Solve (51/3-27/8)div(21/3+1/6)

$$( 5 \frac { 1 } { 3 } - 2 \frac { 7 } { 8 } ) \div ( 2 \frac { 1 } { 3 } + \frac { 1 } { 6 } )$$

Evaluate

$$\frac{59}{60}\approx 0.983333333$$

Solution Steps

Multiply 5 and 3 to get 15.

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

Add 15 and 1 to get 16.

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

Multiply 2 and 8 to get 16.

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

Add 16 and 7 to get 23.

$$\frac{\frac{16}{3}-\frac{23}{8}}{\frac{2\times 3+1}{3}+\frac{1}{6}}$$

Least common multiple of 3 and 8 is 24. Convert \frac{16}{3} and \frac{23}{8} to fractions with denominator 24.

$$\frac{\frac{128}{24}-\frac{69}{24}}{\frac{2\times 3+1}{3}+\frac{1}{6}}$$

Since \frac{128}{24} and \frac{69}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{128-69}{24}}{\frac{2\times 3+1}{3}+\frac{1}{6}}$$

Subtract 69 from 128 to get 59.

$$\frac{\frac{59}{24}}{\frac{2\times 3+1}{3}+\frac{1}{6}}$$

Multiply 2 and 3 to get 6.

$$\frac{\frac{59}{24}}{\frac{6+1}{3}+\frac{1}{6}}$$

Add 6 and 1 to get 7.

$$\frac{\frac{59}{24}}{\frac{7}{3}+\frac{1}{6}}$$

Least common multiple of 3 and 6 is 6. Convert \frac{7}{3} and \frac{1}{6} to fractions with denominator 6.

$$\frac{\frac{59}{24}}{\frac{14}{6}+\frac{1}{6}}$$

Since \frac{14}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{59}{24}}{\frac{14+1}{6}}$$

Add 14 and 1 to get 15.

$$\frac{\frac{59}{24}}{\frac{15}{6}}$$

Reduce the fraction \frac{15}{6} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{59}{24}}{\frac{5}{2}}$$

Divide \frac{59}{24} by \frac{5}{2} by multiplying \frac{59}{24} by the reciprocal of \frac{5}{2}.

$$\frac{59}{24}\times \frac{2}{5}$$

Multiply \frac{59}{24} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{59\times 2}{24\times 5}$$

Do the multiplications in the fraction \frac{59\times 2}{24\times 5}.

$$\frac{118}{120}$$

Reduce the fraction \frac{118}{120} to lowest terms by extracting and canceling out 2.

$$\frac{59}{60}$$

Factor

$$\frac{59}{2 ^ {2} \cdot 3 \cdot 5} = 0.9833333333333333$$