Solve 12/3-31/2/2frac{1{5}-32/3}=

$$\frac { 1 \frac { 2 } { 3 } - 3 \frac { 1 } { 2 } } { 2 \frac { 1 } { 5 } - 3 \frac { 2 } { 3 } } =$$

Evaluate

$$\frac{5}{4}=1.25$$

Solution Steps

Multiply 1 and 3 to get 3.

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

Add 3 and 2 to get 5.

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

Multiply 3 and 2 to get 6.

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

Add 6 and 1 to get 7.

$$\frac{\frac{5}{3}-\frac{7}{2}}{\frac{2\times 5+1}{5}-\frac{3\times 3+2}{3}}$$

Least common multiple of 3 and 2 is 6. Convert \frac{5}{3} and \frac{7}{2} to fractions with denominator 6.

$$\frac{\frac{10}{6}-\frac{21}{6}}{\frac{2\times 5+1}{5}-\frac{3\times 3+2}{3}}$$

Since \frac{10}{6} and \frac{21}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{10-21}{6}}{\frac{2\times 5+1}{5}-\frac{3\times 3+2}{3}}$$

Subtract 21 from 10 to get -11.

$$\frac{-\frac{11}{6}}{\frac{2\times 5+1}{5}-\frac{3\times 3+2}{3}}$$

Multiply 2 and 5 to get 10.

$$\frac{-\frac{11}{6}}{\frac{10+1}{5}-\frac{3\times 3+2}{3}}$$

Add 10 and 1 to get 11.

$$\frac{-\frac{11}{6}}{\frac{11}{5}-\frac{3\times 3+2}{3}}$$

Multiply 3 and 3 to get 9.

$$\frac{-\frac{11}{6}}{\frac{11}{5}-\frac{9+2}{3}}$$

Add 9 and 2 to get 11.

$$\frac{-\frac{11}{6}}{\frac{11}{5}-\frac{11}{3}}$$

Least common multiple of 5 and 3 is 15. Convert \frac{11}{5} and \frac{11}{3} to fractions with denominator 15.

$$\frac{-\frac{11}{6}}{\frac{33}{15}-\frac{55}{15}}$$

Since \frac{33}{15} and \frac{55}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{11}{6}}{\frac{33-55}{15}}$$

Subtract 55 from 33 to get -22.

$$\frac{-\frac{11}{6}}{-\frac{22}{15}}$$

Divide -\frac{11}{6} by -\frac{22}{15} by multiplying -\frac{11}{6} by the reciprocal of -\frac{22}{15}.

$$-\frac{11}{6}\left(-\frac{15}{22}\right)$$

Multiply -\frac{11}{6} times -\frac{15}{22} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-11\left(-15\right)}{6\times 22}$$

Do the multiplications in the fraction \frac{-11\left(-15\right)}{6\times 22}.

$$\frac{165}{132}$$

Reduce the fraction \frac{165}{132} to lowest terms by extracting and canceling out 33.

$$\frac{5}{4}$$

Factor

$$\frac{5}{2 ^ {2}} = 1\frac{1}{4} = 1.25$$