Solve 11/15div-23/5div9/13

$$\frac { 11 } { 15 } \div - 2 \frac { 3 } { 5 } \div \frac { 9 } { 13 }$$

Evaluate

$$-\frac{11}{27}\approx -0.407407407$$

Solution Steps

Divide \frac{\frac{11}{15}}{-\frac{2\times 5+3}{5}} by \frac{9}{13} by multiplying \frac{\frac{11}{15}}{-\frac{2\times 5+3}{5}} by the reciprocal of \frac{9}{13}.

$$\frac{\frac{11}{15}\times 13}{\left(-\frac{2\times 5+3}{5}\right)\times 9}$$

Express \frac{11}{15}\times 13 as a single fraction.

$$\frac{\frac{11\times 13}{15}}{\left(-\frac{2\times 5+3}{5}\right)\times 9}$$

Multiply 11 and 13 to get 143.

$$\frac{\frac{143}{15}}{\left(-\frac{2\times 5+3}{5}\right)\times 9}$$

Multiply 2 and 5 to get 10.

$$\frac{\frac{143}{15}}{\left(-\frac{10+3}{5}\right)\times 9}$$

Add 10 and 3 to get 13.

$$\frac{\frac{143}{15}}{-\frac{13}{5}\times 9}$$

Express -\frac{13}{5}\times 9 as a single fraction.

$$\frac{\frac{143}{15}}{\frac{-13\times 9}{5}}$$

Multiply -13 and 9 to get -117.

$$\frac{\frac{143}{15}}{\frac{-117}{5}}$$

Fraction \frac{-117}{5} can be rewritten as -\frac{117}{5} by extracting the negative sign.

$$\frac{\frac{143}{15}}{-\frac{117}{5}}$$

Divide \frac{143}{15} by -\frac{117}{5} by multiplying \frac{143}{15} by the reciprocal of -\frac{117}{5}.

$$\frac{143}{15}\left(-\frac{5}{117}\right)$$

Multiply \frac{143}{15} times -\frac{5}{117} by multiplying numerator times numerator and denominator times denominator.

$$\frac{143\left(-5\right)}{15\times 117}$$

Do the multiplications in the fraction \frac{143\left(-5\right)}{15\times 117}.

$$\frac{-715}{1755}$$

Reduce the fraction \frac{-715}{1755} to lowest terms by extracting and canceling out 65.

$$-\frac{11}{27}$$

Factor

$$-\frac{11}{27} = -0.4074074074074074$$