Solve [1-(1/20+1/30)*3]div1/30

$$[ 1 - ( \frac { 1 } { 20 } + \frac { 1 } { 30 } ) \times 3 ] \div \frac { 1 } { 30 }$$

Evaluate

$$\frac{45}{2}=22.5$$

Solution Steps

Least common multiple of 20 and 30 is 60. Convert \frac{1}{20} and \frac{1}{30} to fractions with denominator 60.

$$\frac{1-\left(\frac{3}{60}+\frac{2}{60}\right)\times 3}{\frac{1}{30}}$$

Since \frac{3}{60} and \frac{2}{60} have the same denominator, add them by adding their numerators.

$$\frac{1-\frac{3+2}{60}\times 3}{\frac{1}{30}}$$

Add 3 and 2 to get 5.

$$\frac{1-\frac{5}{60}\times 3}{\frac{1}{30}}$$

Reduce the fraction \frac{5}{60} to lowest terms by extracting and canceling out 5.

$$\frac{1-\frac{1}{12}\times 3}{\frac{1}{30}}$$

Multiply \frac{1}{12} and 3 to get \frac{3}{12}.

$$\frac{1-\frac{3}{12}}{\frac{1}{30}}$$

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

$$\frac{1-\frac{1}{4}}{\frac{1}{30}}$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{\frac{4}{4}-\frac{1}{4}}{\frac{1}{30}}$$

Since \frac{4}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4-1}{4}}{\frac{1}{30}}$$

Subtract 1 from 4 to get 3.

$$\frac{\frac{3}{4}}{\frac{1}{30}}$$

Divide \frac{3}{4} by \frac{1}{30} by multiplying \frac{3}{4} by the reciprocal of \frac{1}{30}.

$$\frac{3}{4}\times 30$$

Express \frac{3}{4}\times 30 as a single fraction.

$$\frac{3\times 30}{4}$$

Multiply 3 and 30 to get 90.

$$\frac{90}{4}$$

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

$$\frac{45}{2}$$

Factor

$$\frac{3 ^ {2} \cdot 5}{2} = 22\frac{1}{2} = 22.5$$