Solve 31/2+51/3div13/5

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

Evaluate

$$\frac{41}{6}\approx 6.833333333$$

Solution Steps

Multiply 3 and 2 to get 6.

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

Add 6 and 1 to get 7.

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

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

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

Multiply 5 and 3 to get 15.

$$\frac{7}{2}+\frac{\left(15+1\right)\times 5}{3\left(1\times 5+3\right)}$$

Add 15 and 1 to get 16.

$$\frac{7}{2}+\frac{16\times 5}{3\left(1\times 5+3\right)}$$

Multiply 16 and 5 to get 80.

$$\frac{7}{2}+\frac{80}{3\left(1\times 5+3\right)}$$

Multiply 1 and 5 to get 5.

$$\frac{7}{2}+\frac{80}{3\left(5+3\right)}$$

Add 5 and 3 to get 8.

$$\frac{7}{2}+\frac{80}{3\times 8}$$

Multiply 3 and 8 to get 24.

$$\frac{7}{2}+\frac{80}{24}$$

Reduce the fraction \frac{80}{24} to lowest terms by extracting and canceling out 8.

$$\frac{7}{2}+\frac{10}{3}$$

Least common multiple of 2 and 3 is 6. Convert \frac{7}{2} and \frac{10}{3} to fractions with denominator 6.

$$\frac{21}{6}+\frac{20}{6}$$

Since \frac{21}{6} and \frac{20}{6} have the same denominator, add them by adding their numerators.

$$\frac{21+20}{6}$$

Add 21 and 20 to get 41.

$$\frac{41}{6}$$

Factor

$$\frac{41}{2 \cdot 3} = 6\frac{5}{6} = 6.833333333333333$$