Question

Find the greatest fraction from the given options:

• A. $\frac{3}{5}-\frac{1}{5}$
• B. $\frac{4}{7}-\frac{2}{7}$
• C. $\frac{2}{3}-\frac{1}{3}$
• D. $\frac{1}{2}$

Answer 1

The correct option is D

$\frac{1}{2}$

1. $\frac{3}{5}-\frac{1}{5}=\frac{2}{5}$
2. $\frac{4}{7}-\frac{2}{7}=\frac{2}{7}$
3. $\frac{2}{3}-\frac{1}{3}=\frac{1}{3}$
4. $\frac{1}{2}$

Convert all fractions to equivalent fractions to find the greatest fraction.

LCM of 2, 3, 5, 7,= 210.

$\frac{2}{5}=\frac{84}{210}\frac{2}{7}=\frac{60}{210}\frac{1}{3}=\frac{70}{210}\frac{1}{2}=\frac{105}{210}$

$\therefore$ Greatest fraction is $\frac{105}{210}\text{or}\frac{1}{2}$.

Note: By observing the fractions, we can see that all the fractions $\frac{2}{5},\frac{2}{7}$ and $\frac{1}{3}$ are less than $\frac{1}{2}$ . Hence $\frac{1}{2}$ is the greatest in the given list.