Solve 22/5-13/4/frac{4{5}+1/2}

$$\frac { 2 \frac { 2 } { 5 } - 1 \frac { 3 } { 4 } } { \frac { 4 } { 5 } + \frac { 1 } { 2 } }$$

Evaluate

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

Solution Steps

Multiply 2 and 5 to get 10.

$$\frac{\frac{10+2}{5}-\frac{1\times 4+3}{4}}{\frac{4}{5}+\frac{1}{2}}$$

Add 10 and 2 to get 12.

$$\frac{\frac{12}{5}-\frac{1\times 4+3}{4}}{\frac{4}{5}+\frac{1}{2}}$$

Multiply 1 and 4 to get 4.

$$\frac{\frac{12}{5}-\frac{4+3}{4}}{\frac{4}{5}+\frac{1}{2}}$$

Add 4 and 3 to get 7.

$$\frac{\frac{12}{5}-\frac{7}{4}}{\frac{4}{5}+\frac{1}{2}}$$

Least common multiple of 5 and 4 is 20. Convert \frac{12}{5} and \frac{7}{4} to fractions with denominator 20.

$$\frac{\frac{48}{20}-\frac{35}{20}}{\frac{4}{5}+\frac{1}{2}}$$

Since \frac{48}{20} and \frac{35}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{48-35}{20}}{\frac{4}{5}+\frac{1}{2}}$$

Subtract 35 from 48 to get 13.

$$\frac{\frac{13}{20}}{\frac{4}{5}+\frac{1}{2}}$$

Least common multiple of 5 and 2 is 10. Convert \frac{4}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{\frac{13}{20}}{\frac{8}{10}+\frac{5}{10}}$$

Since \frac{8}{10} and \frac{5}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{13}{20}}{\frac{8+5}{10}}$$

Add 8 and 5 to get 13.

$$\frac{\frac{13}{20}}{\frac{13}{10}}$$

Divide \frac{13}{20} by \frac{13}{10} by multiplying \frac{13}{20} by the reciprocal of \frac{13}{10}.

$$\frac{13}{20}\times \frac{10}{13}$$

Multiply \frac{13}{20} times \frac{10}{13} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13\times 10}{20\times 13}$$

Cancel out 13 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

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