Question

Simplify $:$$($ $\frac{3}{4}$$÷$$\frac{1}{2}$$-$$\frac{1}{3}$$)$ $\times$ $\frac{6}{7}$

Answer 1

Step 1 : Simplifying the first bracket

$\frac{3}{4}$$÷$$\frac{1}{2}$$-$$\frac{1}{3}$

Step 2 : First do division

$\frac{3}{4}$$÷$$\frac{1}{2}$

Step 3: Write the reciprocal of the second fraction ( that one you want to divide by ) with the sign of multiplication (×) and do multiplication

$\frac{3}{4}$$\times$$\frac{2}{1}$ $=$$\frac{3\times 2}{4\times 1}$$=$$\frac{6}{4}$

$\frac{3}{4}$$÷$ $\frac{1}{2}$$-$$\frac{1}{3}$ $=$$\frac{6}{4}$$-$ $\frac{1}{3}$

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

L.C.M of $4$ and $3$ is $12$

Step 5: Convert both the fraction into equivalent like fractions with their L.C.M as common denominator

$\frac{6}{4}$$=$$\frac{6\times 3}{4\times 3}$$=$$\frac{18}{12}$

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

Step 6: Subtract the numerators and put the answer over the denominator

$\frac{18}{12}$ $-$$\frac{4}{12}$$=$$\frac{18-4}{12}$ $=$$\frac{14}{12}$

$($ $\frac{3}{4}$$÷$$\frac{1}{2}$$-$$\frac{1}{3}$$)$ $\times$ $\frac{6}{7}$ $=$$\frac{14}{12}$ $\times$$\frac{6}{7}$

Step 7: Do multiplication

$\frac{14}{12}$$\times$$\frac{6}{7}$ $=$$\frac{14\times 6}{12\times 7}$ $=$$\frac{84}{84}$$=$$1$

Hence$,$ $($ $\frac{3}{4}$$÷$$\frac{1}{2}$$-$$\frac{1}{3}$$)$ $\times$ $\frac{6}{7}$ $=$$1$.