Solve 1/8+7/80/frac{5{6}-4/15}

$$\frac { \frac { 1 } { 8 } + \frac { 7 } { 80 } } { \frac { 5 } { 6 } - \frac { 4 } { 15 } }$$

Evaluate

$$\frac{3}{8}=0.375$$

Solution Steps

Least common multiple of 8 and 80 is 80. Convert \frac{1}{8} and \frac{7}{80} to fractions with denominator 80.

$$\frac{\frac{10}{80}+\frac{7}{80}}{\frac{5}{6}-\frac{4}{15}}$$

Since \frac{10}{80} and \frac{7}{80} have the same denominator, add them by adding their numerators.

$$\frac{\frac{10+7}{80}}{\frac{5}{6}-\frac{4}{15}}$$

Add 10 and 7 to get 17.

$$\frac{\frac{17}{80}}{\frac{5}{6}-\frac{4}{15}}$$

Least common multiple of 6 and 15 is 30. Convert \frac{5}{6} and \frac{4}{15} to fractions with denominator 30.

$$\frac{\frac{17}{80}}{\frac{25}{30}-\frac{8}{30}}$$

Since \frac{25}{30} and \frac{8}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{17}{80}}{\frac{25-8}{30}}$$

Subtract 8 from 25 to get 17.

$$\frac{\frac{17}{80}}{\frac{17}{30}}$$

Divide \frac{17}{80} by \frac{17}{30} by multiplying \frac{17}{80} by the reciprocal of \frac{17}{30}.

$$\frac{17}{80}\times \frac{30}{17}$$

Multiply \frac{17}{80} times \frac{30}{17} by multiplying numerator times numerator and denominator times denominator.

$$\frac{17\times 30}{80\times 17}$$

Cancel out 17 in both numerator and denominator.

$$\frac{30}{80}$$

Reduce the fraction \frac{30}{80} to lowest terms by extracting and canceling out 10.

$$\frac{3}{8}$$

Factor

$$\frac{3}{2 ^ {3}} = 0.375$$