Solve 1/4+1/5/frac{9{10}}

$$\frac{ \frac{ 1 }{ 4 } + \frac{ 1 }{ 5 } }{ \frac{ 9 }{ 10 } }$$

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

Least common multiple of 4 and 5 is 20. Convert \frac{1}{4} and \frac{1}{5} to fractions with denominator 20.

$$\frac{\frac{5}{20}+\frac{4}{20}}{\frac{9}{10}}$$

Since \frac{5}{20} and \frac{4}{20} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+4}{20}}{\frac{9}{10}}$$

Add 5 and 4 to get 9.

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

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

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

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

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

Cancel out 9 in both numerator and denominator.

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

Reduce the fraction \frac{10}{20} to lowest terms by extracting and canceling out 10.

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$