Solve (33/4-1/5+1/2)*1/9

$$( 3 \frac { 3 } { 4 } - \frac { 1 } { 5 } + \frac { 1 } { 2 } ) \times \frac { 1 } { 9 }$$

Evaluate

$$\frac{9}{20}=0.45$$

Solution Steps

Multiply 3 and 4 to get 12.

$$\left(\frac{12+3}{4}-\frac{1}{5}+\frac{1}{2}\right)\times \frac{1}{9}$$

Add 12 and 3 to get 15.

$$\left(\frac{15}{4}-\frac{1}{5}+\frac{1}{2}\right)\times \frac{1}{9}$$

Least common multiple of 4 and 5 is 20. Convert \frac{15}{4} and \frac{1}{5} to fractions with denominator 20.

$$\left(\frac{75}{20}-\frac{4}{20}+\frac{1}{2}\right)\times \frac{1}{9}$$

Since \frac{75}{20} and \frac{4}{20} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{75-4}{20}+\frac{1}{2}\right)\times \frac{1}{9}$$

Subtract 4 from 75 to get 71.

$$\left(\frac{71}{20}+\frac{1}{2}\right)\times \frac{1}{9}$$

Least common multiple of 20 and 2 is 20. Convert \frac{71}{20} and \frac{1}{2} to fractions with denominator 20.

$$\left(\frac{71}{20}+\frac{10}{20}\right)\times \frac{1}{9}$$

Since \frac{71}{20} and \frac{10}{20} have the same denominator, add them by adding their numerators.

$$\frac{71+10}{20}\times \frac{1}{9}$$

Add 71 and 10 to get 81.

$$\frac{81}{20}\times \frac{1}{9}$$

Multiply \frac{81}{20} times \frac{1}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{81\times 1}{20\times 9}$$

Do the multiplications in the fraction \frac{81\times 1}{20\times 9}.

$$\frac{81}{180}$$

Reduce the fraction \frac{81}{180} to lowest terms by extracting and canceling out 9.

$$\frac{9}{20}$$

Factor

$$\frac{3 ^ {2}}{2 ^ {2} \cdot 5} = 0.45$$