Solve 75 / (5/6 + 2/3) * (- 0.21) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$0.75\div(\frac{5}{6}+\frac{2}{3})\times-0.21$$

Evaluate

$-0.105$

Solution Steps

Least common multiple of $6$ and $3$ is $6$. Convert $\frac{5}{6}$ and $\frac{2}{3}$ to fractions with denominator $6$.

$$\frac{0.75}{\frac{5}{6}+\frac{4}{6}}\left(-0.21\right)$$

Since $\frac{5}{6}$ and $\frac{4}{6}$ have the same denominator, add them by adding their numerators.

$$\frac{0.75}{\frac{5+4}{6}}\left(-0.21\right)$$

Add $5$ and $4$ to get $9$.

$$\frac{0.75}{\frac{9}{6}}\left(-0.21\right)$$

Reduce the fraction $\frac{9}{6}$ to lowest terms by extracting and canceling out $3$.

$$\frac{0.75}{\frac{3}{2}}\left(-0.21\right)$$

Divide $0.75$ by $\frac{3}{2}$ by multiplying $0.75$ by the reciprocal of $\frac{3}{2}$.

$$0.75\times \frac{2}{3}\left(-0.21\right)$$

Convert decimal number $0.75$ to fraction $\frac{75}{100}$. Reduce the fraction $\frac{75}{100}$ to lowest terms by extracting and canceling out $25$.

$$\frac{3}{4}\times \frac{2}{3}\left(-0.21\right)$$

Multiply $\frac{3}{4}$ times $\frac{2}{3}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 2}{4\times 3}\left(-0.21\right)$$

Cancel out $3$ in both numerator and denominator.

$$\frac{2}{4}\left(-0.21\right)$$

Reduce the fraction $\frac{2}{4}$ to lowest terms by extracting and canceling out $2$.

$$\frac{1}{2}\left(-0.21\right)$$

Convert decimal number $-0.21$ to fraction $-\frac{21}{100}$.

$$\frac{1}{2}\left(-\frac{21}{100}\right)$$

Multiply $\frac{1}{2}$ times $-\frac{21}{100}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\left(-21\right)}{2\times 100}$$

Do the multiplications in the fraction $\frac{1\left(-21\right)}{2\times 100}$.

$$\frac{-21}{200}$$

Fraction $\frac{-21}{200}$ can be rewritten as $-\frac{21}{200}$ by extracting the negative sign.

$$-\frac{21}{200}$$

Factor

$-0.105$