Solve 51/2+71/3div11/6=

$$5 \frac{ 1 }{ 2 } +7 \frac{ 1 }{ 3 } \div 1 \frac { 1 } { 6 } =$$

Evaluate

$$\frac{165}{14}\approx 11.785714286$$

Solution Steps

Multiply 5 and 2 to get 10.

$$\frac{10+1}{2}+\frac{\frac{7\times 3+1}{3}}{\frac{1\times 6+1}{6}}$$

Add 10 and 1 to get 11.

$$\frac{11}{2}+\frac{\frac{7\times 3+1}{3}}{\frac{1\times 6+1}{6}}$$

Divide \frac{7\times 3+1}{3} by \frac{1\times 6+1}{6} by multiplying \frac{7\times 3+1}{3} by the reciprocal of \frac{1\times 6+1}{6}.

$$\frac{11}{2}+\frac{\left(7\times 3+1\right)\times 6}{3\left(1\times 6+1\right)}$$

Cancel out 3 in both numerator and denominator.

$$\frac{11}{2}+\frac{2\left(1+3\times 7\right)}{1+6}$$

Multiply 3 and 7 to get 21.

$$\frac{11}{2}+\frac{2\left(1+21\right)}{1+6}$$

Add 1 and 21 to get 22.

$$\frac{11}{2}+\frac{2\times 22}{1+6}$$

Multiply 2 and 22 to get 44.

$$\frac{11}{2}+\frac{44}{1+6}$$

Add 1 and 6 to get 7.

$$\frac{11}{2}+\frac{44}{7}$$

Least common multiple of 2 and 7 is 14. Convert \frac{11}{2} and \frac{44}{7} to fractions with denominator 14.

$$\frac{77}{14}+\frac{88}{14}$$

Since \frac{77}{14} and \frac{88}{14} have the same denominator, add them by adding their numerators.

$$\frac{77+88}{14}$$

Add 77 and 88 to get 165.

$$\frac{165}{14}$$

Factor

$$\frac{3 \cdot 5 \cdot 11}{2 \cdot 7} = 11\frac{11}{14} = 11.785714285714286$$