Question

Subtract and simplify:
$\frac{5}{3}-\frac{2}{5}=$

• A. $1\frac{4}{15}$
• B. $2\frac{2}{15}$
• C. $2\frac{7}{15}$

Answer 1

The correct option is A $1\frac{4}{15}$

$\frac{5}{3}-\frac{2}{5}$
As these are unlike fractions, we need to convert them into like fractions.

Step 1: Find the LCM of denominators 3 and 5.
Multiples of 3: 3, 6, 9, 12, 15, 18, ...
Multiples of 5: 5, 10, 15, 20, 25, ...

15 is the common multiple of 3 and 5. So, LCM of 3 and 5 is 15.

Step 2: Now, we have to convert the denominators of both the fractions into 15 (LCM of 3 and 15) without changing the fraction value.

$\frac{5}{3}=\frac{5\times 5}{3\times 5}=\frac{25}{15}$
$\frac{2}{5}=\frac{2\times 3}{5\times 3}=\frac{6}{15}$

$\therefore \frac{5}{3}-\frac{2}{5}=\frac{25}{15}-\frac{6}{15}$

$=\frac{25-6}{15}$

$=\frac{19}{15}$

$\frac{19}{15}$ is an improper fraction, convert it into the mixed fraction as follows

$\frac{19}{15}=\frac{15+4}{15}$

$=\frac{15}{15}+\frac{4}{15}$

$=1+\frac{4}{15}$

$=1\frac{4}{15}$