Solve (1/18+1/3)\div(1/3+1/6) | Equatix

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Question

$$(1/18+1/3) \div (1/3+1/6)$$

Evaluate

$\frac{7}{9}\approx 0.777777778$

Solution Steps

Least common multiple of $18$ and $3$ is $18$. Convert $\frac{1}{18}$ and $\frac{1}{3}$ to fractions with denominator $18$.

$$\frac{\frac{1}{18}+\frac{6}{18}}{\frac{1}{3}+\frac{1}{6}}$$

Since $\frac{1}{18}$ and $\frac{6}{18}$ have the same denominator, add them by adding their numerators.

$$\frac{\frac{1+6}{18}}{\frac{1}{3}+\frac{1}{6}}$$

Add $1$ and $6$ to get $7$.

$$\frac{\frac{7}{18}}{\frac{1}{3}+\frac{1}{6}}$$

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

$$\frac{\frac{7}{18}}{\frac{2}{6}+\frac{1}{6}}$$

Since $\frac{2}{6}$ and $\frac{1}{6}$ have the same denominator, add them by adding their numerators.

$$\frac{\frac{7}{18}}{\frac{2+1}{6}}$$

Add $2$ and $1$ to get $3$.

$$\frac{\frac{7}{18}}{\frac{3}{6}}$$

Reduce the fraction $\frac{3}{6}$ to lowest terms by extracting and canceling out $3$.

$$\frac{\frac{7}{18}}{\frac{1}{2}}$$

Divide $\frac{7}{18}$ by $\frac{1}{2}$ by multiplying $\frac{7}{18}$ by the reciprocal of $\frac{1}{2}$.

$$\frac{7}{18}\times 2$$

Express $\frac{7}{18}\times 2$ as a single fraction.

$$\frac{7\times 2}{18}$$

Multiply $7$ and $2$ to get $14$.

$$\frac{14}{18}$$

Reduce the fraction $\frac{14}{18}$ to lowest terms by extracting and canceling out $2$.

$$\frac{7}{9}$$

Show Solution

Factor

$\frac{7}{3 ^ {2}} = 0.7777777777777778$