Solve (1)/(3)\div(-(1)/(3)+(2)/(5))=

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Question

$$\frac{ 1 }{ 3 } \div (- \frac{ 1 }{ 3 } + \frac{ 2 }{ 5 } )=$$

$5$

Least common multiple of $3$ and $5$ is $15$. Convert $-\frac{1}{3}$ and $\frac{2}{5}$ to fractions with denominator $15$.

$$\frac{\frac{1}{3}}{-\frac{5}{15}+\frac{6}{15}}$$

Since $-\frac{5}{15}$ and $\frac{6}{15}$ have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{3}}{\frac{-5+6}{15}}$$

Add $-5$ and $6$ to get $1$.

$$\frac{\frac{1}{3}}{\frac{1}{15}}$$

Divide $\frac{1}{3}$ by $\frac{1}{15}$ by multiplying $\frac{1}{3}$ by the reciprocal of $\frac{1}{15}$.

$$\frac{1}{3}\times 15$$

Multiply $\frac{1}{3}$ and $15$ to get $\frac{15}{3}$.

$$\frac{15}{3}$$

Divide $15$ by $3$ to get $5$.

$$5$$

$5$