Solve 9/16div[(1/8+0.2)*5/13]

$$\frac { 9 } { 16 } \div [ ( \frac { 1 } { 8 } + 0.2 ) \times \frac { 5 } { 13 } ]$$

Evaluate

$$4.5$$

Solution Steps

Convert decimal number 0.2 to fraction \frac{2}{10}. Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{9}{16}}{\left(\frac{1}{8}+\frac{1}{5}\right)\times \frac{5}{13}}$$

Least common multiple of 8 and 5 is 40. Convert \frac{1}{8} and \frac{1}{5} to fractions with denominator 40.

$$\frac{\frac{9}{16}}{\left(\frac{5}{40}+\frac{8}{40}\right)\times \frac{5}{13}}$$

Since \frac{5}{40} and \frac{8}{40} have the same denominator, add them by adding their numerators.

$$\frac{\frac{9}{16}}{\frac{5+8}{40}\times \frac{5}{13}}$$

Add 5 and 8 to get 13.

$$\frac{\frac{9}{16}}{\frac{13}{40}\times \frac{5}{13}}$$

Multiply \frac{13}{40} times \frac{5}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{9}{16}}{\frac{13\times 5}{40\times 13}}$$

Cancel out 13 in both numerator and denominator.

$$\frac{\frac{9}{16}}{\frac{5}{40}}$$

Reduce the fraction \frac{5}{40} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{9}{16}}{\frac{1}{8}}$$

Divide \frac{9}{16} by \frac{1}{8} by multiplying \frac{9}{16} by the reciprocal of \frac{1}{8}.

$$\frac{9}{16}\times 8$$

Express \frac{9}{16}\times 8 as a single fraction.

$$\frac{9\times 8}{16}$$

Multiply 9 and 8 to get 72.

$$\frac{72}{16}$$

Reduce the fraction \frac{72}{16} to lowest terms by extracting and canceling out 8.

$$\frac{9}{2}$$

Factor

$$\frac{3 ^ {2}}{2} = 4\frac{1}{2} = 4.5$$