Solve 51/3+51/8+62/3+47/8

$$5 \frac { 1 } { 3 } + 5 \frac { 1 } { 8 } + 6 \frac { 2 } { 3 } + 4 \frac { 7 } { 8 }$$

Evaluate

$$22$$

Solution Steps

Multiply 5 and 3 to get 15.

$$\frac{15+1}{3}+\frac{5\times 8+1}{8}+\frac{6\times 3+2}{3}+\frac{4\times 8+7}{8}$$

Add 15 and 1 to get 16.

$$\frac{16}{3}+\frac{5\times 8+1}{8}+\frac{6\times 3+2}{3}+\frac{4\times 8+7}{8}$$

Multiply 5 and 8 to get 40.

$$\frac{16}{3}+\frac{40+1}{8}+\frac{6\times 3+2}{3}+\frac{4\times 8+7}{8}$$

Add 40 and 1 to get 41.

$$\frac{16}{3}+\frac{41}{8}+\frac{6\times 3+2}{3}+\frac{4\times 8+7}{8}$$

Least common multiple of 3 and 8 is 24. Convert \frac{16}{3} and \frac{41}{8} to fractions with denominator 24.

$$\frac{128}{24}+\frac{123}{24}+\frac{6\times 3+2}{3}+\frac{4\times 8+7}{8}$$

Since \frac{128}{24} and \frac{123}{24} have the same denominator, add them by adding their numerators.

$$\frac{128+123}{24}+\frac{6\times 3+2}{3}+\frac{4\times 8+7}{8}$$

Add 128 and 123 to get 251.

$$\frac{251}{24}+\frac{6\times 3+2}{3}+\frac{4\times 8+7}{8}$$

Multiply 6 and 3 to get 18.

$$\frac{251}{24}+\frac{18+2}{3}+\frac{4\times 8+7}{8}$$

Add 18 and 2 to get 20.

$$\frac{251}{24}+\frac{20}{3}+\frac{4\times 8+7}{8}$$

Least common multiple of 24 and 3 is 24. Convert \frac{251}{24} and \frac{20}{3} to fractions with denominator 24.

$$\frac{251}{24}+\frac{160}{24}+\frac{4\times 8+7}{8}$$

Since \frac{251}{24} and \frac{160}{24} have the same denominator, add them by adding their numerators.

$$\frac{251+160}{24}+\frac{4\times 8+7}{8}$$

Add 251 and 160 to get 411.

$$\frac{411}{24}+\frac{4\times 8+7}{8}$$

Reduce the fraction \frac{411}{24} to lowest terms by extracting and canceling out 3.

$$\frac{137}{8}+\frac{4\times 8+7}{8}$$

Multiply 4 and 8 to get 32.

$$\frac{137}{8}+\frac{32+7}{8}$$

Add 32 and 7 to get 39.

$$\frac{137}{8}+\frac{39}{8}$$

Since \frac{137}{8} and \frac{39}{8} have the same denominator, add them by adding their numerators.

$$\frac{137+39}{8}$$

Add 137 and 39 to get 176.

$$\frac{176}{8}$$

Divide 176 by 8 to get 22.

$$22$$

Factor

$$2\times 11$$