Solve (11/2-2/3)div21/4

$$( 1 \frac { 1 } { 2 } - \frac { 2 } { 3 } ) \div 2 \frac { 1 } { 4 }$$

Evaluate

$$\frac{10}{27}\approx 0.37037037$$

Solution Steps

Multiply 1 and 2 to get 2.

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

Add 2 and 1 to get 3.

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

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

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

Since \frac{9}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 4 from 9 to get 5.

$$\frac{\frac{5}{6}}{\frac{2\times 4+1}{4}}$$

Multiply 2 and 4 to get 8.

$$\frac{\frac{5}{6}}{\frac{8+1}{4}}$$

Add 8 and 1 to get 9.

$$\frac{\frac{5}{6}}{\frac{9}{4}}$$

Divide \frac{5}{6} by \frac{9}{4} by multiplying \frac{5}{6} by the reciprocal of \frac{9}{4}.

$$\frac{5}{6}\times \frac{4}{9}$$

Multiply \frac{5}{6} times \frac{4}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 4}{6\times 9}$$

Do the multiplications in the fraction \frac{5\times 4}{6\times 9}.

$$\frac{20}{54}$$

Reduce the fraction \frac{20}{54} to lowest terms by extracting and canceling out 2.

$$\frac{10}{27}$$

Factor

$$\frac{2 \cdot 5}{3 ^ {3}} = 0.37037037037037035$$