Solve 518/119+7/8div7/5-5/7

$$\frac { 518 } { 119 } + \frac { 7 } { 8 } \div \frac { 7 } { 5 } - \frac { 5 } { 7 }$$

Evaluate

$$\frac{4059}{952}\approx 4.263655462$$

Solution Steps

Reduce the fraction \frac{518}{119} to lowest terms by extracting and canceling out 7.

$$\frac{74}{17}+\frac{\frac{7}{8}}{\frac{7}{5}}-\frac{5}{7}$$

Divide \frac{7}{8} by \frac{7}{5} by multiplying \frac{7}{8} by the reciprocal of \frac{7}{5}.

$$\frac{74}{17}+\frac{7}{8}\times \frac{5}{7}-\frac{5}{7}$$

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

$$\frac{74}{17}+\frac{7\times 5}{8\times 7}-\frac{5}{7}$$

Cancel out 7 in both numerator and denominator.

$$\frac{74}{17}+\frac{5}{8}-\frac{5}{7}$$

Least common multiple of 17 and 8 is 136. Convert \frac{74}{17} and \frac{5}{8} to fractions with denominator 136.

$$\frac{592}{136}+\frac{85}{136}-\frac{5}{7}$$

Since \frac{592}{136} and \frac{85}{136} have the same denominator, add them by adding their numerators.

$$\frac{592+85}{136}-\frac{5}{7}$$

Add 592 and 85 to get 677.

$$\frac{677}{136}-\frac{5}{7}$$

Least common multiple of 136 and 7 is 952. Convert \frac{677}{136} and \frac{5}{7} to fractions with denominator 952.

$$\frac{4739}{952}-\frac{680}{952}$$

Since \frac{4739}{952} and \frac{680}{952} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4739-680}{952}$$

Subtract 680 from 4739 to get 4059.

$$\frac{4059}{952}$$

Factor

$$\frac{3 ^ {2} \cdot 11 \cdot 41}{2 ^ {3} \cdot 7 \cdot 17} = 4\frac{251}{952} = 4.263655462184874$$