Solve (11/2-5/8)div3/4

$$( 1 \frac { 1 } { 2 } - \frac { 5 } { 8 } ) \div \frac { 3 } { 4 }$$

Evaluate

$$\frac{7}{6}\approx 1.166666667$$

Solution Steps

Multiply 1 and 2 to get 2.

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

Add 2 and 1 to get 3.

$$\frac{\frac{3}{2}-\frac{5}{8}}{\frac{3}{4}}$$

Least common multiple of 2 and 8 is 8. Convert \frac{3}{2} and \frac{5}{8} to fractions with denominator 8.

$$\frac{\frac{12}{8}-\frac{5}{8}}{\frac{3}{4}}$$

Since \frac{12}{8} and \frac{5}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{12-5}{8}}{\frac{3}{4}}$$

Subtract 5 from 12 to get 7.

$$\frac{\frac{7}{8}}{\frac{3}{4}}$$

Divide \frac{7}{8} by \frac{3}{4} by multiplying \frac{7}{8} by the reciprocal of \frac{3}{4}.

$$\frac{7}{8}\times \frac{4}{3}$$

Multiply \frac{7}{8} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 4}{8\times 3}$$

Do the multiplications in the fraction \frac{7\times 4}{8\times 3}.

$$\frac{28}{24}$$

Reduce the fraction \frac{28}{24} to lowest terms by extracting and canceling out 4.

$$\frac{7}{6}$$

Factor

$$\frac{7}{2 \cdot 3} = 1\frac{1}{6} = 1.1666666666666667$$