Solve -12/3x(0.5-2/3)div12/9=

$$- 1 \frac { 2 } { 3 } x ( 0.5 - \frac { 2 } { 3 } ) \div 1 \frac { 2 } { 9 } =$$

Evaluate

$$\frac{5x}{22}$$

Solution Steps

Multiply 1 and 3 to get 3.

$$\frac{\left(-\frac{3+2}{3}\right)x\left(0.5-\frac{2}{3}\right)}{\frac{1\times 9+2}{9}}$$

Add 3 and 2 to get 5.

$$\frac{-\frac{5}{3}x\left(0.5-\frac{2}{3}\right)}{\frac{1\times 9+2}{9}}$$

Convert decimal number 0.5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{-\frac{5}{3}x\left(\frac{1}{2}-\frac{2}{3}\right)}{\frac{1\times 9+2}{9}}$$

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{2}{3} to fractions with denominator 6.

$$\frac{-\frac{5}{3}x\left(\frac{3}{6}-\frac{4}{6}\right)}{\frac{1\times 9+2}{9}}$$

Since \frac{3}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{5}{3}x\times \frac{3-4}{6}}{\frac{1\times 9+2}{9}}$$

Subtract 4 from 3 to get -1.

$$\frac{-\frac{5}{3}x\left(-\frac{1}{6}\right)}{\frac{1\times 9+2}{9}}$$

Multiply -\frac{5}{3} times -\frac{1}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-5\left(-1\right)}{3\times 6}x}{\frac{1\times 9+2}{9}}$$

Do the multiplications in the fraction \frac{-5\left(-1\right)}{3\times 6}.

$$\frac{\frac{5}{18}x}{\frac{1\times 9+2}{9}}$$

Multiply 1 and 9 to get 9.

$$\frac{\frac{5}{18}x}{\frac{9+2}{9}}$$

Add 9 and 2 to get 11.

$$\frac{\frac{5}{18}x}{\frac{11}{9}}$$

Divide \frac{5}{18}x by \frac{11}{9} by multiplying \frac{5}{18}x by the reciprocal of \frac{11}{9}.

$$\frac{\frac{5}{18}x\times 9}{11}$$

Express \frac{5}{18}\times 9 as a single fraction.

$$\frac{\frac{5\times 9}{18}x}{11}$$

Multiply 5 and 9 to get 45.

$$\frac{\frac{45}{18}x}{11}$$

Reduce the fraction \frac{45}{18} to lowest terms by extracting and canceling out 9.

$$\frac{\frac{5}{2}x}{11}$$

Divide \frac{5}{2}x by 11 to get \frac{5}{22}x.

$$\frac{5}{22}x$$

Expand

$$\frac{5x}{22}$$

Solution Steps

Multiply 1 and 3 to get 3.

$$\frac{\left(-\frac{3+2}{3}\right)x\left(0.5-\frac{2}{3}\right)}{\frac{1\times 9+2}{9}}$$

Add 3 and 2 to get 5.

$$\frac{-\frac{5}{3}x\left(0.5-\frac{2}{3}\right)}{\frac{1\times 9+2}{9}}$$

Convert decimal number 0.5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{-\frac{5}{3}x\left(\frac{1}{2}-\frac{2}{3}\right)}{\frac{1\times 9+2}{9}}$$

Least common multiple of 2 and 3 is 6. Convert \frac{1}{2} and \frac{2}{3} to fractions with denominator 6.

$$\frac{-\frac{5}{3}x\left(\frac{3}{6}-\frac{4}{6}\right)}{\frac{1\times 9+2}{9}}$$

Since \frac{3}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{5}{3}x\times \frac{3-4}{6}}{\frac{1\times 9+2}{9}}$$

Subtract 4 from 3 to get -1.

$$\frac{-\frac{5}{3}x\left(-\frac{1}{6}\right)}{\frac{1\times 9+2}{9}}$$

Multiply -\frac{5}{3} times -\frac{1}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-5\left(-1\right)}{3\times 6}x}{\frac{1\times 9+2}{9}}$$

Do the multiplications in the fraction \frac{-5\left(-1\right)}{3\times 6}.

$$\frac{\frac{5}{18}x}{\frac{1\times 9+2}{9}}$$

Multiply 1 and 9 to get 9.

$$\frac{\frac{5}{18}x}{\frac{9+2}{9}}$$

Add 9 and 2 to get 11.

$$\frac{\frac{5}{18}x}{\frac{11}{9}}$$

Divide \frac{5}{18}x by \frac{11}{9} by multiplying \frac{5}{18}x by the reciprocal of \frac{11}{9}.

$$\frac{\frac{5}{18}x\times 9}{11}$$

Express \frac{5}{18}\times 9 as a single fraction.

$$\frac{\frac{5\times 9}{18}x}{11}$$

Multiply 5 and 9 to get 45.

$$\frac{\frac{45}{18}x}{11}$$

Reduce the fraction \frac{45}{18} to lowest terms by extracting and canceling out 9.

$$\frac{\frac{5}{2}x}{11}$$

Divide \frac{5}{2}x by 11 to get \frac{5}{22}x.

$$\frac{5}{22}x$$