Solve 16/25+2*(-4/5)*3/5/2*frac{16{25}-frac{9}{25}}

$$\frac { \frac { 16 } { 25 } + 2 \times ( - \frac { 4 } { 5 } ) \times \frac { 3 } { 5 } } { 2 \times \frac { 16 } { 25 } - \frac { 9 } { 25 } }$$

Evaluate

$$-\frac{8}{23}\approx -0.347826087$$

Solution Steps

Express 2\left(-\frac{4}{5}\right) as a single fraction.

$$\frac{\frac{16}{25}+\frac{2\left(-4\right)}{5}\times \frac{3}{5}}{2\times \frac{16}{25}-\frac{9}{25}}$$

Multiply 2 and -4 to get -8.

$$\frac{\frac{16}{25}+\frac{-8}{5}\times \frac{3}{5}}{2\times \frac{16}{25}-\frac{9}{25}}$$

Fraction \frac{-8}{5} can be rewritten as -\frac{8}{5} by extracting the negative sign.

$$\frac{\frac{16}{25}-\frac{8}{5}\times \frac{3}{5}}{2\times \frac{16}{25}-\frac{9}{25}}$$

Multiply -\frac{8}{5} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{16}{25}+\frac{-8\times 3}{5\times 5}}{2\times \frac{16}{25}-\frac{9}{25}}$$

Do the multiplications in the fraction \frac{-8\times 3}{5\times 5}.

$$\frac{\frac{16}{25}+\frac{-24}{25}}{2\times \frac{16}{25}-\frac{9}{25}}$$

Fraction \frac{-24}{25} can be rewritten as -\frac{24}{25} by extracting the negative sign.

$$\frac{\frac{16}{25}-\frac{24}{25}}{2\times \frac{16}{25}-\frac{9}{25}}$$

Since \frac{16}{25} and \frac{24}{25} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{16-24}{25}}{2\times \frac{16}{25}-\frac{9}{25}}$$

Subtract 24 from 16 to get -8.

$$\frac{-\frac{8}{25}}{2\times \frac{16}{25}-\frac{9}{25}}$$

Express 2\times \frac{16}{25} as a single fraction.

$$\frac{-\frac{8}{25}}{\frac{2\times 16}{25}-\frac{9}{25}}$$

Multiply 2 and 16 to get 32.

$$\frac{-\frac{8}{25}}{\frac{32}{25}-\frac{9}{25}}$$

Since \frac{32}{25} and \frac{9}{25} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{8}{25}}{\frac{32-9}{25}}$$

Subtract 9 from 32 to get 23.

$$\frac{-\frac{8}{25}}{\frac{23}{25}}$$

Divide -\frac{8}{25} by \frac{23}{25} by multiplying -\frac{8}{25} by the reciprocal of \frac{23}{25}.

$$-\frac{8}{25}\times \frac{25}{23}$$

Multiply -\frac{8}{25} times \frac{25}{23} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-8\times 25}{25\times 23}$$

Cancel out 25 in both numerator and denominator.

$$\frac{-8}{23}$$

Fraction \frac{-8}{23} can be rewritten as -\frac{8}{23} by extracting the negative sign.

$$-\frac{8}{23}$$

Factor

$$-\frac{8}{23} = -0.34782608695652173$$