Solve 152/7+133/8+165/7-121/8

$$15 \frac { 2 } { 7 } + 13 \frac { 3 } { 8 } + 16 \frac { 5 } { 7 } - 12 \frac { 1 } { 8 }$$

Evaluate

$$\frac{133}{4}=33.25$$

Solution Steps

Multiply 15 and 7 to get 105.

$$\frac{105+2}{7}+\frac{13\times 8+3}{8}+\frac{16\times 7+5}{7}-\frac{12\times 8+1}{8}$$

Add 105 and 2 to get 107.

$$\frac{107}{7}+\frac{13\times 8+3}{8}+\frac{16\times 7+5}{7}-\frac{12\times 8+1}{8}$$

Multiply 13 and 8 to get 104.

$$\frac{107}{7}+\frac{104+3}{8}+\frac{16\times 7+5}{7}-\frac{12\times 8+1}{8}$$

Add 104 and 3 to get 107.

$$\frac{107}{7}+\frac{107}{8}+\frac{16\times 7+5}{7}-\frac{12\times 8+1}{8}$$

Least common multiple of 7 and 8 is 56. Convert \frac{107}{7} and \frac{107}{8} to fractions with denominator 56.

$$\frac{856}{56}+\frac{749}{56}+\frac{16\times 7+5}{7}-\frac{12\times 8+1}{8}$$

Since \frac{856}{56} and \frac{749}{56} have the same denominator, add them by adding their numerators.

$$\frac{856+749}{56}+\frac{16\times 7+5}{7}-\frac{12\times 8+1}{8}$$

Add 856 and 749 to get 1605.

$$\frac{1605}{56}+\frac{16\times 7+5}{7}-\frac{12\times 8+1}{8}$$

Multiply 16 and 7 to get 112.

$$\frac{1605}{56}+\frac{112+5}{7}-\frac{12\times 8+1}{8}$$

Add 112 and 5 to get 117.

$$\frac{1605}{56}+\frac{117}{7}-\frac{12\times 8+1}{8}$$

Least common multiple of 56 and 7 is 56. Convert \frac{1605}{56} and \frac{117}{7} to fractions with denominator 56.

$$\frac{1605}{56}+\frac{936}{56}-\frac{12\times 8+1}{8}$$

Since \frac{1605}{56} and \frac{936}{56} have the same denominator, add them by adding their numerators.

$$\frac{1605+936}{56}-\frac{12\times 8+1}{8}$$

Add 1605 and 936 to get 2541.

$$\frac{2541}{56}-\frac{12\times 8+1}{8}$$

Reduce the fraction \frac{2541}{56} to lowest terms by extracting and canceling out 7.

$$\frac{363}{8}-\frac{12\times 8+1}{8}$$

Multiply 12 and 8 to get 96.

$$\frac{363}{8}-\frac{96+1}{8}$$

Add 96 and 1 to get 97.

$$\frac{363}{8}-\frac{97}{8}$$

Since \frac{363}{8} and \frac{97}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{363-97}{8}$$

Subtract 97 from 363 to get 266.

$$\frac{266}{8}$$

Reduce the fraction \frac{266}{8} to lowest terms by extracting and canceling out 2.

$$\frac{133}{4}$$

Factor

$$\frac{7 \cdot 19}{2 ^ {2}} = 33\frac{1}{4} = 33.25$$