Solve 94/5div42/3+32/3div1frac{1/3-frac{1}{20}}{6div2frac{1}{2}}

$$\frac { 9 \frac { 4 } { 5 } \div 4 \frac { 2 } { 3 } + 3 \frac { 2 } { 3 } \div 1 \frac { 1 } { 3 } - \frac { 1 } { 20 } } { 6 \div 2 \frac { 1 } { 2 } }$$

Evaluate

$$2$$

Solution Steps

Divide \frac{9\times 5+4}{5} by \frac{4\times 3+2}{3} by multiplying \frac{9\times 5+4}{5} by the reciprocal of \frac{4\times 3+2}{3}.

$$\frac{\frac{\left(9\times 5+4\right)\times 3}{5\left(4\times 3+2\right)}+\frac{\frac{3\times 3+2}{3}}{\frac{1\times 3+1}{3}}-\frac{1}{20}}{\frac{6}{\frac{2\times 2+1}{2}}}$$

Multiply 9 and 5 to get 45.

$$\frac{\frac{\left(45+4\right)\times 3}{5\left(4\times 3+2\right)}+\frac{\frac{3\times 3+2}{3}}{\frac{1\times 3+1}{3}}-\frac{1}{20}}{\frac{6}{\frac{2\times 2+1}{2}}}$$

Add 45 and 4 to get 49.

$$\frac{\frac{49\times 3}{5\left(4\times 3+2\right)}+\frac{\frac{3\times 3+2}{3}}{\frac{1\times 3+1}{3}}-\frac{1}{20}}{\frac{6}{\frac{2\times 2+1}{2}}}$$

Multiply 49 and 3 to get 147.

$$\frac{\frac{147}{5\left(4\times 3+2\right)}+\frac{\frac{3\times 3+2}{3}}{\frac{1\times 3+1}{3}}-\frac{1}{20}}{\frac{6}{\frac{2\times 2+1}{2}}}$$

Multiply 4 and 3 to get 12.

$$\frac{\frac{147}{5\left(12+2\right)}+\frac{\frac{3\times 3+2}{3}}{\frac{1\times 3+1}{3}}-\frac{1}{20}}{\frac{6}{\frac{2\times 2+1}{2}}}$$

Add 12 and 2 to get 14.

$$\frac{\frac{147}{5\times 14}+\frac{\frac{3\times 3+2}{3}}{\frac{1\times 3+1}{3}}-\frac{1}{20}}{\frac{6}{\frac{2\times 2+1}{2}}}$$

Multiply 5 and 14 to get 70.

$$\frac{\frac{147}{70}+\frac{\frac{3\times 3+2}{3}}{\frac{1\times 3+1}{3}}-\frac{1}{20}}{\frac{6}{\frac{2\times 2+1}{2}}}$$

Reduce the fraction \frac{147}{70} to lowest terms by extracting and canceling out 7.

$$\frac{\frac{21}{10}+\frac{\frac{3\times 3+2}{3}}{\frac{1\times 3+1}{3}}-\frac{1}{20}}{\frac{6}{\frac{2\times 2+1}{2}}}$$

Divide \frac{3\times 3+2}{3} by \frac{1\times 3+1}{3} by multiplying \frac{3\times 3+2}{3} by the reciprocal of \frac{1\times 3+1}{3}.

$$\frac{\frac{21}{10}+\frac{\left(3\times 3+2\right)\times 3}{3\left(1\times 3+1\right)}-\frac{1}{20}}{\frac{6}{\frac{2\times 2+1}{2}}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\frac{21}{10}+\frac{2+3\times 3}{1+3}-\frac{1}{20}}{\frac{6}{\frac{2\times 2+1}{2}}}$$

Multiply 3 and 3 to get 9.

$$\frac{\frac{21}{10}+\frac{2+9}{1+3}-\frac{1}{20}}{\frac{6}{\frac{2\times 2+1}{2}}}$$

Add 2 and 9 to get 11.

$$\frac{\frac{21}{10}+\frac{11}{1+3}-\frac{1}{20}}{\frac{6}{\frac{2\times 2+1}{2}}}$$

Add 1 and 3 to get 4.

$$\frac{\frac{21}{10}+\frac{11}{4}-\frac{1}{20}}{\frac{6}{\frac{2\times 2+1}{2}}}$$

Least common multiple of 10 and 4 is 20. Convert \frac{21}{10} and \frac{11}{4} to fractions with denominator 20.

$$\frac{\frac{42}{20}+\frac{55}{20}-\frac{1}{20}}{\frac{6}{\frac{2\times 2+1}{2}}}$$

Since \frac{42}{20} and \frac{55}{20} have the same denominator, add them by adding their numerators.

$$\frac{\frac{42+55}{20}-\frac{1}{20}}{\frac{6}{\frac{2\times 2+1}{2}}}$$

Add 42 and 55 to get 97.

$$\frac{\frac{97}{20}-\frac{1}{20}}{\frac{6}{\frac{2\times 2+1}{2}}}$$

Since \frac{97}{20} and \frac{1}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{97-1}{20}}{\frac{6}{\frac{2\times 2+1}{2}}}$$

Subtract 1 from 97 to get 96.

$$\frac{\frac{96}{20}}{\frac{6}{\frac{2\times 2+1}{2}}}$$

Reduce the fraction \frac{96}{20} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{24}{5}}{\frac{6}{\frac{2\times 2+1}{2}}}$$

Divide 6 by \frac{2\times 2+1}{2} by multiplying 6 by the reciprocal of \frac{2\times 2+1}{2}.

$$\frac{\frac{24}{5}}{\frac{6\times 2}{2\times 2+1}}$$

Multiply 6 and 2 to get 12.

$$\frac{\frac{24}{5}}{\frac{12}{2\times 2+1}}$$

Multiply 2 and 2 to get 4.

$$\frac{\frac{24}{5}}{\frac{12}{4+1}}$$

Add 4 and 1 to get 5.

$$\frac{\frac{24}{5}}{\frac{12}{5}}$$

Divide \frac{24}{5} by \frac{12}{5} by multiplying \frac{24}{5} by the reciprocal of \frac{12}{5}.

$$\frac{24}{5}\times \frac{5}{12}$$

Multiply \frac{24}{5} times \frac{5}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{24\times 5}{5\times 12}$$

Cancel out 5 in both numerator and denominator.

$$\frac{24}{12}$$

Divide 24 by 12 to get 2.

$$2$$

Factor

$$2$$