Solve (60/9-105/90)div55/10+(126/99-frac{108}{99})divfrac{18}{99}

$$( \frac{ 60 }{ 9 } - \frac{ 105 }{ 90 } ) \div \frac{ 55 }{ 10 } +( \frac{ 126 }{ 99 } - \frac{ 108 }{ 99 } ) \div \frac{ 18 }{ 99 }$$

Evaluate

$$2$$

Solution Steps

Reduce the fraction \frac{60}{9} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{20}{3}-\frac{105}{90}}{\frac{55}{10}}+\frac{\frac{126}{99}-\frac{108}{99}}{\frac{18}{99}}$$

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

$$\frac{\frac{20}{3}-\frac{7}{6}}{\frac{55}{10}}+\frac{\frac{126}{99}-\frac{108}{99}}{\frac{18}{99}}$$

Least common multiple of 3 and 6 is 6. Convert \frac{20}{3} and \frac{7}{6} to fractions with denominator 6.

$$\frac{\frac{40}{6}-\frac{7}{6}}{\frac{55}{10}}+\frac{\frac{126}{99}-\frac{108}{99}}{\frac{18}{99}}$$

Since \frac{40}{6} and \frac{7}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{40-7}{6}}{\frac{55}{10}}+\frac{\frac{126}{99}-\frac{108}{99}}{\frac{18}{99}}$$

Subtract 7 from 40 to get 33.

$$\frac{\frac{33}{6}}{\frac{55}{10}}+\frac{\frac{126}{99}-\frac{108}{99}}{\frac{18}{99}}$$

Reduce the fraction \frac{33}{6} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{11}{2}}{\frac{55}{10}}+\frac{\frac{126}{99}-\frac{108}{99}}{\frac{18}{99}}$$

Reduce the fraction \frac{55}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{11}{2}}{\frac{11}{2}}+\frac{\frac{126}{99}-\frac{108}{99}}{\frac{18}{99}}$$

Divide \frac{11}{2} by \frac{11}{2} to get 1.

$$1+\frac{\frac{126}{99}-\frac{108}{99}}{\frac{18}{99}}$$

Reduce the fraction \frac{126}{99} to lowest terms by extracting and canceling out 9.

$$1+\frac{\frac{14}{11}-\frac{108}{99}}{\frac{18}{99}}$$

Reduce the fraction \frac{108}{99} to lowest terms by extracting and canceling out 9.

$$1+\frac{\frac{14}{11}-\frac{12}{11}}{\frac{18}{99}}$$

Since \frac{14}{11} and \frac{12}{11} have the same denominator, subtract them by subtracting their numerators.

$$1+\frac{\frac{14-12}{11}}{\frac{18}{99}}$$

Subtract 12 from 14 to get 2.

$$1+\frac{\frac{2}{11}}{\frac{18}{99}}$$

Reduce the fraction \frac{18}{99} to lowest terms by extracting and canceling out 9.

$$1+\frac{\frac{2}{11}}{\frac{2}{11}}$$

Divide \frac{2}{11} by \frac{2}{11} to get 1.

$$1+1$$

Add 1 and 1 to get 2.

$$2$$

Factor

$$2$$