Solve [(4/7*5/8)-(4/7*3/8)]div[(frac{3}{8}*frac{6}{7})+(frac{3}{8}*frac{2}{7})]

$$[ ( \frac { 4 } { 7 } \times \frac { 5 } { 8 } ) - ( \frac { 4 } { 7 } \times \frac { 3 } { 8 } ) ] \div [ ( \frac { 3 } { 8 } \times \frac { 6 } { 7 } ) + ( \frac { 3 } { 8 } \times \frac { 2 } { 7 } ) ]$$

Evaluate

$$\frac{1}{3}\approx 0.333333333$$

Solution Steps

Multiply \frac{4}{7} times \frac{5}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{4\times 5}{7\times 8}-\frac{4}{7}\times \frac{3}{8}}{\frac{3}{8}\times \frac{6}{7}+\frac{3}{8}\times \frac{2}{7}}$$

Do the multiplications in the fraction \frac{4\times 5}{7\times 8}.

$$\frac{\frac{20}{56}-\frac{4}{7}\times \frac{3}{8}}{\frac{3}{8}\times \frac{6}{7}+\frac{3}{8}\times \frac{2}{7}}$$

Reduce the fraction \frac{20}{56} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{5}{14}-\frac{4}{7}\times \frac{3}{8}}{\frac{3}{8}\times \frac{6}{7}+\frac{3}{8}\times \frac{2}{7}}$$

Multiply \frac{4}{7} times \frac{3}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{5}{14}-\frac{4\times 3}{7\times 8}}{\frac{3}{8}\times \frac{6}{7}+\frac{3}{8}\times \frac{2}{7}}$$

Do the multiplications in the fraction \frac{4\times 3}{7\times 8}.

$$\frac{\frac{5}{14}-\frac{12}{56}}{\frac{3}{8}\times \frac{6}{7}+\frac{3}{8}\times \frac{2}{7}}$$

Reduce the fraction \frac{12}{56} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{5}{14}-\frac{3}{14}}{\frac{3}{8}\times \frac{6}{7}+\frac{3}{8}\times \frac{2}{7}}$$

Since \frac{5}{14} and \frac{3}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5-3}{14}}{\frac{3}{8}\times \frac{6}{7}+\frac{3}{8}\times \frac{2}{7}}$$

Subtract 3 from 5 to get 2.

$$\frac{\frac{2}{14}}{\frac{3}{8}\times \frac{6}{7}+\frac{3}{8}\times \frac{2}{7}}$$

Reduce the fraction \frac{2}{14} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{1}{7}}{\frac{3}{8}\times \frac{6}{7}+\frac{3}{8}\times \frac{2}{7}}$$

Multiply \frac{3}{8} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1}{7}}{\frac{3\times 6}{8\times 7}+\frac{3}{8}\times \frac{2}{7}}$$

Do the multiplications in the fraction \frac{3\times 6}{8\times 7}.

$$\frac{\frac{1}{7}}{\frac{18}{56}+\frac{3}{8}\times \frac{2}{7}}$$

Reduce the fraction \frac{18}{56} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{1}{7}}{\frac{9}{28}+\frac{3}{8}\times \frac{2}{7}}$$

Multiply \frac{3}{8} times \frac{2}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1}{7}}{\frac{9}{28}+\frac{3\times 2}{8\times 7}}$$

Do the multiplications in the fraction \frac{3\times 2}{8\times 7}.

$$\frac{\frac{1}{7}}{\frac{9}{28}+\frac{6}{56}}$$

Reduce the fraction \frac{6}{56} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{1}{7}}{\frac{9}{28}+\frac{3}{28}}$$

Since \frac{9}{28} and \frac{3}{28} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{7}}{\frac{9+3}{28}}$$

Add 9 and 3 to get 12.

$$\frac{\frac{1}{7}}{\frac{12}{28}}$$

Reduce the fraction \frac{12}{28} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{1}{7}}{\frac{3}{7}}$$

Divide \frac{1}{7} by \frac{3}{7} by multiplying \frac{1}{7} by the reciprocal of \frac{3}{7}.

$$\frac{1}{7}\times \frac{7}{3}$$

Multiply \frac{1}{7} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 7}{7\times 3}$$

Cancel out 7 in both numerator and denominator.

$$\frac{1}{3}$$

Factor

$$\frac{1}{3} = 0.3333333333333333$$