Question

Find the greatest fraction:

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Op 1 $\frac{3}{5}-\frac{1}{5}=\frac{2}{5}$
Op 2 $\frac{4}{7}-\frac{2}{7}=\frac{2}{7}$
Op 3 $\frac{2}{3}-\frac{1}{3}=\frac{1}{3}$
Op 4 $\frac{1}{2}$, convert all fractions to equivalent fractions to find the greatest.
LCM of 2,3,5,7, is 210
$\therefore \frac{2}{5}=\frac{84}{210},\frac{2}{7}=\frac{60}{210},\frac{1}{3}=\frac{70}{210}\frac{1}{2}=\frac{105}{210}$
$\therefore$ greatest fraction is $\frac{1}{2}$
Since the denominators are prime numbers we can find their LCM by just multiplying them. $2\times 3\times 5\times 7=210$

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.