Solve 1/5*2/3-12/3div22/9

$$\frac { 1 } { 5 } \times \frac { 2 } { 3 } - 1 \frac { 2 } { 3 } \div 2 \frac { 2 } { 9 }$$

Evaluate

$$-\frac{37}{60}\approx -0.616666667$$

Solution Steps

Multiply \frac{1}{5} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\times 2}{5\times 3}.

$$\frac{2}{15}-\frac{\frac{1\times 3+2}{3}}{\frac{2\times 9+2}{9}}$$

Divide \frac{1\times 3+2}{3} by \frac{2\times 9+2}{9} by multiplying \frac{1\times 3+2}{3} by the reciprocal of \frac{2\times 9+2}{9}.

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

Cancel out 3 in both numerator and denominator.

$$\frac{2}{15}-\frac{3\left(2+3\right)}{2+2\times 9}$$

Add 2 and 3 to get 5.

$$\frac{2}{15}-\frac{3\times 5}{2+2\times 9}$$

Multiply 3 and 5 to get 15.

$$\frac{2}{15}-\frac{15}{2+2\times 9}$$

Multiply 2 and 9 to get 18.

$$\frac{2}{15}-\frac{15}{2+18}$$

Add 2 and 18 to get 20.

$$\frac{2}{15}-\frac{15}{20}$$

Reduce the fraction \frac{15}{20} to lowest terms by extracting and canceling out 5.

$$\frac{2}{15}-\frac{3}{4}$$

Least common multiple of 15 and 4 is 60. Convert \frac{2}{15} and \frac{3}{4} to fractions with denominator 60.

$$\frac{8}{60}-\frac{45}{60}$$

Since \frac{8}{60} and \frac{45}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-45}{60}$$

Subtract 45 from 8 to get -37.

$$-\frac{37}{60}$$

Factor

$$-\frac{37}{60} = -0.6166666666666667$$