Solve 9/10div(3/5+21/10)

$$\frac { 9 } { 10 } \div ( \frac { 3 } { 5 } + 2 \frac { 1 } { 10 } )$$

Evaluate

$$\frac{1}{3}\approx 0.333333333$$

Solution Steps

Multiply 2 and 10 to get 20.

$$\frac{\frac{9}{10}}{\frac{3}{5}+\frac{20+1}{10}}$$

Add 20 and 1 to get 21.

$$\frac{\frac{9}{10}}{\frac{3}{5}+\frac{21}{10}}$$

Least common multiple of 5 and 10 is 10. Convert \frac{3}{5} and \frac{21}{10} to fractions with denominator 10.

$$\frac{\frac{9}{10}}{\frac{6}{10}+\frac{21}{10}}$$

Since \frac{6}{10} and \frac{21}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{9}{10}}{\frac{6+21}{10}}$$

Add 6 and 21 to get 27.

$$\frac{\frac{9}{10}}{\frac{27}{10}}$$

Divide \frac{9}{10} by \frac{27}{10} by multiplying \frac{9}{10} by the reciprocal of \frac{27}{10}.

$$\frac{9}{10}\times \frac{10}{27}$$

Multiply \frac{9}{10} times \frac{10}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 10}{10\times 27}$$

Cancel out 10 in both numerator and denominator.

$$\frac{9}{27}$$

Reduce the fraction \frac{9}{27} to lowest terms by extracting and canceling out 9.

$$\frac{1}{3}$$

Factor

$$\frac{1}{3} = 0.3333333333333333$$