Solve -(2)/(3)\div((4)/(3)-(7)/(30))

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Question

$$- \frac{ 2 }{ 3 } \div ( \frac{ 4 }{ 3 } - \frac{ 7 }{ 30 } )$$

Evaluate

$-\frac{20}{33}\approx -0.606060606$

Solution Steps

Least common multiple of $3$ and $30$ is $30$. Convert $\frac{4}{3}$ and $\frac{7}{30}$ to fractions with denominator $30$.

$$\frac{-\frac{2}{3}}{\frac{40}{30}-\frac{7}{30}}$$

Since $\frac{40}{30}$ and $\frac{7}{30}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{2}{3}}{\frac{40-7}{30}}$$

Subtract $7$ from $40$ to get $33$.

$$\frac{-\frac{2}{3}}{\frac{33}{30}}$$

Reduce the fraction $\frac{33}{30}$ to lowest terms by extracting and canceling out $3$.

$$\frac{-\frac{2}{3}}{\frac{11}{10}}$$

Divide $-\frac{2}{3}$ by $\frac{11}{10}$ by multiplying $-\frac{2}{3}$ by the reciprocal of $\frac{11}{10}$.

$$-\frac{2}{3}\times \frac{10}{11}$$

Multiply $-\frac{2}{3}$ times $\frac{10}{11}$ by multiplying numerator times numerator and denominator times denominator.

$$\frac{-2\times 10}{3\times 11}$$

Do the multiplications in the fraction $\frac{-2\times 10}{3\times 11}$.

$$\frac{-20}{33}$$

Fraction $\frac{-20}{33}$ can be rewritten as $-\frac{20}{33}$ by extracting the negative sign.

$$-\frac{20}{33}$$

Show Solution

Factor

$-\frac{20}{33} = -0.6060606060606061$