Solve |-7/9|div(2/3-1/5)-1/3*(-4)div(-frac{1}{2})^2*2

$$| - \frac { 7 } { 9 } | \div ( \frac { 2 } { 3 } - \frac { 1 } { 5 } ) - \frac { 1 } { 3 } \times ( - 4 ) \div ( - \frac { 1 } { 2 } ) ^ { 2 } \times 2$$

Evaluate

$$\frac{37}{3}\approx 12.333333333$$

Solution Steps

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{7}{9} is \frac{7}{9}.

$$\frac{\frac{7}{9}}{\frac{2}{3}-\frac{1}{5}}-\frac{\frac{1}{3}\left(-4\right)}{\left(-\frac{1}{2}\right)^{2}}\times 2$$

Least common multiple of 3 and 5 is 15. Convert \frac{2}{3} and \frac{1}{5} to fractions with denominator 15.

$$\frac{\frac{7}{9}}{\frac{10}{15}-\frac{3}{15}}-\frac{\frac{1}{3}\left(-4\right)}{\left(-\frac{1}{2}\right)^{2}}\times 2$$

Since \frac{10}{15} and \frac{3}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7}{9}}{\frac{10-3}{15}}-\frac{\frac{1}{3}\left(-4\right)}{\left(-\frac{1}{2}\right)^{2}}\times 2$$

Subtract 3 from 10 to get 7.

$$\frac{\frac{7}{9}}{\frac{7}{15}}-\frac{\frac{1}{3}\left(-4\right)}{\left(-\frac{1}{2}\right)^{2}}\times 2$$

Divide \frac{7}{9} by \frac{7}{15} by multiplying \frac{7}{9} by the reciprocal of \frac{7}{15}.

$$\frac{7}{9}\times \frac{15}{7}-\frac{\frac{1}{3}\left(-4\right)}{\left(-\frac{1}{2}\right)^{2}}\times 2$$

Multiply \frac{7}{9} times \frac{15}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 15}{9\times 7}-\frac{\frac{1}{3}\left(-4\right)}{\left(-\frac{1}{2}\right)^{2}}\times 2$$

Cancel out 7 in both numerator and denominator.

$$\frac{15}{9}-\frac{\frac{1}{3}\left(-4\right)}{\left(-\frac{1}{2}\right)^{2}}\times 2$$

Reduce the fraction \frac{15}{9} to lowest terms by extracting and canceling out 3.

$$\frac{5}{3}-\frac{\frac{1}{3}\left(-4\right)}{\left(-\frac{1}{2}\right)^{2}}\times 2$$

Multiply \frac{1}{3} and -4 to get \frac{-4}{3}.

$$\frac{5}{3}-\frac{\frac{-4}{3}}{\left(-\frac{1}{2}\right)^{2}}\times 2$$

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

$$\frac{5}{3}-\frac{-\frac{4}{3}}{\left(-\frac{1}{2}\right)^{2}}\times 2$$

Calculate -\frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{5}{3}-\frac{-\frac{4}{3}}{\frac{1}{4}}\times 2$$

Divide -\frac{4}{3} by \frac{1}{4} by multiplying -\frac{4}{3} by the reciprocal of \frac{1}{4}.

$$\frac{5}{3}-\left(-\frac{4}{3}\times 4\times 2\right)$$

Express -\frac{4}{3}\times 4 as a single fraction.

$$\frac{5}{3}-\frac{-4\times 4}{3}\times 2$$

Multiply -4 and 4 to get -16.

$$\frac{5}{3}-\frac{-16}{3}\times 2$$

Fraction \frac{-16}{3} can be rewritten as -\frac{16}{3} by extracting the negative sign.

$$\frac{5}{3}-\left(-\frac{16}{3}\times 2\right)$$

Express -\frac{16}{3}\times 2 as a single fraction.

$$\frac{5}{3}-\frac{-16\times 2}{3}$$

Multiply -16 and 2 to get -32.

$$\frac{5}{3}-\frac{-32}{3}$$

Fraction \frac{-32}{3} can be rewritten as -\frac{32}{3} by extracting the negative sign.

$$\frac{5}{3}-\left(-\frac{32}{3}\right)$$

The opposite of -\frac{32}{3} is \frac{32}{3}.

$$\frac{5}{3}+\frac{32}{3}$$

Since \frac{5}{3} and \frac{32}{3} have the same denominator, add them by adding their numerators.

$$\frac{5+32}{3}$$

Add 5 and 32 to get 37.

$$\frac{37}{3}$$

Factor

$$\frac{37}{3} = 12\frac{1}{3} = 12.333333333333334$$