Solve 1+1/2*5/4-2/3(5/2-frac{2}{5})

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

Evaluate

$$\frac{9}{40}=0.225$$

Solution Steps

Multiply \frac{1}{2} times \frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$1+\frac{1\times 5}{2\times 4}-\frac{2}{3}\left(\frac{5}{2}-\frac{2}{5}\right)$$

Do the multiplications in the fraction \frac{1\times 5}{2\times 4}.

$$1+\frac{5}{8}-\frac{2}{3}\left(\frac{5}{2}-\frac{2}{5}\right)$$

Convert 1 to fraction \frac{8}{8}.

$$\frac{8}{8}+\frac{5}{8}-\frac{2}{3}\left(\frac{5}{2}-\frac{2}{5}\right)$$

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

$$\frac{8+5}{8}-\frac{2}{3}\left(\frac{5}{2}-\frac{2}{5}\right)$$

Add 8 and 5 to get 13.

$$\frac{13}{8}-\frac{2}{3}\left(\frac{5}{2}-\frac{2}{5}\right)$$

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

$$\frac{13}{8}-\frac{2}{3}\left(\frac{25}{10}-\frac{4}{10}\right)$$

Since \frac{25}{10} and \frac{4}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13}{8}-\frac{2}{3}\times \frac{25-4}{10}$$

Subtract 4 from 25 to get 21.

$$\frac{13}{8}-\frac{2}{3}\times \frac{21}{10}$$

Multiply \frac{2}{3} times \frac{21}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13}{8}-\frac{2\times 21}{3\times 10}$$

Do the multiplications in the fraction \frac{2\times 21}{3\times 10}.

$$\frac{13}{8}-\frac{42}{30}$$

Reduce the fraction \frac{42}{30} to lowest terms by extracting and canceling out 6.

$$\frac{13}{8}-\frac{7}{5}$$

Least common multiple of 8 and 5 is 40. Convert \frac{13}{8} and \frac{7}{5} to fractions with denominator 40.

$$\frac{65}{40}-\frac{56}{40}$$

Since \frac{65}{40} and \frac{56}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{65-56}{40}$$

Subtract 56 from 65 to get 9.

$$\frac{9}{40}$$

Factor

$$\frac{3 ^ {2}}{2 ^ {3} \cdot 5} = 0.225$$