Solve 9/10div(31/2-11/5)

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

Evaluate

$$\frac{9}{23}\approx 0.391304348$$

Solution Steps

Multiply 3 and 2 to get 6.

$$\frac{\frac{9}{10}}{\frac{6+1}{2}-\frac{1\times 5+1}{5}}$$

Add 6 and 1 to get 7.

$$\frac{\frac{9}{10}}{\frac{7}{2}-\frac{1\times 5+1}{5}}$$

Multiply 1 and 5 to get 5.

$$\frac{\frac{9}{10}}{\frac{7}{2}-\frac{5+1}{5}}$$

Add 5 and 1 to get 6.

$$\frac{\frac{9}{10}}{\frac{7}{2}-\frac{6}{5}}$$

Least common multiple of 2 and 5 is 10. Convert \frac{7}{2} and \frac{6}{5} to fractions with denominator 10.

$$\frac{\frac{9}{10}}{\frac{35}{10}-\frac{12}{10}}$$

Since \frac{35}{10} and \frac{12}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{9}{10}}{\frac{35-12}{10}}$$

Subtract 12 from 35 to get 23.

$$\frac{\frac{9}{10}}{\frac{23}{10}}$$

Divide \frac{9}{10} by \frac{23}{10} by multiplying \frac{9}{10} by the reciprocal of \frac{23}{10}.

$$\frac{9}{10}\times \frac{10}{23}$$

Multiply \frac{9}{10} times \frac{10}{23} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 10}{10\times 23}$$

Cancel out 10 in both numerator and denominator.

$$\frac{9}{23}$$

Factor

$$\frac{3 ^ {2}}{23} = 0.391304347826087$$