Question

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

Answer 1

Step 1 : Convert the mixed fractions into improper fractions

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

$1$$\frac{1}{5}$ $=$$\frac{(1\times 5)+1}{5}$ $=$ $\frac{5+1}{5}$ $=$ $\frac{6}{5}$

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

Step 2 : Simplifying the first bracket

$($ $3$$-$$\frac{1}{4}$ $)$ $,$$3$ we can write it as $\frac{3}{1}$

$3$$-$$\frac{1}{4}$ $=$ $\frac{3}{1}$ $-$$\frac{1}{4}$

Step 3: The bottom numbers are different, To make it same take the L.C.M of 1 and 4

L.C.M of $1$and $4$ is $4$

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

$\frac{3}{1}$$=$$\frac{3\times 4}{1\times 4}$ $=$$\frac{12}{4}$

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

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

$\frac{12}{4}$$-$$\frac{1}{4}$ $=$$\frac{11}{4}$

Step 6 : Simplifying the second bracket

$($ $\frac{2}{5}$$÷$$1$$\frac{1}{5}$$)$ $=$$($ $\frac{2}{5}$$÷$$\frac{6}{5}$$)$

Step 7: Write the reciprocal of the second fraction ( that one you want to divide by ) with the sign of multiplication (×) and do multiplication

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

$3$$\frac{2}{4}$$÷$$($ $3$$-$$\frac{1}{4}$ $)$ $+$$($ $\frac{2}{5}$$÷$$1$$\frac{1}{5}$$)$ $=$$\frac{14}{4}$$÷$$\frac{11}{4}$$+$$\frac{10}{30}$

Step 8 : First do division

$\frac{14}{4}$$÷$$\frac{11}{4}$

Step 9: Write the reciprocal of the second fraction ( that one you want to divide by ) with the sign of multiplication (×) and do multiplication

$\frac{14}{4}$$\times$$\frac{4}{11}$$=$$\frac{14\times 4}{4\times 11}$ $=$$\frac{56}{44}$

$\frac{14}{4}$$÷$$\frac{11}{4}$$+$$\frac{10}{30}$ $=$$\frac{56}{44}$$+$$\frac{10}{30}$

Step 10: The bottom numbers are different, To make it same take the L.C.M of 44 and 30

L.C.M of $44$and $30$ is $660$

Step 11: Convert both the fraction into equivalent like fractions with their L.C.M as common denominator

$\frac{56}{44}$$=$$\frac{56\times 15}{44\times 15}$ $=$$\frac{840}{660}$

$\frac{10}{30}$$=$$\frac{10\times 22}{30\times 22}$ $=$$\frac{220}{660}$

Step 12:Add the numerators and put the answer over the denominator

$\frac{840}{660}$$+$$\frac{220}{660}$ $=$$\frac{1060}{660}$

Step13: Simplify the fraction

Divide numerator $1060$ by the denominator $660$

$\frac{1060}{660}$$=$$1$$\frac{400}{660}$

Here $,$$\frac{400}{660}$$=$$\frac{400÷20}{660÷20}$$=$$\frac{20}{33}$

$1$$\frac{400}{660}$ $=$$1$$\frac{20}{33}$

Hence$,$ $3$$\frac{2}{4}$$÷$$($ $3$$-$$\frac{1}{4}$ $)$ $+$$($ $\frac{2}{5}$$÷$$1$$\frac{1}{5}$$)$ $=$$1$$\frac{20}{33}$