Solve (42/9-25/6)div11/2=

$$( 4 \frac { 2 } { 9 } - 2 \frac { 5 } { 6 } ) \div 1 \frac { 1 } { 2 } =$$

Evaluate

$$\frac{25}{27}\approx 0.925925926$$

Solution Steps

Multiply 4 and 9 to get 36.

$$\frac{\frac{36+2}{9}-\frac{2\times 6+5}{6}}{\frac{1\times 2+1}{2}}$$

Add 36 and 2 to get 38.

$$\frac{\frac{38}{9}-\frac{2\times 6+5}{6}}{\frac{1\times 2+1}{2}}$$

Multiply 2 and 6 to get 12.

$$\frac{\frac{38}{9}-\frac{12+5}{6}}{\frac{1\times 2+1}{2}}$$

Add 12 and 5 to get 17.

$$\frac{\frac{38}{9}-\frac{17}{6}}{\frac{1\times 2+1}{2}}$$

Least common multiple of 9 and 6 is 18. Convert \frac{38}{9} and \frac{17}{6} to fractions with denominator 18.

$$\frac{\frac{76}{18}-\frac{51}{18}}{\frac{1\times 2+1}{2}}$$

Since \frac{76}{18} and \frac{51}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{76-51}{18}}{\frac{1\times 2+1}{2}}$$

Subtract 51 from 76 to get 25.

$$\frac{\frac{25}{18}}{\frac{1\times 2+1}{2}}$$

Multiply 1 and 2 to get 2.

$$\frac{\frac{25}{18}}{\frac{2+1}{2}}$$

Add 2 and 1 to get 3.

$$\frac{\frac{25}{18}}{\frac{3}{2}}$$

Divide \frac{25}{18} by \frac{3}{2} by multiplying \frac{25}{18} by the reciprocal of \frac{3}{2}.

$$\frac{25}{18}\times \frac{2}{3}$$

Multiply \frac{25}{18} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{25\times 2}{18\times 3}$$

Do the multiplications in the fraction \frac{25\times 2}{18\times 3}.

$$\frac{50}{54}$$

Reduce the fraction \frac{50}{54} to lowest terms by extracting and canceling out 2.

$$\frac{25}{27}$$

Factor

$$\frac{5 ^ {2}}{3 ^ {3}} = 0.9259259259259259$$