Question

Simplify $:$ $\frac{2}{5}$of $\frac{3}{7}$ $-$$\frac{1}{14}$$+$$\frac{3}{7}$ of $\frac{3}{5}$

Answer 1

Step 1: Replace the first ‘ of ’ with the multiplication sign ‘ $\times$ ’ and do multiplication

$\frac{2}{5}$ $\times$$\frac{3}{7}$ $=$$\frac{2\times 3}{5\times 7}$ $=$$\frac{6}{35}$

Step 2: Replace the second ‘ of ’ with the multiplication sign ‘ $\times$ ’ and do multiplication

$\frac{3}{7}$ $\times$$\frac{3}{5}$ $=$$\frac{3\times 3}{7\times 5}$ $=$$\frac{9}{35}$

$\frac{2}{5}$of $\frac{3}{7}$ $-$$\frac{1}{14}$$+$$\frac{3}{7}$ of $\frac{3}{5}$ $=$$\frac{6}{35}$$-$$\frac{1}{14}$$+$$\frac{9}{35}$

Step 3: The bottom numbers are different, To make it same take the L.C.M of 35,14 and 35

L.C.M of $35$$,$$14$ and $35$ is $70$

Step 4: Convert both the fraction into equivalent like fractions with their L.C.M as common denominator

$\frac{6}{35}$ $=$$\frac{6\times 2}{35\times 2}$ $=$$\frac{12}{70}$

$\frac{1}{14}$ $=$$\frac{1\times 5}{14\times 5}$ $=$$\frac{5}{70}$

$\frac{9}{35}$ $=$$\frac{9\times 2}{35\times 2}$ $=$$\frac{18}{70}$

Step 5: Add and Subtract the numerators according to the question and put the answer over the denominator

$\frac{6}{35}$$-$$\frac{1}{14}$$+$$\frac{9}{35}$ $=$$\frac{12}{70}$$-$$\frac{5}{70}$$+$$\frac{18}{70}$ $=$$\frac{12-5+18}{70}$ $=$$\frac{25}{70}$

Step 6: Simplify the fraction

$\frac{25}{70}$ $=$$\frac{25÷5}{70÷5}$ $=$$\frac{5}{14}$

Hence $,$ $\frac{2}{5}$of $\frac{3}{7}$ $-$$\frac{1}{14}$$+$$\frac{3}{7}$ of $\frac{3}{5}$ $=$$\frac{5}{14}$