Solve y1/2text{of}(3/4-2/5)

$$y \frac { 1 } { 2 } \text { of } ( \frac { 3 } { 4 } - \frac { 2 } { 5 } )$$

Evaluate

$$\frac{7y}{40}$$

Solution Steps

Least common multiple of 4 and 5 is 20. Convert \frac{3}{4} and \frac{2}{5} to fractions with denominator 20.

$$y\times \frac{1}{2}\left(\frac{15}{20}-\frac{8}{20}\right)$$

Since \frac{15}{20} and \frac{8}{20} have the same denominator, subtract them by subtracting their numerators.

$$y\times \frac{1}{2}\times \frac{15-8}{20}$$

Subtract 8 from 15 to get 7.

$$y\times \frac{1}{2}\times \frac{7}{20}$$

Multiply \frac{1}{2} times \frac{7}{20} by multiplying numerator times numerator and denominator times denominator.

$$y\times \frac{1\times 7}{2\times 20}$$

Do the multiplications in the fraction \frac{1\times 7}{2\times 20}.

$$y\times \frac{7}{40}$$

Expand

$$\frac{7y}{40}$$

Solution Steps

Least common multiple of 4 and 5 is 20. Convert \frac{3}{4} and \frac{2}{5} to fractions with denominator 20.

$$y\times \frac{1}{2}\left(\frac{15}{20}-\frac{8}{20}\right)$$

Since \frac{15}{20} and \frac{8}{20} have the same denominator, subtract them by subtracting their numerators.

$$y\times \frac{1}{2}\times \frac{15-8}{20}$$

Subtract 8 from 15 to get 7.

$$y\times \frac{1}{2}\times \frac{7}{20}$$

Multiply \frac{1}{2} times \frac{7}{20} by multiplying numerator times numerator and denominator times denominator.

$$y\times \frac{1\times 7}{2\times 20}$$

Do the multiplications in the fraction \frac{1\times 7}{2\times 20}.

$$y\times \frac{7}{40}$$