Solve 6+3/5+1/10div51/2

$$6+ \frac{ 3 }{ 5 } + \frac{ 1 }{ 10 } \div 5 \frac{ 1 }{ 2 }$$

Evaluate

$$\frac{364}{55}\approx 6.618181818$$

Solution Steps

Convert 6 to fraction \frac{30}{5}.

$$\frac{30}{5}+\frac{3}{5}+\frac{\frac{1}{10}}{\frac{5\times 2+1}{2}}$$

Since \frac{30}{5} and \frac{3}{5} have the same denominator, add them by adding their numerators.

$$\frac{30+3}{5}+\frac{\frac{1}{10}}{\frac{5\times 2+1}{2}}$$

Add 30 and 3 to get 33.

$$\frac{33}{5}+\frac{\frac{1}{10}}{\frac{5\times 2+1}{2}}$$

Divide \frac{1}{10} by \frac{5\times 2+1}{2} by multiplying \frac{1}{10} by the reciprocal of \frac{5\times 2+1}{2}.

$$\frac{33}{5}+\frac{2}{10\left(5\times 2+1\right)}$$

Multiply 5 and 2 to get 10.

$$\frac{33}{5}+\frac{2}{10\left(10+1\right)}$$

Add 10 and 1 to get 11.

$$\frac{33}{5}+\frac{2}{10\times 11}$$

Multiply 10 and 11 to get 110.

$$\frac{33}{5}+\frac{2}{110}$$

Reduce the fraction \frac{2}{110} to lowest terms by extracting and canceling out 2.

$$\frac{33}{5}+\frac{1}{55}$$

Least common multiple of 5 and 55 is 55. Convert \frac{33}{5} and \frac{1}{55} to fractions with denominator 55.

$$\frac{363}{55}+\frac{1}{55}$$

Since \frac{363}{55} and \frac{1}{55} have the same denominator, add them by adding their numerators.

$$\frac{363+1}{55}$$

Add 363 and 1 to get 364.

$$\frac{364}{55}$$

Factor

$$\frac{2 ^ {2} \cdot 7 \cdot 13}{5 \cdot 11} = 6\frac{34}{55} = 6.618181818181818$$