Algebra Examples

$\frac{3}{4} r + 2 r + \frac{1}{2} r$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{3}{4}$ and $r$ .

$\frac{3 r}{4} + 2 r + \frac{1}{2} r$

Step 1.2

Combine $\frac{1}{2}$ and $r$ .

$\frac{3 r}{4} + 2 r + \frac{r}{2}$

Step 2

Find the common denominator.

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Step 2.1

Write $2 r$ as a fraction with denominator $1$ .

$\frac{3 r}{4} + \frac{2 r}{1} + \frac{r}{2}$

Step 2.2

Multiply $\frac{2 r}{1}$ by $\frac{4}{4}$ .

$\frac{3 r}{4} + \frac{2 r}{1} \cdot \frac{4}{4} + \frac{r}{2}$

Step 2.3

Multiply $\frac{2 r}{1}$ by $\frac{4}{4}$ .

$\frac{3 r}{4} + \frac{2 r \cdot 4}{4} + \frac{r}{2}$

Step 2.4

Multiply $\frac{r}{2}$ by $\frac{2}{2}$ .

$\frac{3 r}{4} + \frac{2 r \cdot 4}{4} + \frac{r}{2} \cdot \frac{2}{2}$

Step 2.5

Multiply $\frac{r}{2}$ by $\frac{2}{2}$ .

$\frac{3 r}{4} + \frac{2 r \cdot 4}{4} + \frac{r \cdot 2}{2 \cdot 2}$

Step 2.6

Multiply $2$ by $2$ .

$\frac{3 r}{4} + \frac{2 r \cdot 4}{4} + \frac{r \cdot 2}{4}$

Step 3

Combine the numerators over the common denominator.

$\frac{3 r + 2 r \cdot 4 + r \cdot 2}{4}$

Step 4

Simplify each term.

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Step 4.1

Multiply $4$ by $2$ .

$\frac{3 r + 8 r + r \cdot 2}{4}$

Step 4.2

Move $2$ to the left of $r$ .

$\frac{3 r + 8 r + 2 r}{4}$

Step 5

Simplify by adding terms.

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Step 5.1

Add $3 r$ and $8 r$ .

$\frac{11 r + 2 r}{4}$

Step 5.2

Add $11 r$ and $2 r$ .

$\frac{13 r}{4}$