Solve (2/3div4/9)(10-5/2)

$$( \frac { 2 } { 3 } \div \frac { 4 } { 9 } ) ( 10 - \frac { 5 } { 2 } )$$

Evaluate

$$\frac{45}{4}=11.25$$

Solution Steps

Divide \frac{2}{3} by \frac{4}{9} by multiplying \frac{2}{3} by the reciprocal of \frac{4}{9}.

$$\frac{2}{3}\times \frac{9}{4}\left(10-\frac{5}{2}\right)$$

Multiply \frac{2}{3} times \frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 9}{3\times 4}\left(10-\frac{5}{2}\right)$$

Do the multiplications in the fraction \frac{2\times 9}{3\times 4}.

$$\frac{18}{12}\left(10-\frac{5}{2}\right)$$

Reduce the fraction \frac{18}{12} to lowest terms by extracting and canceling out 6.

$$\frac{3}{2}\left(10-\frac{5}{2}\right)$$

Convert 10 to fraction \frac{20}{2}.

$$\frac{3}{2}\left(\frac{20}{2}-\frac{5}{2}\right)$$

Since \frac{20}{2} and \frac{5}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{2}\times \frac{20-5}{2}$$

Subtract 5 from 20 to get 15.

$$\frac{3}{2}\times \frac{15}{2}$$

Multiply \frac{3}{2} times \frac{15}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 15}{2\times 2}$$

Do the multiplications in the fraction \frac{3\times 15}{2\times 2}.

$$\frac{45}{4}$$

Factor

$$\frac{3 ^ {2} \cdot 5}{2 ^ {2}} = 11\frac{1}{4} = 11.25$$