Pre-Algebra Examples

$\frac{r}{3} + 7 - \frac{r}{5} = - 3$

Step 1

Simplify $\frac{r}{3} + 7 - \frac{r}{5}$ .

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Step 1.1

To write $\frac{r}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{r}{3} \cdot \frac{5}{5} - \frac{r}{5} + 7 = - 3$

Step 1.2

To write $- \frac{r}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{r}{3} \cdot \frac{5}{5} - \frac{r}{5} \cdot \frac{3}{3} + 7 = - 3$

Step 1.3

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{r}{3}$ by $\frac{5}{5}$ .

$\frac{r \cdot 5}{3 \cdot 5} - \frac{r}{5} \cdot \frac{3}{3} + 7 = - 3$

Step 1.3.2

Multiply $3$ by $5$ .

$\frac{r \cdot 5}{15} - \frac{r}{5} \cdot \frac{3}{3} + 7 = - 3$

Step 1.3.3

Multiply $\frac{r}{5}$ by $\frac{3}{3}$ .

$\frac{r \cdot 5}{15} - \frac{r \cdot 3}{5 \cdot 3} + 7 = - 3$

Step 1.3.4

Multiply $5$ by $3$ .

$\frac{r \cdot 5}{15} - \frac{r \cdot 3}{15} + 7 = - 3$

Step 1.4

Combine the numerators over the common denominator.

$\frac{r \cdot 5 - r \cdot 3}{15} + 7 = - 3$

Step 1.5

Simplify each term.

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Step 1.5.1

Simplify the numerator.

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Step 1.5.1.1

Factor $r$ out of $r \cdot 5 - r \cdot 3$ .

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Step 1.5.1.1.1

Factor $r$ out of $r \cdot 5$ .

$\frac{r (5) - r \cdot 3}{15} + 7 = - 3$

Step 1.5.1.1.2

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

$\frac{r (5) + r (- 1 \cdot 3)}{15} + 7 = - 3$

Step 1.5.1.1.3

Factor $r$ out of $r (5) + r (- 1 \cdot 3)$ .

$\frac{r (5 - 1 \cdot 3)}{15} + 7 = - 3$

Step 1.5.1.2

Multiply $- 1$ by $3$ .

$\frac{r (5 - 3)}{15} + 7 = - 3$

Step 1.5.1.3

Subtract $3$ from $5$ .

$\frac{r \cdot 2}{15} + 7 = - 3$

Step 1.5.2

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

$\frac{2 r}{15} + 7 = - 3$

Step 2

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

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Step 2.1

Subtract $7$ from both sides of the equation.

$\frac{2 r}{15} = - 3 - 7$

Step 2.2

Subtract $7$ from $- 3$ .

$\frac{2 r}{15} = - 10$

Step 3

Multiply both sides of the equation by $\frac{15}{2}$ .

$\frac{15}{2} \cdot \frac{2 r}{15} = \frac{15}{2} \cdot - 10$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{15}{2} \cdot \frac{2 r}{15}$ .

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Step 4.1.1.1

Cancel the common factor of $15$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{15}{2} \cdot \frac{2 r}{15} = \frac{15}{2} \cdot - 10$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{2} (2 r) = \frac{15}{2} \cdot - 10$

Step 4.1.1.2

Cancel the common factor of $2$ .

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Step 4.1.1.2.1

Factor $2$ out of $2 r$ .

$\frac{1}{2} (2 (r)) = \frac{15}{2} \cdot - 10$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{2} (2 r) = \frac{15}{2} \cdot - 10$

Step 4.1.1.2.3

Rewrite the expression.

$r = \frac{15}{2} \cdot - 10$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{15}{2} \cdot - 10$ .

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Step 4.2.1.1

Cancel the common factor of $2$ .

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Step 4.2.1.1.1

Factor $2$ out of $- 10$ .

$r = \frac{15}{2} \cdot (2 (- 5))$

Step 4.2.1.1.2

Cancel the common factor.

$r = \frac{15}{2} \cdot (2 \cdot - 5)$

Step 4.2.1.1.3

Rewrite the expression.

$r = 15 \cdot - 5$

Step 4.2.1.2

Multiply $15$ by $- 5$ .

$r = - 75$