Algebra Examples

$7 + \frac{1}{6} r + 3 - \frac{3}{4} r$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{1}{6}$ and $r$ .

$7 + \frac{r}{6} + 3 - \frac{3}{4} r$

Step 1.2

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

$7 + \frac{r}{6} + 3 - \frac{r \cdot 3}{4}$

Step 1.3

Move $3$ to the left of $r$ .

$7 + \frac{r}{6} + 3 - \frac{3 r}{4}$

Step 2

Add $7$ and $3$ .

$\frac{r}{6} + 10 - \frac{3 r}{4}$

Step 3

To write $\frac{r}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{r}{6} \cdot \frac{2}{2} - \frac{3 r}{4} + 10$

Step 4

To write $- \frac{3 r}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{r}{6} \cdot \frac{2}{2} - \frac{3 r}{4} \cdot \frac{3}{3} + 10$

Step 5

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{r}{6}$ by $\frac{2}{2}$ .

$\frac{r \cdot 2}{6 \cdot 2} - \frac{3 r}{4} \cdot \frac{3}{3} + 10$

Step 5.2

Multiply $6$ by $2$ .

$\frac{r \cdot 2}{12} - \frac{3 r}{4} \cdot \frac{3}{3} + 10$

Step 5.3

Multiply $\frac{3 r}{4}$ by $\frac{3}{3}$ .

$\frac{r \cdot 2}{12} - \frac{3 r \cdot 3}{4 \cdot 3} + 10$

Step 5.4

Multiply $4$ by $3$ .

$\frac{r \cdot 2}{12} - \frac{3 r \cdot 3}{12} + 10$

Step 6

Combine the numerators over the common denominator.

$\frac{r \cdot 2 - 3 r \cdot 3}{12} + 10$

Step 7

Simplify each term.

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Step 7.1

Simplify the numerator.

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Step 7.1.1

Factor $r$ out of $r \cdot 2 - 3 r \cdot 3$ .

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Step 7.1.1.1

Factor $r$ out of $r \cdot 2$ .

$\frac{r (2) - 3 r \cdot 3}{12} + 10$

Step 7.1.1.2

Factor $r$ out of $- 3 r \cdot 3$ .

$\frac{r (2) + r (- 3 \cdot 3)}{12} + 10$

Step 7.1.1.3

Factor $r$ out of $r (2) + r (- 3 \cdot 3)$ .

$\frac{r (2 - 3 \cdot 3)}{12} + 10$

Step 7.1.2

Multiply $- 3$ by $3$ .

$\frac{r (2 - 9)}{12} + 10$

Step 7.1.3

Subtract $9$ from $2$ .

$\frac{r \cdot - 7}{12} + 10$

Step 7.2

Move $- 7$ to the left of $r$ .

$\frac{- 7 \cdot r}{12} + 10$

Step 7.3

Move the negative in front of the fraction.

$- \frac{7 r}{12} + 10$