Solve 85+15/28:42/7-35/6*15/23

$$85 + \frac { 15 } { 28 } : 4 \frac { 2 } { 7 } - 3 \frac { 5 } { 6 } \cdot \frac { 15 } { 23 }$$

Evaluate

$$\frac{661}{8}=82.625$$

Solution Steps

Divide \frac{15}{28} by \frac{4\times 7+2}{7} by multiplying \frac{15}{28} by the reciprocal of \frac{4\times 7+2}{7}.

$$85+\frac{15\times 7}{28\left(4\times 7+2\right)}-\frac{3\times 6+5}{6}\times \frac{15}{23}$$

Cancel out 7 in both numerator and denominator.

$$85+\frac{15}{4\left(2+4\times 7\right)}-\frac{3\times 6+5}{6}\times \frac{15}{23}$$

Multiply 4 and 7 to get 28.

$$85+\frac{15}{4\left(2+28\right)}-\frac{3\times 6+5}{6}\times \frac{15}{23}$$

Add 2 and 28 to get 30.

$$85+\frac{15}{4\times 30}-\frac{3\times 6+5}{6}\times \frac{15}{23}$$

Multiply 4 and 30 to get 120.

$$85+\frac{15}{120}-\frac{3\times 6+5}{6}\times \frac{15}{23}$$

Reduce the fraction \frac{15}{120} to lowest terms by extracting and canceling out 15.

$$85+\frac{1}{8}-\frac{3\times 6+5}{6}\times \frac{15}{23}$$

Convert 85 to fraction \frac{680}{8}.

$$\frac{680}{8}+\frac{1}{8}-\frac{3\times 6+5}{6}\times \frac{15}{23}$$

Since \frac{680}{8} and \frac{1}{8} have the same denominator, add them by adding their numerators.

$$\frac{680+1}{8}-\frac{3\times 6+5}{6}\times \frac{15}{23}$$

Add 680 and 1 to get 681.

$$\frac{681}{8}-\frac{3\times 6+5}{6}\times \frac{15}{23}$$

Multiply 3 and 6 to get 18.

$$\frac{681}{8}-\frac{18+5}{6}\times \frac{15}{23}$$

Add 18 and 5 to get 23.

$$\frac{681}{8}-\frac{23}{6}\times \frac{15}{23}$$

Multiply \frac{23}{6} times \frac{15}{23} by multiplying numerator times numerator and denominator times denominator.

$$\frac{681}{8}-\frac{23\times 15}{6\times 23}$$

Cancel out 23 in both numerator and denominator.

$$\frac{681}{8}-\frac{15}{6}$$

Reduce the fraction \frac{15}{6} to lowest terms by extracting and canceling out 3.

$$\frac{681}{8}-\frac{5}{2}$$

Least common multiple of 8 and 2 is 8. Convert \frac{681}{8} and \frac{5}{2} to fractions with denominator 8.

$$\frac{681}{8}-\frac{20}{8}$$

Since \frac{681}{8} and \frac{20}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{681-20}{8}$$

Subtract 20 from 681 to get 661.

$$\frac{661}{8}$$

Factor

$$\frac{661}{2 ^ {3}} = 82\frac{5}{8} = 82.625$$