Solve ((2)/(1+(1)/(3))+(1-(1)/(3))/(2))\div22

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Question

$$( \frac{ 2 }{ 1+ \frac{ 1 }{ 3 } } + \frac{ 1- \frac{ 1 }{ 3 } }{ 2 } ) \div 22$$

Evaluate

$\frac{1}{12}\approx 0.083333333$

Solution Steps

Convert $1$ to fraction $\frac{3}{3}$.

$$\frac{\frac{2}{\frac{3}{3}+\frac{1}{3}}+\frac{1-\frac{1}{3}}{2}}{22}$$

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

$$\frac{\frac{2}{\frac{3+1}{3}}+\frac{1-\frac{1}{3}}{2}}{22}$$

Add $3$ and $1$ to get $4$.

$$\frac{\frac{2}{\frac{4}{3}}+\frac{1-\frac{1}{3}}{2}}{22}$$

Divide $2$ by $\frac{4}{3}$ by multiplying $2$ by the reciprocal of $\frac{4}{3}$.

$$\frac{2\times \frac{3}{4}+\frac{1-\frac{1}{3}}{2}}{22}$$

Express $2\times \frac{3}{4}$ as a single fraction.

$$\frac{\frac{2\times 3}{4}+\frac{1-\frac{1}{3}}{2}}{22}$$

Multiply $2$ and $3$ to get $6$.

$$\frac{\frac{6}{4}+\frac{1-\frac{1}{3}}{2}}{22}$$

Reduce the fraction $\frac{6}{4}$ to lowest terms by extracting and canceling out $2$.

$$\frac{\frac{3}{2}+\frac{1-\frac{1}{3}}{2}}{22}$$

Convert $1$ to fraction $\frac{3}{3}$.

$$\frac{\frac{3}{2}+\frac{\frac{3}{3}-\frac{1}{3}}{2}}{22}$$

Since $\frac{3}{3}$ and $\frac{1}{3}$ have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3}{2}+\frac{\frac{3-1}{3}}{2}}{22}$$

Subtract $1$ from $3$ to get $2$.

$$\frac{\frac{3}{2}+\frac{\frac{2}{3}}{2}}{22}$$

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

$$\frac{\frac{3}{2}+\frac{2}{3\times 2}}{22}$$

Cancel out $2$ in both numerator and denominator.

$$\frac{\frac{3}{2}+\frac{1}{3}}{22}$$

Least common multiple of $2$ and $3$ is $6$. Convert $\frac{3}{2}$ and $\frac{1}{3}$ to fractions with denominator $6$.

$$\frac{\frac{9}{6}+\frac{2}{6}}{22}$$

Since $\frac{9}{6}$ and $\frac{2}{6}$ have the same denominator, add them by adding their numerators.

$$\frac{\frac{9+2}{6}}{22}$$

Add $9$ and $2$ to get $11$.

$$\frac{\frac{11}{6}}{22}$$

Express $\frac{\frac{11}{6}}{22}$ as a single fraction.

$$\frac{11}{6\times 22}$$

Multiply $6$ and $22$ to get $132$.

$$\frac{11}{132}$$

Reduce the fraction $\frac{11}{132}$ to lowest terms by extracting and canceling out $11$.

$$\frac{1}{12}$$

Show Solution

Factor

$\frac{1}{2 ^ {2} \cdot 3} = 0.08333333333333333$