Solve [17/19-(5/19+10/19)]div8/13=

$$[ \frac { 17 } { 19 } - ( \frac { 5 } { 19 } + \frac { 10 } { 19 } ) ] \div \frac { 8 } { 13 } =$$

Evaluate

$$\frac{13}{76}\approx 0.171052632$$

Solution Steps

Since \frac{5}{19} and \frac{10}{19} have the same denominator, add them by adding their numerators.

$$\frac{\frac{17}{19}-\frac{5+10}{19}}{\frac{8}{13}}$$

Add 5 and 10 to get 15.

$$\frac{\frac{17}{19}-\frac{15}{19}}{\frac{8}{13}}$$

Since \frac{17}{19} and \frac{15}{19} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{17-15}{19}}{\frac{8}{13}}$$

Subtract 15 from 17 to get 2.

$$\frac{\frac{2}{19}}{\frac{8}{13}}$$

Divide \frac{2}{19} by \frac{8}{13} by multiplying \frac{2}{19} by the reciprocal of \frac{8}{13}.

$$\frac{2}{19}\times \frac{13}{8}$$

Multiply \frac{2}{19} times \frac{13}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 13}{19\times 8}$$

Do the multiplications in the fraction \frac{2\times 13}{19\times 8}.

$$\frac{26}{152}$$

Reduce the fraction \frac{26}{152} to lowest terms by extracting and canceling out 2.

$$\frac{13}{76}$$

Factor

$$\frac{13}{2 ^ {2} \cdot 19} = 0.17105263157894737$$