Solve (105/90-1/1+12/90):(3/9-frac{24}{90})=

$$( \frac { 105 } { 90 } - \frac { 1 } { 1 } + \frac { 12 } { 90 } ) : ( \frac { 3 } { 9 } - \frac { 24 } { 90 } ) =$$

Evaluate

$$\frac{9}{2}=4.5$$

Solution Steps

Divide 1 by 1 to get 1.

$$\frac{\frac{105}{90}-1+\frac{12}{90}}{\frac{3}{9}-\frac{24}{90}}$$

Reduce the fraction \frac{105}{90} to lowest terms by extracting and canceling out 15.

$$\frac{\frac{7}{6}-1+\frac{12}{90}}{\frac{3}{9}-\frac{24}{90}}$$

Convert 1 to fraction \frac{6}{6}.

$$\frac{\frac{7}{6}-\frac{6}{6}+\frac{12}{90}}{\frac{3}{9}-\frac{24}{90}}$$

Since \frac{7}{6} and \frac{6}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7-6}{6}+\frac{12}{90}}{\frac{3}{9}-\frac{24}{90}}$$

Subtract 6 from 7 to get 1.

$$\frac{\frac{1}{6}+\frac{12}{90}}{\frac{3}{9}-\frac{24}{90}}$$

Reduce the fraction \frac{12}{90} to lowest terms by extracting and canceling out 6.

$$\frac{\frac{1}{6}+\frac{2}{15}}{\frac{3}{9}-\frac{24}{90}}$$

Least common multiple of 6 and 15 is 30. Convert \frac{1}{6} and \frac{2}{15} to fractions with denominator 30.

$$\frac{\frac{5}{30}+\frac{4}{30}}{\frac{3}{9}-\frac{24}{90}}$$

Since \frac{5}{30} and \frac{4}{30} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+4}{30}}{\frac{3}{9}-\frac{24}{90}}$$

Add 5 and 4 to get 9.

$$\frac{\frac{9}{30}}{\frac{3}{9}-\frac{24}{90}}$$

Reduce the fraction \frac{9}{30} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{3}{10}}{\frac{3}{9}-\frac{24}{90}}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{3}{10}}{\frac{1}{3}-\frac{24}{90}}$$

Reduce the fraction \frac{24}{90} to lowest terms by extracting and canceling out 6.

$$\frac{\frac{3}{10}}{\frac{1}{3}-\frac{4}{15}}$$

Least common multiple of 3 and 15 is 15. Convert \frac{1}{3} and \frac{4}{15} to fractions with denominator 15.

$$\frac{\frac{3}{10}}{\frac{5}{15}-\frac{4}{15}}$$

Since \frac{5}{15} and \frac{4}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3}{10}}{\frac{5-4}{15}}$$

Subtract 4 from 5 to get 1.

$$\frac{\frac{3}{10}}{\frac{1}{15}}$$

Divide \frac{3}{10} by \frac{1}{15} by multiplying \frac{3}{10} by the reciprocal of \frac{1}{15}.

$$\frac{3}{10}\times 15$$

Express \frac{3}{10}\times 15 as a single fraction.

$$\frac{3\times 15}{10}$$

Multiply 3 and 15 to get 45.

$$\frac{45}{10}$$

Reduce the fraction \frac{45}{10} to lowest terms by extracting and canceling out 5.

$$\frac{9}{2}$$

Factor

$$\frac{3 ^ {2}}{2} = 4\frac{1}{2} = 4.5$$