Solve (2/5+1/22+3/2)+frac{3/10}{frac{3}{9}}

$$\frac { ( \frac { 2 } { 5 } + \frac { 1 } { 22 } + \frac { 3 } { 2 } ) + \frac { 3 } { 10 } } { \frac { 3 } { 9 } }$$

Evaluate

$$\frac{741}{110}\approx 6.736363636$$

Solution Steps

Least common multiple of 5 and 22 is 110. Convert \frac{2}{5} and \frac{1}{22} to fractions with denominator 110.

$$\frac{\frac{44}{110}+\frac{5}{110}+\frac{3}{2}+\frac{3}{10}}{\frac{3}{9}}$$

Since \frac{44}{110} and \frac{5}{110} have the same denominator, add them by adding their numerators.

$$\frac{\frac{44+5}{110}+\frac{3}{2}+\frac{3}{10}}{\frac{3}{9}}$$

Add 44 and 5 to get 49.

$$\frac{\frac{49}{110}+\frac{3}{2}+\frac{3}{10}}{\frac{3}{9}}$$

Least common multiple of 110 and 2 is 110. Convert \frac{49}{110} and \frac{3}{2} to fractions with denominator 110.

$$\frac{\frac{49}{110}+\frac{165}{110}+\frac{3}{10}}{\frac{3}{9}}$$

Since \frac{49}{110} and \frac{165}{110} have the same denominator, add them by adding their numerators.

$$\frac{\frac{49+165}{110}+\frac{3}{10}}{\frac{3}{9}}$$

Add 49 and 165 to get 214.

$$\frac{\frac{214}{110}+\frac{3}{10}}{\frac{3}{9}}$$

Reduce the fraction \frac{214}{110} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{107}{55}+\frac{3}{10}}{\frac{3}{9}}$$

Least common multiple of 55 and 10 is 110. Convert \frac{107}{55} and \frac{3}{10} to fractions with denominator 110.

$$\frac{\frac{214}{110}+\frac{33}{110}}{\frac{3}{9}}$$

Since \frac{214}{110} and \frac{33}{110} have the same denominator, add them by adding their numerators.

$$\frac{\frac{214+33}{110}}{\frac{3}{9}}$$

Add 214 and 33 to get 247.

$$\frac{\frac{247}{110}}{\frac{3}{9}}$$

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{247}{110}}{\frac{1}{3}}$$

Divide \frac{247}{110} by \frac{1}{3} by multiplying \frac{247}{110} by the reciprocal of \frac{1}{3}.

$$\frac{247}{110}\times 3$$

Express \frac{247}{110}\times 3 as a single fraction.

$$\frac{247\times 3}{110}$$

Multiply 247 and 3 to get 741.

$$\frac{741}{110}$$

Factor

$$\frac{3 \cdot 13 \cdot 19}{2 \cdot 5 \cdot 11} = 6\frac{81}{110} = 6.736363636363636$$