Basic Math Examples

$\frac{2}{9} \cdot (r + 4) = \frac{8}{9} - r$

Step 1

Simplify $\frac{2}{9} \cdot (r + 4)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{2}{9} \cdot (r + 4) = \frac{8}{9} - r$

Step 1.2

Simplify by adding zeros.

$\frac{2}{9} \cdot (r + 4) = \frac{8}{9} - r$

Step 1.3

Apply the distributive property.

$\frac{2}{9} r + \frac{2}{9} \cdot 4 = \frac{8}{9} - r$

Step 1.4

Combine $\frac{2}{9}$ and $r$ .

$\frac{2 r}{9} + \frac{2}{9} \cdot 4 = \frac{8}{9} - r$

Step 1.5

Multiply $\frac{2}{9} \cdot 4$ .

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Step 1.5.1

Combine $\frac{2}{9}$ and $4$ .

$\frac{2 r}{9} + \frac{2 \cdot 4}{9} = \frac{8}{9} - r$

Step 1.5.2

Multiply $2$ by $4$ .

$\frac{2 r}{9} + \frac{8}{9} = \frac{8}{9} - r$

Step 2

Move all terms containing $r$ to the left side of the equation.

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Step 2.1

Add $r$ to both sides of the equation.

$\frac{2 r}{9} + \frac{8}{9} + r = \frac{8}{9}$

Step 2.2

To write $r$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{2 r}{9} + r \cdot \frac{9}{9} + \frac{8}{9} = \frac{8}{9}$

Step 2.3

Combine $r$ and $\frac{9}{9}$ .

$\frac{2 r}{9} + \frac{r \cdot 9}{9} + \frac{8}{9} = \frac{8}{9}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{2 r + r \cdot 9}{9} + \frac{8}{9} = \frac{8}{9}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{2 r + r \cdot 9 + 8}{9} = \frac{8}{9}$

Step 2.6

Move $9$ to the left of $r$ .

$\frac{2 r + 9 r + 8}{9} = \frac{8}{9}$

Step 2.7

Add $2 r$ and $9 r$ .

$\frac{11 r + 8}{9} = \frac{8}{9}$

Step 3

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

$11 r + 8 = 8$

Step 4

Move all terms not containing $r$ to the right side of the equation.

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Step 4.1

Subtract $8$ from both sides of the equation.

$11 r = 8 - 8$

Step 4.2

Subtract $8$ from $8$ .

$11 r = 0$

Step 5

Divide each term in $11 r = 0$ by $11$ and simplify.

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Step 5.1

Divide each term in $11 r = 0$ by $11$ .

$\frac{11 r}{11} = \frac{0}{11}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $11$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{11 r}{11} = \frac{0}{11}$

Step 5.2.1.2

Divide $r$ by $1$ .

$r = \frac{0}{11}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $0$ by $11$ .

$r = 0$