Solve [11/5*(11/2-2/3)+53/5]div3frac{1}{7}=

$$[ 1 \frac { 1 } { 5 } \times ( 1 \frac { 1 } { 2 } - \frac { 2 } { 3 } ) + 5 \frac { 3 } { 5 } ] \div 3 \frac { 1 } { 7 } =$$

Evaluate

$$\frac{21}{10}=2.1$$

Solution Steps

Multiply 1 and 5 to get 5.

$$\frac{\frac{5+1}{5}\left(\frac{1\times 2+1}{2}-\frac{2}{3}\right)+\frac{5\times 5+3}{5}}{\frac{3\times 7+1}{7}}$$

Add 5 and 1 to get 6.

$$\frac{\frac{6}{5}\left(\frac{1\times 2+1}{2}-\frac{2}{3}\right)+\frac{5\times 5+3}{5}}{\frac{3\times 7+1}{7}}$$

Multiply 1 and 2 to get 2.

$$\frac{\frac{6}{5}\left(\frac{2+1}{2}-\frac{2}{3}\right)+\frac{5\times 5+3}{5}}{\frac{3\times 7+1}{7}}$$

Add 2 and 1 to get 3.

$$\frac{\frac{6}{5}\left(\frac{3}{2}-\frac{2}{3}\right)+\frac{5\times 5+3}{5}}{\frac{3\times 7+1}{7}}$$

Least common multiple of 2 and 3 is 6. Convert \frac{3}{2} and \frac{2}{3} to fractions with denominator 6.

$$\frac{\frac{6}{5}\left(\frac{9}{6}-\frac{4}{6}\right)+\frac{5\times 5+3}{5}}{\frac{3\times 7+1}{7}}$$

Since \frac{9}{6} and \frac{4}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{6}{5}\times \frac{9-4}{6}+\frac{5\times 5+3}{5}}{\frac{3\times 7+1}{7}}$$

Subtract 4 from 9 to get 5.

$$\frac{\frac{6}{5}\times \frac{5}{6}+\frac{5\times 5+3}{5}}{\frac{3\times 7+1}{7}}$$

Cancel out \frac{6}{5} and its reciprocal \frac{5}{6}.

$$\frac{1+\frac{5\times 5+3}{5}}{\frac{3\times 7+1}{7}}$$

Multiply 5 and 5 to get 25.

$$\frac{1+\frac{25+3}{5}}{\frac{3\times 7+1}{7}}$$

Add 25 and 3 to get 28.

$$\frac{1+\frac{28}{5}}{\frac{3\times 7+1}{7}}$$

Convert 1 to fraction \frac{5}{5}.

$$\frac{\frac{5}{5}+\frac{28}{5}}{\frac{3\times 7+1}{7}}$$

Since \frac{5}{5} and \frac{28}{5} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+28}{5}}{\frac{3\times 7+1}{7}}$$

Add 5 and 28 to get 33.

$$\frac{\frac{33}{5}}{\frac{3\times 7+1}{7}}$$

Multiply 3 and 7 to get 21.

$$\frac{\frac{33}{5}}{\frac{21+1}{7}}$$

Add 21 and 1 to get 22.

$$\frac{\frac{33}{5}}{\frac{22}{7}}$$

Divide \frac{33}{5} by \frac{22}{7} by multiplying \frac{33}{5} by the reciprocal of \frac{22}{7}.

$$\frac{33}{5}\times \frac{7}{22}$$

Multiply \frac{33}{5} times \frac{7}{22} by multiplying numerator times numerator and denominator times denominator.

$$\frac{33\times 7}{5\times 22}$$

Do the multiplications in the fraction \frac{33\times 7}{5\times 22}.

$$\frac{231}{110}$$

Reduce the fraction \frac{231}{110} to lowest terms by extracting and canceling out 11.

$$\frac{21}{10}$$

Factor

$$\frac{3 \cdot 7}{2 \cdot 5} = 2\frac{1}{10} = 2.1$$