Solve 15/6-(5/6+7/13)

$$1 \frac { 5 } { 6 } - ( \frac { 5 } { 6 } + \frac { 7 } { 13 } )$$

Evaluate

$$\frac{6}{13}\approx 0.461538462$$

Solution Steps

Multiply 1 and 6 to get 6.

$$\frac{6+5}{6}-\left(\frac{5}{6}+\frac{7}{13}\right)$$

Add 6 and 5 to get 11.

$$\frac{11}{6}-\left(\frac{5}{6}+\frac{7}{13}\right)$$

Least common multiple of 6 and 13 is 78. Convert \frac{5}{6} and \frac{7}{13} to fractions with denominator 78.

$$\frac{11}{6}-\left(\frac{65}{78}+\frac{42}{78}\right)$$

Since \frac{65}{78} and \frac{42}{78} have the same denominator, add them by adding their numerators.

$$\frac{11}{6}-\frac{65+42}{78}$$

Add 65 and 42 to get 107.

$$\frac{11}{6}-\frac{107}{78}$$

Least common multiple of 6 and 78 is 78. Convert \frac{11}{6} and \frac{107}{78} to fractions with denominator 78.

$$\frac{143}{78}-\frac{107}{78}$$

Since \frac{143}{78} and \frac{107}{78} have the same denominator, subtract them by subtracting their numerators.

$$\frac{143-107}{78}$$

Subtract 107 from 143 to get 36.

$$\frac{36}{78}$$

Reduce the fraction \frac{36}{78} to lowest terms by extracting and canceling out 6.

$$\frac{6}{13}$$

Factor

$$\frac{2 \cdot 3}{13} = 0.46153846153846156$$