Basic Math Examples

$r \div 3 = 2 \frac{2}{3}$

Step 1

Simplify the left side.

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Step 1.1

Rewrite the division as a fraction.

$\frac{r}{3} = 2 \frac{2}{3}$

Step 2

Simplify the right side.

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Step 2.1

Convert $2 \frac{2}{3}$ to an improper fraction.

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Step 2.1.1

A mixed number is an addition of its whole and fractional parts.

$\frac{r}{3} = 2 + \frac{2}{3}$

Step 2.1.2

Add $2$ and $\frac{2}{3}$ .

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Step 2.1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{r}{3} = 2 \cdot \frac{3}{3} + \frac{2}{3}$

Step 2.1.2.2

Combine $2$ and $\frac{3}{3}$ .

$\frac{r}{3} = \frac{2 \cdot 3}{3} + \frac{2}{3}$

Step 2.1.2.3

Combine the numerators over the common denominator.

$\frac{r}{3} = \frac{2 \cdot 3 + 2}{3}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $2$ by $3$ .

$\frac{r}{3} = \frac{6 + 2}{3}$

Step 2.1.2.4.2

Add $6$ and $2$ .

$\frac{r}{3} = \frac{8}{3}$

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$r = 8$