Solve 1-(1/4+3/8)div9/4

$$1 - ( \frac { 1 } { 4 } + \frac { 3 } { 8 } ) \div \frac { 9 } { 4 }$$

Evaluate

$$\frac{13}{18}\approx 0.722222222$$

Solution Steps

Least common multiple of 4 and 8 is 8. Convert \frac{1}{4} and \frac{3}{8} to fractions with denominator 8.

$$1-\frac{\frac{2}{8}+\frac{3}{8}}{\frac{9}{4}}$$

Since \frac{2}{8} and \frac{3}{8} have the same denominator, add them by adding their numerators.

$$1-\frac{\frac{2+3}{8}}{\frac{9}{4}}$$

Add 2 and 3 to get 5.

$$1-\frac{\frac{5}{8}}{\frac{9}{4}}$$

Divide \frac{5}{8} by \frac{9}{4} by multiplying \frac{5}{8} by the reciprocal of \frac{9}{4}.

$$1-\frac{5}{8}\times \frac{4}{9}$$

Multiply \frac{5}{8} times \frac{4}{9} by multiplying numerator times numerator and denominator times denominator.

$$1-\frac{5\times 4}{8\times 9}$$

Do the multiplications in the fraction \frac{5\times 4}{8\times 9}.

$$1-\frac{20}{72}$$

Reduce the fraction \frac{20}{72} to lowest terms by extracting and canceling out 4.

$$1-\frac{5}{18}$$

Convert 1 to fraction \frac{18}{18}.

$$\frac{18}{18}-\frac{5}{18}$$

Since \frac{18}{18} and \frac{5}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{18-5}{18}$$

Subtract 5 from 18 to get 13.

$$\frac{13}{18}$$

Factor

$$\frac{13}{2 \cdot 3 ^ {2}} = 0.7222222222222222$$