Solve 27/100:(11/4-3/2+11/2+frac{1}{4})]

$$\frac { 27 } { 100 } : ( \frac { 11 } { 4 } - \frac { 3 } { 2 } + 1 \frac { 1 } { 2 } + \frac { 1 } { 4 } ) ]$$

Evaluate

$$\frac{9}{100}=0.09$$

Solution Steps

Least common multiple of 4 and 2 is 4. Convert \frac{11}{4} and \frac{3}{2} to fractions with denominator 4.

$$\frac{\frac{27}{100}}{\frac{11}{4}-\frac{6}{4}+\frac{1\times 2+1}{2}+\frac{1}{4}}$$

Since \frac{11}{4} and \frac{6}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{27}{100}}{\frac{11-6}{4}+\frac{1\times 2+1}{2}+\frac{1}{4}}$$

Subtract 6 from 11 to get 5.

$$\frac{\frac{27}{100}}{\frac{5}{4}+\frac{1\times 2+1}{2}+\frac{1}{4}}$$

Multiply 1 and 2 to get 2.

$$\frac{\frac{27}{100}}{\frac{5}{4}+\frac{2+1}{2}+\frac{1}{4}}$$

Add 2 and 1 to get 3.

$$\frac{\frac{27}{100}}{\frac{5}{4}+\frac{3}{2}+\frac{1}{4}}$$

Least common multiple of 4 and 2 is 4. Convert \frac{5}{4} and \frac{3}{2} to fractions with denominator 4.

$$\frac{\frac{27}{100}}{\frac{5}{4}+\frac{6}{4}+\frac{1}{4}}$$

Since \frac{5}{4} and \frac{6}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{27}{100}}{\frac{5+6}{4}+\frac{1}{4}}$$

Add 5 and 6 to get 11.

$$\frac{\frac{27}{100}}{\frac{11}{4}+\frac{1}{4}}$$

Since \frac{11}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{27}{100}}{\frac{11+1}{4}}$$

Add 11 and 1 to get 12.

$$\frac{\frac{27}{100}}{\frac{12}{4}}$$

Divide 12 by 4 to get 3.

$$\frac{\frac{27}{100}}{3}$$

Express \frac{\frac{27}{100}}{3} as a single fraction.

$$\frac{27}{100\times 3}$$

Multiply 100 and 3 to get 300.

$$\frac{27}{300}$$

Reduce the fraction \frac{27}{300} to lowest terms by extracting and canceling out 3.

$$\frac{9}{100}$$

Factor

$$\frac{3 ^ {2}}{2 ^ {2} \cdot 5 ^ {2}} = 0.09$$