Question

Simplify $($ $\frac{2}{5}$of $\frac{3}{7}$$)$ $-$$($ $\frac{1}{6}$of $\frac{3}{5}$$)$ $+$$($ $\frac{1}{14}$of $\frac{2}{5}$$)$

Answer 1

Simplifying using BODMAS rule :

Step 1 : Simplifying the first bracket

$\frac{2}{5}$of $\frac{3}{7}$

Step 2 : Replace the word ‘ of ’ with the symbol $‘\times ’$and do multiplication

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

Step 3: Simplifying the second bracket

$\frac{1}{6}$of $\frac{3}{5}$

Step 4 : Replace the word ‘ of ’ with the symbol$‘\times ’$ and do multiplication

$\frac{1}{6}$$\times$$\frac{3}{5}$ $=$$\frac{1\times 3}{6\times 5}$ $=$$\frac{3}{30}$

Step 5 : Simplifying the third bracket

$\frac{1}{14}$of $\frac{2}{5}$

Step 6 : Replace the word ‘ of ’ with the symbol ‘ x ’ and do multiplication

$\frac{1}{14}$$\times$$\frac{2}{5}$ $=$$\frac{1\times 2}{14\times 5}$ $=$$\frac{2}{70}$

$($ $\frac{2}{5}$of $\frac{3}{7}$$)$ $-$$($ $\frac{1}{6}$of $\frac{3}{5}$$)$ $+$$($ $\frac{1}{14}$of $\frac{2}{5}$$)$ $=$$\frac{6}{35}$$-$$\frac{3}{30}$$+$$\frac{2}{70}$

Step 7: The bottom numbers are different, To make it same take the L.C.M of $35,30,70$

L.C.M of $35$$,$$30$ and $70$ is $210$

Step 8: Convert both the fraction into equivalent like fractions with their L.C.M as common denominator

$\frac{6}{35}$ $=$$\frac{6\times 6}{35\times 6}$ $=$$\frac{36}{210}$

$\frac{3}{30}$ $=$$\frac{3\times 7}{30\times 7}$ $=$$\frac{21}{210}$

$\frac{2}{70}$ $=$$\frac{2\times 3}{70\times 3}$ $=$$\frac{6}{210}$

Step 9: Subtract and add the numerators according to the question and put the answer over the denominator

$\frac{6}{35}$$-$$\frac{3}{30}$$+$ $\frac{2}{70}$ $=$$\frac{36}{210}$$-$$\frac{21}{210}$$+$$\frac{6}{210}$ $=$$\frac{36-21+6}{210}$ $=$$\frac{21}{210}$

Step 10: Simplify the fraction

$\frac{21}{210}$ $=$$\frac{21÷21}{210÷21}$ $=$$\frac{1}{10}$

Hence $,$ $($ $\frac{2}{5}$of $\frac{3}{7}$$)$ $-$$($ $\frac{1}{6}$of $\frac{3}{5}$$)$ $+$$($ $\frac{1}{14}$of $\frac{2}{5}$$)$ $=$$\frac{1}{10}$.