Solve [3/2+1/2+frac{1{3}}]div[1/frac{3{5}}+frac{2/5}{3}]

$$[ \frac { 3 } { 2 } + \frac { 1 } { 2 + \frac { 1 } { 3 } } ] \div [ \frac { 1 } { \frac { 3 } { 5 } } + \frac { \frac { 2 } { 5 } } { 3 } ]$$

Evaluate

$$\frac{15}{14}\approx 1.071428571$$

Solution Steps

Convert 2 to fraction \frac{6}{3}.

$$\frac{\frac{3}{2}+\frac{1}{\frac{6}{3}+\frac{1}{3}}}{\frac{1}{\frac{3}{5}}+\frac{\frac{2}{5}}{3}}$$

Since \frac{6}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3}{2}+\frac{1}{\frac{6+1}{3}}}{\frac{1}{\frac{3}{5}}+\frac{\frac{2}{5}}{3}}$$

Add 6 and 1 to get 7.

$$\frac{\frac{3}{2}+\frac{1}{\frac{7}{3}}}{\frac{1}{\frac{3}{5}}+\frac{\frac{2}{5}}{3}}$$

Divide 1 by \frac{7}{3} by multiplying 1 by the reciprocal of \frac{7}{3}.

$$\frac{\frac{3}{2}+1\times \frac{3}{7}}{\frac{1}{\frac{3}{5}}+\frac{\frac{2}{5}}{3}}$$

Multiply 1 and \frac{3}{7} to get \frac{3}{7}.

$$\frac{\frac{3}{2}+\frac{3}{7}}{\frac{1}{\frac{3}{5}}+\frac{\frac{2}{5}}{3}}$$

Least common multiple of 2 and 7 is 14. Convert \frac{3}{2} and \frac{3}{7} to fractions with denominator 14.

$$\frac{\frac{21}{14}+\frac{6}{14}}{\frac{1}{\frac{3}{5}}+\frac{\frac{2}{5}}{3}}$$

Since \frac{21}{14} and \frac{6}{14} have the same denominator, add them by adding their numerators.

$$\frac{\frac{21+6}{14}}{\frac{1}{\frac{3}{5}}+\frac{\frac{2}{5}}{3}}$$

Add 21 and 6 to get 27.

$$\frac{\frac{27}{14}}{\frac{1}{\frac{3}{5}}+\frac{\frac{2}{5}}{3}}$$

Divide 1 by \frac{3}{5} by multiplying 1 by the reciprocal of \frac{3}{5}.

$$\frac{\frac{27}{14}}{1\times \frac{5}{3}+\frac{\frac{2}{5}}{3}}$$

Multiply 1 and \frac{5}{3} to get \frac{5}{3}.

$$\frac{\frac{27}{14}}{\frac{5}{3}+\frac{\frac{2}{5}}{3}}$$

Express \frac{\frac{2}{5}}{3} as a single fraction.

$$\frac{\frac{27}{14}}{\frac{5}{3}+\frac{2}{5\times 3}}$$

Multiply 5 and 3 to get 15.

$$\frac{\frac{27}{14}}{\frac{5}{3}+\frac{2}{15}}$$

Least common multiple of 3 and 15 is 15. Convert \frac{5}{3} and \frac{2}{15} to fractions with denominator 15.

$$\frac{\frac{27}{14}}{\frac{25}{15}+\frac{2}{15}}$$

Since \frac{25}{15} and \frac{2}{15} have the same denominator, add them by adding their numerators.

$$\frac{\frac{27}{14}}{\frac{25+2}{15}}$$

Add 25 and 2 to get 27.

$$\frac{\frac{27}{14}}{\frac{27}{15}}$$

Reduce the fraction \frac{27}{15} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{27}{14}}{\frac{9}{5}}$$

Divide \frac{27}{14} by \frac{9}{5} by multiplying \frac{27}{14} by the reciprocal of \frac{9}{5}.

$$\frac{27}{14}\times \frac{5}{9}$$

Multiply \frac{27}{14} times \frac{5}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{27\times 5}{14\times 9}$$

Do the multiplications in the fraction \frac{27\times 5}{14\times 9}.

$$\frac{135}{126}$$

Reduce the fraction \frac{135}{126} to lowest terms by extracting and canceling out 9.

$$\frac{15}{14}$$

Factor

$$\frac{3 \cdot 5}{2 \cdot 7} = 1\frac{1}{14} = 1.0714285714285714$$