Solve 77/13-(53/7+17/13)

$$7 \frac { 7 } { 13 } - ( 5 \frac { 3 } { 7 } + 1 \frac { 7 } { 13 } )$$

Evaluate

$$\frac{4}{7}\approx 0.571428571$$

Solution Steps

Multiply 7 and 13 to get 91.

$$\frac{91+7}{13}-\left(\frac{5\times 7+3}{7}+\frac{1\times 13+7}{13}\right)$$

Add 91 and 7 to get 98.

$$\frac{98}{13}-\left(\frac{5\times 7+3}{7}+\frac{1\times 13+7}{13}\right)$$

Multiply 5 and 7 to get 35.

$$\frac{98}{13}-\left(\frac{35+3}{7}+\frac{1\times 13+7}{13}\right)$$

Add 35 and 3 to get 38.

$$\frac{98}{13}-\left(\frac{38}{7}+\frac{1\times 13+7}{13}\right)$$

Multiply 1 and 13 to get 13.

$$\frac{98}{13}-\left(\frac{38}{7}+\frac{13+7}{13}\right)$$

Add 13 and 7 to get 20.

$$\frac{98}{13}-\left(\frac{38}{7}+\frac{20}{13}\right)$$

Least common multiple of 7 and 13 is 91. Convert \frac{38}{7} and \frac{20}{13} to fractions with denominator 91.

$$\frac{98}{13}-\left(\frac{494}{91}+\frac{140}{91}\right)$$

Since \frac{494}{91} and \frac{140}{91} have the same denominator, add them by adding their numerators.

$$\frac{98}{13}-\frac{494+140}{91}$$

Add 494 and 140 to get 634.

$$\frac{98}{13}-\frac{634}{91}$$

Least common multiple of 13 and 91 is 91. Convert \frac{98}{13} and \frac{634}{91} to fractions with denominator 91.

$$\frac{686}{91}-\frac{634}{91}$$

Since \frac{686}{91} and \frac{634}{91} have the same denominator, subtract them by subtracting their numerators.

$$\frac{686-634}{91}$$

Subtract 634 from 686 to get 52.

$$\frac{52}{91}$$

Reduce the fraction \frac{52}{91} to lowest terms by extracting and canceling out 13.

$$\frac{4}{7}$$

Factor

$$\frac{2 ^ {2}}{7} = 0.5714285714285714$$