Solve 4/9 / \{4/5 * (4/25 - 7/10)\} + 1/2

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

Question

$$\frac{4}{9}\div\{\frac{4}{5}\times(\frac{4}{25}-\frac{7}{10})\}+\frac{1}{2}$$

Evaluate

$-\frac{257}{486}\approx -0.528806584$

Solution Steps

Least common multiple of $25$ and $10$ is $50$. Convert $\frac{4}{25}$ and $\frac{7}{10}$ to fractions with denominator $50$.

$$\frac{\frac{4}{9}}{\frac{4}{5}\left(\frac{8}{50}-\frac{35}{50}\right)}+\frac{1}{2}$$

Since $\frac{8}{50}$ and $\frac{35}{50}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4}{9}}{\frac{4}{5}\times \frac{8-35}{50}}+\frac{1}{2}$$

Subtract $35$ from $8$ to get $-27$.

$$\frac{\frac{4}{9}}{\frac{4}{5}\left(-\frac{27}{50}\right)}+\frac{1}{2}$$

Multiply $\frac{4}{5}$ times $-\frac{27}{50}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{4}{9}}{\frac{4\left(-27\right)}{5\times 50}}+\frac{1}{2}$$

Do the multiplications in the fraction $\frac{4\left(-27\right)}{5\times 50}$.

$$\frac{\frac{4}{9}}{\frac{-108}{250}}+\frac{1}{2}$$

Reduce the fraction $\frac{-108}{250}$ to lowest terms by extracting and canceling out $2$.

$$\frac{\frac{4}{9}}{-\frac{54}{125}}+\frac{1}{2}$$

Divide $\frac{4}{9}$ by $-\frac{54}{125}$ by multiplying $\frac{4}{9}$ by the reciprocal of $-\frac{54}{125}$.

$$\frac{4}{9}\left(-\frac{125}{54}\right)+\frac{1}{2}$$

Multiply $\frac{4}{9}$ times $-\frac{125}{54}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\left(-125\right)}{9\times 54}+\frac{1}{2}$$

Do the multiplications in the fraction $\frac{4\left(-125\right)}{9\times 54}$.

$$\frac{-500}{486}+\frac{1}{2}$$

Reduce the fraction $\frac{-500}{486}$ to lowest terms by extracting and canceling out $2$.

$$-\frac{250}{243}+\frac{1}{2}$$

Least common multiple of $243$ and $2$ is $486$. Convert $-\frac{250}{243}$ and $\frac{1}{2}$ to fractions with denominator $486$.

$$-\frac{500}{486}+\frac{243}{486}$$

Since $-\frac{500}{486}$ and $\frac{243}{486}$ have the same denominator, add them by adding their numerators.

$$\frac{-500+243}{486}$$

Add $-500$ and $243$ to get $-257$.

$$-\frac{257}{486}$$

Show Solution

Factor

$-\frac{257}{486} = -0.5288065843621399$