Question

Simplify $:$ $8$$-$$($$\frac{3}{4}$$+$$\frac{2}{10}$$)$ $÷$$($$2\frac{2}{4}$$-$$\frac{3}{5}$$)$

Answer 1

Step 1 : convert mixed fraction into improper fraction

$2\frac{2}{4}$ $=$$\frac{(2\times 4)+2}{4}$ $=$$\frac{8+2}{4}$ $=$$\frac{10}{4}$

Step 2: Simplifying the first bracket

$\frac{3}{4}$$+$$\frac{2}{10}$

Step 3: The bottom numbers are different, To make it same take the L.C.M of 4 and 10

L.C.M of $4$ and $10$ is $20$

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

$\frac{3}{4}$ $=$$\frac{3\times 5}{4\times 5}$ $=$$\frac{15}{20}$

$\frac{2}{10}$$=$$\frac{2\times 2}{10\times 2}$$=$$\frac{4}{20}$

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

$\frac{15}{20}$$+$$\frac{4}{20}$$=$$\frac{19}{20}$

Step 6 : Simplifying the second bracket

$2\frac{2}{4}$$-$$\frac{3}{5}$ $=$$\frac{10}{4}$$-$$\frac{3}{5}$

Step 7: The bottom numbers are different, To make it same take the L.C.M of 4 and 5

L.C.M of $4$ and $5$ is $20$

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

$\frac{10}{4}$$=$$\frac{10\times 5}{4\times 5}$$=$$\frac{50}{20}$

$\frac{3}{5}$ $=$ $\frac{3\times 4}{5\times 4}$ $=$$\frac{12}{20}$

Step 9: Subtract the numerators and put the answer over the denominator

$\frac{50}{20}$$-$$\frac{12}{20}$$=$$\frac{38}{20}$

$\Rightarrow$ $8$$-$$($$\frac{3}{4}$$+$$\frac{2}{10}$$)$ $÷$$($$2\frac{2}{4}$$-$$\frac{3}{5}$$)$ $=$$8$$-$$\frac{19}{20}$$÷$$\frac{38}{20}$

Step 10: First do division

$\frac{19}{20}$$÷$$\frac{38}{20}$

Step 11: Write the reciprocal of the second fraction ( that one you want to divide by ) with the sign of multiplication (×) and do multiplication

$\frac{19}{20}$$\times$$\frac{20}{38}$ $=$$\frac{19\times 20}{20\times 38}$ $=$$\frac{380}{760}$$=$$\frac{1}{2}$

$\Rightarrow$$8$$-$$\frac{19}{20}$$÷$$\frac{38}{20}$$=$$8$$-$$\frac{1}{2}$

Step 12: Simplify the answer

$8$$-$$\frac{1}{2}$ $=$$\frac{(8\times 2)-1}{2}$$=$$\frac{16-1}{2}$$=$$\frac{15}{2}$$=$$7\frac{1}{2}$

Hence$,$ $8$$-$$($$\frac{3}{4}$$+$$\frac{2}{10}$$)$ $÷$$($$2\frac{2}{4}$$-$$\frac{3}{5}$$)$ $=$$7\frac{1}{2}$