Solve (51/2-21/5)div32/3

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

Evaluate

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

Solution Steps

Multiply 5 and 2 to get 10.

$$\frac{\frac{10+1}{2}-\frac{2\times 5+1}{5}}{\frac{3\times 3+2}{3}}$$

Add 10 and 1 to get 11.

$$\frac{\frac{11}{2}-\frac{2\times 5+1}{5}}{\frac{3\times 3+2}{3}}$$

Multiply 2 and 5 to get 10.

$$\frac{\frac{11}{2}-\frac{10+1}{5}}{\frac{3\times 3+2}{3}}$$

Add 10 and 1 to get 11.

$$\frac{\frac{11}{2}-\frac{11}{5}}{\frac{3\times 3+2}{3}}$$

Least common multiple of 2 and 5 is 10. Convert \frac{11}{2} and \frac{11}{5} to fractions with denominator 10.

$$\frac{\frac{55}{10}-\frac{22}{10}}{\frac{3\times 3+2}{3}}$$

Since \frac{55}{10} and \frac{22}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{55-22}{10}}{\frac{3\times 3+2}{3}}$$

Subtract 22 from 55 to get 33.

$$\frac{\frac{33}{10}}{\frac{3\times 3+2}{3}}$$

Multiply 3 and 3 to get 9.

$$\frac{\frac{33}{10}}{\frac{9+2}{3}}$$

Add 9 and 2 to get 11.

$$\frac{\frac{33}{10}}{\frac{11}{3}}$$

Divide \frac{33}{10} by \frac{11}{3} by multiplying \frac{33}{10} by the reciprocal of \frac{11}{3}.

$$\frac{33}{10}\times \frac{3}{11}$$

Multiply \frac{33}{10} times \frac{3}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{33\times 3}{10\times 11}$$

Do the multiplications in the fraction \frac{33\times 3}{10\times 11}.

$$\frac{99}{110}$$

Reduce the fraction \frac{99}{110} to lowest terms by extracting and canceling out 11.

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

Factor

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