Solve (105/90-1/11+12/90):(3/9-frac{24}{90})

$$( \frac { 105 } { 90 } - \frac { 1 } { 11 } + \frac { 12 } { 90 } ) : ( \frac { 3 } { 9 } - \frac { 24 } { 90 } )$$

Evaluate

$$\frac{399}{22}\approx 18.136363636$$

Solution Steps

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

$$\frac{\frac{7}{6}-\frac{1}{11}+\frac{12}{90}}{\frac{3}{9}-\frac{24}{90}}$$

Least common multiple of 6 and 11 is 66. Convert \frac{7}{6} and \frac{1}{11} to fractions with denominator 66.

$$\frac{\frac{77}{66}-\frac{6}{66}+\frac{12}{90}}{\frac{3}{9}-\frac{24}{90}}$$

Since \frac{77}{66} and \frac{6}{66} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{77-6}{66}+\frac{12}{90}}{\frac{3}{9}-\frac{24}{90}}$$

Subtract 6 from 77 to get 71.

$$\frac{\frac{71}{66}+\frac{12}{90}}{\frac{3}{9}-\frac{24}{90}}$$

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

$$\frac{\frac{71}{66}+\frac{2}{15}}{\frac{3}{9}-\frac{24}{90}}$$

Least common multiple of 66 and 15 is 330. Convert \frac{71}{66} and \frac{2}{15} to fractions with denominator 330.

$$\frac{\frac{355}{330}+\frac{44}{330}}{\frac{3}{9}-\frac{24}{90}}$$

Since \frac{355}{330} and \frac{44}{330} have the same denominator, add them by adding their numerators.

$$\frac{\frac{355+44}{330}}{\frac{3}{9}-\frac{24}{90}}$$

Add 355 and 44 to get 399.

$$\frac{\frac{399}{330}}{\frac{3}{9}-\frac{24}{90}}$$

Reduce the fraction \frac{399}{330} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{133}{110}}{\frac{3}{9}-\frac{24}{90}}$$

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

$$\frac{\frac{133}{110}}{\frac{1}{3}-\frac{24}{90}}$$

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

$$\frac{\frac{133}{110}}{\frac{1}{3}-\frac{4}{15}}$$

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

$$\frac{\frac{133}{110}}{\frac{5}{15}-\frac{4}{15}}$$

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

$$\frac{\frac{133}{110}}{\frac{5-4}{15}}$$

Subtract 4 from 5 to get 1.

$$\frac{\frac{133}{110}}{\frac{1}{15}}$$

Divide \frac{133}{110} by \frac{1}{15} by multiplying \frac{133}{110} by the reciprocal of \frac{1}{15}.

$$\frac{133}{110}\times 15$$

Express \frac{133}{110}\times 15 as a single fraction.

$$\frac{133\times 15}{110}$$

Multiply 133 and 15 to get 1995.

$$\frac{1995}{110}$$

Reduce the fraction \frac{1995}{110} to lowest terms by extracting and canceling out 5.

$$\frac{399}{22}$$

Factor

$$\frac{3 \cdot 7 \cdot 19}{2 \cdot 11} = 18\frac{3}{22} = 18.136363636363637$$