Question

Simplify $:$ $6$ $+$$($$\frac{2}{3}$$-$$\frac{7}{9}$$)$

Answer 1

Step 1 : Simplifying the bracket first

$($$\frac{2}{3}$$-$$\frac{7}{9}$$)$

Step 2: The bottom numbers are different, To make it same take the L.C.M of 3 and 9

L$.$C$.$M of $3$ and $9$ is $9$

Step 3: Convert both the fraction into equivalent like fractions with their L.C.M as common denominator

$\frac{2}{3}$ $=$$\frac{2\times 3}{3\times 3}$ $=$$\frac{6}{9}$

$\frac{7}{9}$ $=$$\frac{7\times 1}{9\times 1}$ $=$$\frac{7}{9}$

Step 4:Subtract the numerators and put the answer over the denominator

$($$\frac{2}{3}$$-$$\frac{7}{9}$$)$ $=$ $\frac{6}{9}$$-$$\frac{7}{9}$ $=$$\frac{6-7}{9}$$=$$\frac{-1}{9}$

$6$ $+$$($$\frac{2}{3}$$-$$\frac{7}{9}$$)$ $=$ $6$ $+$$\frac{-1}{9}$

$6$ we can write it as $\frac{6}{1}$ $,$Therefore $\frac{6}{1}$ $+$$\frac{-1}{9}$

Step 5: The bottom numbers are different, To make it same take the L.C.M of 1 and 9

L$.$C$.$M of $1$ and $9$ is $9$

Step 6: Convert both the fraction into equivalent like fractions with their L.C.M as common denominator

$\frac{6}{1}$ $=$$\frac{6\times 9}{1\times 9}$ $=$$\frac{54}{9}$

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

Step 7:Subtract the numerators and put the answer over the denominator

$($$\frac{54}{9}$$+$$\frac{-1}{9}$$)$ $=$ $\frac{54}{9}$$-$$\frac{1}{9}$ $=$$\frac{54-1}{9}$$=$$\frac{53}{9}$

Step8: Simplify the fraction

Divide numerator $53$ by the denominator $9$

$$

Hence $6$ $+$$($$\frac{2}{3}$$-$$\frac{7}{9}$$)$ $=$ $5\frac{8}{9}$