Solve 7/8*(4/7+1/2)*8/9

$$\frac { 7 } { 8 } \times ( \frac { 4 } { 7 } + \frac { 1 } { 2 } ) \times \frac { 8 } { 9 }$$

Evaluate

$$\frac{5}{6}\approx 0.833333333$$

Solution Steps

Least common multiple of 7 and 2 is 14. Convert \frac{4}{7} and \frac{1}{2} to fractions with denominator 14.

$$\frac{7}{8}\left(\frac{8}{14}+\frac{7}{14}\right)\times \frac{8}{9}$$

Since \frac{8}{14} and \frac{7}{14} have the same denominator, add them by adding their numerators.

$$\frac{7}{8}\times \frac{8+7}{14}\times \frac{8}{9}$$

Add 8 and 7 to get 15.

$$\frac{7}{8}\times \frac{15}{14}\times \frac{8}{9}$$

Multiply \frac{7}{8} times \frac{15}{14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 15}{8\times 14}\times \frac{8}{9}$$

Do the multiplications in the fraction \frac{7\times 15}{8\times 14}.

$$\frac{105}{112}\times \frac{8}{9}$$

Reduce the fraction \frac{105}{112} to lowest terms by extracting and canceling out 7.

$$\frac{15}{16}\times \frac{8}{9}$$

Multiply \frac{15}{16} times \frac{8}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{15\times 8}{16\times 9}$$

Do the multiplications in the fraction \frac{15\times 8}{16\times 9}.

$$\frac{120}{144}$$

Reduce the fraction \frac{120}{144} to lowest terms by extracting and canceling out 24.

$$\frac{5}{6}$$

Factor

$$\frac{5}{2 \cdot 3} = 0.8333333333333334$$