Solve 7/20-3/10+4/9/(frac{7{20}-frac{3}{10})*frac{4}{9}}=

$$\frac { \frac { 7 } { 20 } - \frac { 3 } { 10 } + \frac { 4 } { 9 } } { ( \frac { 7 } { 20 } - \frac { 3 } { 10 } ) \times \frac { 4 } { 9 } } =$$

Evaluate

$$\frac{89}{4}=22.25$$

Solution Steps

Least common multiple of 20 and 10 is 20. Convert \frac{7}{20} and \frac{3}{10} to fractions with denominator 20.

$$\frac{\frac{7}{20}-\frac{6}{20}+\frac{4}{9}}{\left(\frac{7}{20}-\frac{3}{10}\right)\times \frac{4}{9}}$$

Since \frac{7}{20} and \frac{6}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7-6}{20}+\frac{4}{9}}{\left(\frac{7}{20}-\frac{3}{10}\right)\times \frac{4}{9}}$$

Subtract 6 from 7 to get 1.

$$\frac{\frac{1}{20}+\frac{4}{9}}{\left(\frac{7}{20}-\frac{3}{10}\right)\times \frac{4}{9}}$$

Least common multiple of 20 and 9 is 180. Convert \frac{1}{20} and \frac{4}{9} to fractions with denominator 180.

$$\frac{\frac{9}{180}+\frac{80}{180}}{\left(\frac{7}{20}-\frac{3}{10}\right)\times \frac{4}{9}}$$

Since \frac{9}{180} and \frac{80}{180} have the same denominator, add them by adding their numerators.

$$\frac{\frac{9+80}{180}}{\left(\frac{7}{20}-\frac{3}{10}\right)\times \frac{4}{9}}$$

Add 9 and 80 to get 89.

$$\frac{\frac{89}{180}}{\left(\frac{7}{20}-\frac{3}{10}\right)\times \frac{4}{9}}$$

Least common multiple of 20 and 10 is 20. Convert \frac{7}{20} and \frac{3}{10} to fractions with denominator 20.

$$\frac{\frac{89}{180}}{\left(\frac{7}{20}-\frac{6}{20}\right)\times \frac{4}{9}}$$

Since \frac{7}{20} and \frac{6}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{89}{180}}{\frac{7-6}{20}\times \frac{4}{9}}$$

Subtract 6 from 7 to get 1.

$$\frac{\frac{89}{180}}{\frac{1}{20}\times \frac{4}{9}}$$

Multiply \frac{1}{20} times \frac{4}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{89}{180}}{\frac{1\times 4}{20\times 9}}$$

Do the multiplications in the fraction \frac{1\times 4}{20\times 9}.

$$\frac{\frac{89}{180}}{\frac{4}{180}}$$

Reduce the fraction \frac{4}{180} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{89}{180}}{\frac{1}{45}}$$

Divide \frac{89}{180} by \frac{1}{45} by multiplying \frac{89}{180} by the reciprocal of \frac{1}{45}.

$$\frac{89}{180}\times 45$$

Express \frac{89}{180}\times 45 as a single fraction.

$$\frac{89\times 45}{180}$$

Multiply 89 and 45 to get 4005.

$$\frac{4005}{180}$$

Reduce the fraction \frac{4005}{180} to lowest terms by extracting and canceling out 45.

$$\frac{89}{4}$$

Factor

$$\frac{89}{2 ^ {2}} = 22\frac{1}{4} = 22.25$$