Solve 9/10/frac{1{2}left(6/5-3/10right)}

$$\frac{ \frac{ 9 }{ 10 } }{ \frac{ 1 }{ 2 } \left( \frac{ 6 }{ 5 } - \frac{ 3 }{ 10 } \right) }$$

Evaluate

$$2$$

Solution Steps

Least common multiple of 5 and 10 is 10. Convert \frac{6}{5} and \frac{3}{10} to fractions with denominator 10.

$$\frac{\frac{9}{10}}{\frac{1}{2}\left(\frac{12}{10}-\frac{3}{10}\right)}$$

Since \frac{12}{10} and \frac{3}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{9}{10}}{\frac{1}{2}\times \frac{12-3}{10}}$$

Subtract 3 from 12 to get 9.

$$\frac{\frac{9}{10}}{\frac{1}{2}\times \frac{9}{10}}$$

Multiply \frac{1}{2} times \frac{9}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{9}{10}}{\frac{1\times 9}{2\times 10}}$$

Do the multiplications in the fraction \frac{1\times 9}{2\times 10}.

$$\frac{\frac{9}{10}}{\frac{9}{20}}$$

Divide \frac{9}{10} by \frac{9}{20} by multiplying \frac{9}{10} by the reciprocal of \frac{9}{20}.

$$\frac{9}{10}\times \frac{20}{9}$$

Multiply \frac{9}{10} times \frac{20}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 20}{10\times 9}$$

Cancel out 9 in both numerator and denominator.

$$\frac{20}{10}$$

Divide 20 by 10 to get 2.

$$2$$

Factor

$$2$$