Solve 101/8+(35/8+27/8)

$$10 \frac { 1 } { 8 } + ( 3 \frac { 5 } { 8 } + 2 \frac { 7 } { 8 } )$$

Evaluate

$$\frac{133}{8}=16.625$$

Solution Steps

Multiply 10 and 8 to get 80.

$$\frac{80+1}{8}+\frac{3\times 8+5}{8}+\frac{2\times 8+7}{8}$$

Add 80 and 1 to get 81.

$$\frac{81}{8}+\frac{3\times 8+5}{8}+\frac{2\times 8+7}{8}$$

Multiply 3 and 8 to get 24.

$$\frac{81}{8}+\frac{24+5}{8}+\frac{2\times 8+7}{8}$$

Add 24 and 5 to get 29.

$$\frac{81}{8}+\frac{29}{8}+\frac{2\times 8+7}{8}$$

Since \frac{81}{8} and \frac{29}{8} have the same denominator, add them by adding their numerators.

$$\frac{81+29}{8}+\frac{2\times 8+7}{8}$$

Add 81 and 29 to get 110.

$$\frac{110}{8}+\frac{2\times 8+7}{8}$$

Reduce the fraction \frac{110}{8} to lowest terms by extracting and canceling out 2.

$$\frac{55}{4}+\frac{2\times 8+7}{8}$$

Multiply 2 and 8 to get 16.

$$\frac{55}{4}+\frac{16+7}{8}$$

Add 16 and 7 to get 23.

$$\frac{55}{4}+\frac{23}{8}$$

Least common multiple of 4 and 8 is 8. Convert \frac{55}{4} and \frac{23}{8} to fractions with denominator 8.

$$\frac{110}{8}+\frac{23}{8}$$

Since \frac{110}{8} and \frac{23}{8} have the same denominator, add them by adding their numerators.

$$\frac{110+23}{8}$$

Add 110 and 23 to get 133.

$$\frac{133}{8}$$

Factor

$$\frac{7 \cdot 19}{2 ^ {3}} = 16\frac{5}{8} = 16.625$$