Solve 12.5+107.5-98/5/frac{107.5+98{2}}

$$\frac { 12.5 + \frac { 107.5 - 98 } { 5 } } { \frac { 107.5 + 98 } { 2 } }$$

Evaluate

$$\frac{96}{685}\approx 0.140145985$$

Solution Steps

Subtract 98 from 107.5 to get 9.5.

$$\frac{12.5+\frac{9.5}{5}}{\frac{107.5+98}{2}}$$

Expand \frac{9.5}{5} by multiplying both numerator and the denominator by 10.

$$\frac{12.5+\frac{95}{50}}{\frac{107.5+98}{2}}$$

Reduce the fraction \frac{95}{50} to lowest terms by extracting and canceling out 5.

$$\frac{12.5+\frac{19}{10}}{\frac{107.5+98}{2}}$$

Convert decimal number 12.5 to fraction \frac{125}{10}. Reduce the fraction \frac{125}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{25}{2}+\frac{19}{10}}{\frac{107.5+98}{2}}$$

Least common multiple of 2 and 10 is 10. Convert \frac{25}{2} and \frac{19}{10} to fractions with denominator 10.

$$\frac{\frac{125}{10}+\frac{19}{10}}{\frac{107.5+98}{2}}$$

Since \frac{125}{10} and \frac{19}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{125+19}{10}}{\frac{107.5+98}{2}}$$

Add 125 and 19 to get 144.

$$\frac{\frac{144}{10}}{\frac{107.5+98}{2}}$$

Reduce the fraction \frac{144}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{72}{5}}{\frac{107.5+98}{2}}$$

Add 107.5 and 98 to get 205.5.

$$\frac{\frac{72}{5}}{\frac{205.5}{2}}$$

Expand \frac{205.5}{2} by multiplying both numerator and the denominator by 10.

$$\frac{\frac{72}{5}}{\frac{2055}{20}}$$

Reduce the fraction \frac{2055}{20} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{72}{5}}{\frac{411}{4}}$$

Divide \frac{72}{5} by \frac{411}{4} by multiplying \frac{72}{5} by the reciprocal of \frac{411}{4}.

$$\frac{72}{5}\times \frac{4}{411}$$

Multiply \frac{72}{5} times \frac{4}{411} by multiplying numerator times numerator and denominator times denominator.

$$\frac{72\times 4}{5\times 411}$$

Do the multiplications in the fraction \frac{72\times 4}{5\times 411}.

$$\frac{288}{2055}$$

Reduce the fraction \frac{288}{2055} to lowest terms by extracting and canceling out 3.

$$\frac{96}{685}$$

Factor

$$\frac{3 \cdot 2 ^ {5}}{5 \cdot 137} = 0.14014598540145987$$