Question

Simplify $:$$4$ $\frac{2}{3}$$÷$$($ $3$$-$$\frac{1}{3}$ $)$ $+$$($ $\frac{2}{5}$of $\frac{5}{6}$$)$ $$

Answer 1

Step 1 : Convert the mixed fractions into improper fractions

$4$$\frac{2}{3}$ $=$$\frac{(4\times 3)+2}{3}$ $=$$\frac{12+2}{3}$ $=$$\frac{14}{3}$

Step 2 : Simplifying the first bracket

$($ $3$$-$$\frac{1}{3}$ $)$ $,$$3$ we can write it as $\frac{3}{1}$

$3$$-$$\frac{1}{3}$ $=$ $\frac{3}{1}$ $-$$\frac{1}{3}$

Step 3: The bottom numbers are different, To make it same take the L.C.M of 1 and 3

L.C.M of $1$and $3$ is $3$

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

$\frac{3}{1}$$=$$\frac{3\times 3}{1\times 3}$ $=$$\frac{9}{3}$

$\frac{1}{3}$$=$$\frac{1\times 1}{3\times 1}$ $=$$\frac{1}{3}$

Step 5: Subtract the numerators and put the answer over the denominator

$\frac{9}{3}$$-$$\frac{1}{3}$ $=$$\frac{9-1}{3}$ $=$$\frac{8}{3}$

Step 6 : Simplifying the second bracket

$($ $\frac{2}{5}$of $\frac{5}{6}$$)$

Replace the word ‘ of ’ with the multiplication sign ‘ x ’ and do multiplication

$\frac{2}{5}$$\times$$\frac{5}{6}$ $=$ $\frac{2\times 5}{5\times 6}$$=$$\frac{10}{30}$

$4$ $\frac{2}{3}$$÷$$($ $3$$-$$\frac{1}{3}$ $)$ $+$$($ $\frac{2}{5}$of $\frac{5}{6}$$)$ $=$ $\frac{14}{3}$$÷$$\frac{8}{3}$$+$$\frac{10}{30}$

Step 7 : First do division

$\frac{14}{3}$$÷$$\frac{8}{3}$

Write the reciprocal of the second fraction ( that one you want to divide by ) with the sign of multiplication (×) and do multiplication

$\frac{14}{3}$$\times$$\frac{3}{8}$$=$$\frac{14\times 3}{3\times 8}$$=$$\frac{42}{24}$

$\frac{14}{3}$$÷$$\frac{8}{3}$$+$$\frac{10}{30}$ $=$$\frac{42}{24}$$+$$\frac{10}{30}$

Step 8: The bottom numbers are different, To make it same take the L.C.M of 24 and 30

L.C.M of $24$and $30$ is $120$

Step 9: Convert both the fraction into equivalent like fractions with their L.C.M as common denominator

$\frac{42}{24}$$=$$\frac{42\times 5}{24\times 5}$ $=$$\frac{210}{120}$

$\frac{10}{30}$$=$$\frac{10\times 4}{30\times 4}$ $=$$\frac{40}{120}$

Step 10: Add the numerators and put the answer over the denominator

$\frac{210}{120}$$+$$\frac{40}{120}$ $=$$\frac{250}{120}$

Step11: Simplify the fraction

Divide numerator $250$ by the denominator $120$

$\frac{250}{120}$$=$$2$$\frac{10}{120}$

Here $,$$\frac{10}{120}$$=$$\frac{10÷10}{120÷10}$$=$$\frac{1}{12}$

$2$$\frac{10}{120}$ $=$$2$$\frac{1}{12}$

Hence$,$ $4$ $\frac{2}{3}$$÷$$($ $3$$-$$\frac{1}{3}$ $)$ $+$$($ $\frac{2}{5}$of $\frac{5}{6}$$)$ $$ $=$$2$$\frac{1}{12}$