Question

Simplify the following:

$2\frac{3}{14}-3\frac{5}{6}-\frac{2}{5}+2\frac{1}{2}$

Answer 1

Step 1:- First convert the mixed fraction into the improper fraction

$2\frac{3}{14}$$=$$\frac{31}{14}$

$3\frac{5}{6}=\frac{23}{6}$

$2\frac{1}{2}=\frac{5}{2}$

Step 2:- Make the denominator of all the fractions the same

Multiple $\frac{31}{14}$ by $15$

$\frac{31}{14}$$=\frac{31\times 15}{14\times 15}=\frac{465}{210}$

Multiple $\frac{23}{6}$ by $35$

$\frac{23}{6}$$=\frac{23\times 35}{6\times 35}=\frac{805}{210}$

Multiple $\frac{2}{5}$ by $42$

$\frac{2}{5}$$=\frac{2\times 42}{5\times 42}=\frac{84}{210}$

Multiple $\frac{5}{2}$ by $105$

$\frac{5}{2}$$=\frac{5\times 105}{2\times 105}=\frac{525}{210}$

Step 3:-Add $\frac{465}{210}$and $\frac{525}{210}$

$\frac{465}{210}$$+$$\frac{505}{210}$$=\frac{465+505}{210}$$=\frac{970}{210}$

Step 4:- Add$\frac{805}{210}$ and $\frac{84}{210}$

$\frac{805}{210}$$+$$\frac{84}{210}$$=\frac{805+84}{210}=\frac{889}{210}$

Step:-5 Subtract $\frac{889}{210}$ from $\frac{970}{210}$

$\frac{970}{210}$$-$$\frac{889}{210}$$=\frac{970-889}{210}=\frac{101}{210}$

Hence, $\frac{101}{210}$ is the required solution.