Question

Simplify the following:

$1\frac{13}{14}-2\frac{5}{6}+1\frac{6}{7}$

Answer 1

Step1:- First convert the mixed fraction into an improper fraction:

$1\frac{13}{14}=\frac{27}{14}$

$2\frac{5}{6}=\frac{17}{6}$

$1\frac{6}{7}=\frac{13}{7}$

Step 1:- Make the denominator of both fractions same.

Multiply $\frac{27}{14}$by $3$

$\frac{27}{14}$$=\frac{27\times 3}{14\times 3}=\frac{81}{42}$

Multiply $\frac{17}{6}$ by $7$.

$\frac{17}{6}$$=\frac{17\times 7}{6\times 7}=\frac{119}{42}$

Multiply $\frac{13}{7}$by $6$.

$\frac{13}{7}$$=\frac{13\times 6}{7\times 6}=\frac{78}{42}$

Step 2:- Add $\frac{81}{42}$ and $\frac{78}{42}$

$\frac{81}{42}+\frac{78}{42}=\frac{81+78}{42}=\frac{159}{42}$

Step 3:- Subtract$\frac{102}{42}$ from $\frac{159}{42}$

$\frac{159}{42}-\frac{119}{42}=\frac{40}{42}$

Step 4:- Convert the fraction into the simplest form

$\frac{40}{42}=\frac{21}{20}$

Hence, $\frac{21}{20}$ is the required solution.