Solve (2/3 * (- 3/8)) + (4/9 / (- 6/27)) - (5/21 * (- 14/15)) | 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

$$(\frac{2}{3}\times\frac{-3}{8})+(\frac{4}{9}\div\frac{-6}{27})-(\frac{5}{21}\times\frac{-14}{15})$$

Evaluate

$-\frac{73}{36}\approx -2.027777778$

Solution Steps

Fraction $\frac{-3}{8}$ can be rewritten as $-\frac{3}{8}$ by extracting the negative sign.

$$\frac{2}{3}\left(-\frac{3}{8}\right)+\frac{\frac{4}{9}}{\frac{-6}{27}}-\frac{5}{21}\times \frac{-14}{15}$$

Multiply $\frac{2}{3}$ times $-\frac{3}{8}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\left(-3\right)}{3\times 8}+\frac{\frac{4}{9}}{\frac{-6}{27}}-\frac{5}{21}\times \frac{-14}{15}$$

Do the multiplications in the fraction $\frac{2\left(-3\right)}{3\times 8}$.

$$\frac{-6}{24}+\frac{\frac{4}{9}}{\frac{-6}{27}}-\frac{5}{21}\times \frac{-14}{15}$$

Reduce the fraction $\frac{-6}{24}$ to lowest terms by extracting and canceling out $6$.

$$-\frac{1}{4}+\frac{\frac{4}{9}}{\frac{-6}{27}}-\frac{5}{21}\times \frac{-14}{15}$$

Divide $\frac{4}{9}$ by $\frac{-6}{27}$ by multiplying $\frac{4}{9}$ by the reciprocal of $\frac{-6}{27}$.

$$-\frac{1}{4}+\frac{4\times 27}{9\left(-6\right)}-\frac{5}{21}\times \frac{-14}{15}$$

Cancel out $2\times 3\times 9$ in both numerator and denominator.

$$-\frac{1}{4}+\frac{2}{-1}-\frac{5}{21}\times \frac{-14}{15}$$

Fraction $\frac{2}{-1}$ can be rewritten as $-2$ by extracting the negative sign.

$$-\frac{1}{4}-2-\frac{5}{21}\times \frac{-14}{15}$$

Convert $2$ to fraction $\frac{8}{4}$.

$$-\frac{1}{4}-\frac{8}{4}-\frac{5}{21}\times \frac{-14}{15}$$

Since $-\frac{1}{4}$ and $\frac{8}{4}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1-8}{4}-\frac{5}{21}\times \frac{-14}{15}$$

Subtract $8$ from $-1$ to get $-9$.

$$-\frac{9}{4}-\frac{5}{21}\times \frac{-14}{15}$$

Fraction $\frac{-14}{15}$ can be rewritten as $-\frac{14}{15}$ by extracting the negative sign.

$$-\frac{9}{4}-\frac{5}{21}\left(-\frac{14}{15}\right)$$

Multiply $\frac{5}{21}$ times $-\frac{14}{15}$ by multiplying numerator times numerator and denominator times denominator.

$$-\frac{9}{4}-\frac{5\left(-14\right)}{21\times 15}$$

Do the multiplications in the fraction $\frac{5\left(-14\right)}{21\times 15}$.

$$-\frac{9}{4}-\frac{-70}{315}$$

Reduce the fraction $\frac{-70}{315}$ to lowest terms by extracting and canceling out $35$.

$$-\frac{9}{4}-\left(-\frac{2}{9}\right)$$

The opposite of $-\frac{2}{9}$ is $\frac{2}{9}$.

$$-\frac{9}{4}+\frac{2}{9}$$

Least common multiple of $4$ and $9$ is $36$. Convert $-\frac{9}{4}$ and $\frac{2}{9}$ to fractions with denominator $36$.

$$-\frac{81}{36}+\frac{8}{36}$$

Since $-\frac{81}{36}$ and $\frac{8}{36}$ have the same denominator, add them by adding their numerators.

$$\frac{-81+8}{36}$$

Add $-81$ and $8$ to get $-73$.

$$-\frac{73}{36}$$

Factor

$-\frac{73}{36} = -2\frac{1}{36} = -2.0277777777777777$