Solve (8/9-4/5):2*31/2

$$( \frac { 8 } { 9 } - \frac { 4 } { 5 } ) : 2 \cdot 3 \frac { 1 } { 2 }$$

Evaluate

$$\frac{7}{45}\approx 0.155555556$$

Solution Steps

Least common multiple of 9 and 5 is 45. Convert \frac{8}{9} and \frac{4}{5} to fractions with denominator 45.

$$\frac{\frac{40}{45}-\frac{36}{45}}{2}\times \frac{3\times 2+1}{2}$$

Since \frac{40}{45} and \frac{36}{45} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{40-36}{45}}{2}\times \frac{3\times 2+1}{2}$$

Subtract 36 from 40 to get 4.

$$\frac{\frac{4}{45}}{2}\times \frac{3\times 2+1}{2}$$

Express \frac{\frac{4}{45}}{2} as a single fraction.

$$\frac{4}{45\times 2}\times \frac{3\times 2+1}{2}$$

Multiply 45 and 2 to get 90.

$$\frac{4}{90}\times \frac{3\times 2+1}{2}$$

Reduce the fraction \frac{4}{90} to lowest terms by extracting and canceling out 2.

$$\frac{2}{45}\times \frac{3\times 2+1}{2}$$

Multiply 3 and 2 to get 6.

$$\frac{2}{45}\times \frac{6+1}{2}$$

Add 6 and 1 to get 7.

$$\frac{2}{45}\times \frac{7}{2}$$

Multiply \frac{2}{45} times \frac{7}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 7}{45\times 2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{7}{45}$$

Factor

$$\frac{7}{3 ^ {2} \cdot 5} = 0.15555555555555556$$