Solve [(3/4)(1/2)div5/8][3/4divfrac{1}{2}]

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

Evaluate

$$\frac{9}{10}=0.9$$

Solution Steps

Multiply \frac{3}{4} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3\times 1}{4\times 2}}{\frac{5}{8}}\times \frac{\frac{3}{4}}{\frac{1}{2}}$$

Do the multiplications in the fraction \frac{3\times 1}{4\times 2}.

$$\frac{\frac{3}{8}}{\frac{5}{8}}\times \frac{\frac{3}{4}}{\frac{1}{2}}$$

Divide \frac{3}{8} by \frac{5}{8} by multiplying \frac{3}{8} by the reciprocal of \frac{5}{8}.

$$\frac{3}{8}\times \frac{8}{5}\times \frac{\frac{3}{4}}{\frac{1}{2}}$$

Multiply \frac{3}{8} times \frac{8}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 8}{8\times 5}\times \frac{\frac{3}{4}}{\frac{1}{2}}$$

Cancel out 8 in both numerator and denominator.

$$\frac{3}{5}\times \frac{\frac{3}{4}}{\frac{1}{2}}$$

Divide \frac{3}{4} by \frac{1}{2} by multiplying \frac{3}{4} by the reciprocal of \frac{1}{2}.

$$\frac{3}{5}\times \frac{3}{4}\times 2$$

Express \frac{3}{4}\times 2 as a single fraction.

$$\frac{3}{5}\times \frac{3\times 2}{4}$$

Multiply 3 and 2 to get 6.

$$\frac{3}{5}\times \frac{6}{4}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{3}{5}\times \frac{3}{2}$$

Multiply \frac{3}{5} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 3}{5\times 2}$$

Do the multiplications in the fraction \frac{3\times 3}{5\times 2}.

$$\frac{9}{10}$$

Factor

$$\frac{3 ^ {2}}{2 \cdot 5} = 0.9$$