, we divide}\\ \text{its numerator and denominator by their HCF}\end{array}\right]}$