Solve A/5*((6/10+7/10):1/2+(frac{3}{4}-frac{5}{8})=

$$\frac { A } { 5 } \cdot ( ( \frac { 6 } { 10 } + \frac { 7 } { 10 } ) : \frac { 1 } { 2 } + ( \frac { 3 } { 4 } - \frac { 5 } { 8 } ) =$$

Evaluate

$$\frac{109A}{200}$$

Solution Steps

Since \frac{6}{10} and \frac{7}{10} have the same denominator, add them by adding their numerators.

$$\frac{A}{5}\left(\frac{\frac{6+7}{10}}{\frac{1}{2}}+\frac{3}{4}-\frac{5}{8}\right)$$

Add 6 and 7 to get 13.

$$\frac{A}{5}\left(\frac{\frac{13}{10}}{\frac{1}{2}}+\frac{3}{4}-\frac{5}{8}\right)$$

Divide \frac{13}{10} by \frac{1}{2} by multiplying \frac{13}{10} by the reciprocal of \frac{1}{2}.

$$\frac{A}{5}\left(\frac{13}{10}\times 2+\frac{3}{4}-\frac{5}{8}\right)$$

Express \frac{13}{10}\times 2 as a single fraction.

$$\frac{A}{5}\left(\frac{13\times 2}{10}+\frac{3}{4}-\frac{5}{8}\right)$$

Multiply 13 and 2 to get 26.

$$\frac{A}{5}\left(\frac{26}{10}+\frac{3}{4}-\frac{5}{8}\right)$$

Reduce the fraction \frac{26}{10} to lowest terms by extracting and canceling out 2.

$$\frac{A}{5}\left(\frac{13}{5}+\frac{3}{4}-\frac{5}{8}\right)$$

Least common multiple of 5 and 4 is 20. Convert \frac{13}{5} and \frac{3}{4} to fractions with denominator 20.

$$\frac{A}{5}\left(\frac{52}{20}+\frac{15}{20}-\frac{5}{8}\right)$$

Since \frac{52}{20} and \frac{15}{20} have the same denominator, add them by adding their numerators.

$$\frac{A}{5}\left(\frac{52+15}{20}-\frac{5}{8}\right)$$

Add 52 and 15 to get 67.

$$\frac{A}{5}\left(\frac{67}{20}-\frac{5}{8}\right)$$

Least common multiple of 20 and 8 is 40. Convert \frac{67}{20} and \frac{5}{8} to fractions with denominator 40.

$$\frac{A}{5}\left(\frac{134}{40}-\frac{25}{40}\right)$$

Since \frac{134}{40} and \frac{25}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{A}{5}\times \frac{134-25}{40}$$

Subtract 25 from 134 to get 109.

$$\frac{A}{5}\times \frac{109}{40}$$

Multiply \frac{A}{5} times \frac{109}{40} by multiplying numerator times numerator and denominator times denominator.

$$\frac{A\times 109}{5\times 40}$$

Multiply 5 and 40 to get 200.

$$\frac{A\times 109}{200}$$

Expand

$$\frac{109A}{200}$$

Solution Steps

Since \frac{6}{10} and \frac{7}{10} have the same denominator, add them by adding their numerators.

$$\frac{A}{5}\left(\frac{\frac{6+7}{10}}{\frac{1}{2}}+\frac{3}{4}-\frac{5}{8}\right)$$

Add 6 and 7 to get 13.

$$\frac{A}{5}\left(\frac{\frac{13}{10}}{\frac{1}{2}}+\frac{3}{4}-\frac{5}{8}\right)$$

Divide \frac{13}{10} by \frac{1}{2} by multiplying \frac{13}{10} by the reciprocal of \frac{1}{2}.

$$\frac{A}{5}\left(\frac{13}{10}\times 2+\frac{3}{4}-\frac{5}{8}\right)$$

Express \frac{13}{10}\times 2 as a single fraction.

$$\frac{A}{5}\left(\frac{13\times 2}{10}+\frac{3}{4}-\frac{5}{8}\right)$$

Multiply 13 and 2 to get 26.

$$\frac{A}{5}\left(\frac{26}{10}+\frac{3}{4}-\frac{5}{8}\right)$$

Reduce the fraction \frac{26}{10} to lowest terms by extracting and canceling out 2.

$$\frac{A}{5}\left(\frac{13}{5}+\frac{3}{4}-\frac{5}{8}\right)$$

Least common multiple of 5 and 4 is 20. Convert \frac{13}{5} and \frac{3}{4} to fractions with denominator 20.

$$\frac{A}{5}\left(\frac{52}{20}+\frac{15}{20}-\frac{5}{8}\right)$$

Since \frac{52}{20} and \frac{15}{20} have the same denominator, add them by adding their numerators.

$$\frac{A}{5}\left(\frac{52+15}{20}-\frac{5}{8}\right)$$

Add 52 and 15 to get 67.

$$\frac{A}{5}\left(\frac{67}{20}-\frac{5}{8}\right)$$

Least common multiple of 20 and 8 is 40. Convert \frac{67}{20} and \frac{5}{8} to fractions with denominator 40.

$$\frac{A}{5}\left(\frac{134}{40}-\frac{25}{40}\right)$$

Since \frac{134}{40} and \frac{25}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{A}{5}\times \frac{134-25}{40}$$

Subtract 25 from 134 to get 109.

$$\frac{A}{5}\times \frac{109}{40}$$

Multiply \frac{A}{5} times \frac{109}{40} by multiplying numerator times numerator and denominator times denominator.

$$\frac{A\times 109}{5\times 40}$$

Multiply 5 and 40 to get 200.

$$\frac{A\times 109}{200}$$