Pre-Algebra Examples

$r + \frac{2}{6} = - \frac{3}{11}$

Step 1

Cancel the common factor of $2$ and $6$ .

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Step 1.1

Factor $2$ out of $2$ .

$r + \frac{2 (1)}{6} = - \frac{3}{11}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $6$ .

$r + \frac{2 \cdot 1}{2 \cdot 3} = - \frac{3}{11}$

Step 1.2.2

Cancel the common factor.

$r + \frac{2 \cdot 1}{2 \cdot 3} = - \frac{3}{11}$

Step 1.2.3

Rewrite the expression.

$r + \frac{1}{3} = - \frac{3}{11}$

Step 2

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

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Step 2.1

Subtract $\frac{1}{3}$ from both sides of the equation.

$r = - \frac{3}{11} - \frac{1}{3}$

Step 2.2

To write $- \frac{3}{11}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$r = - \frac{3}{11} \cdot \frac{3}{3} - \frac{1}{3}$

Step 2.3

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$r = - \frac{3}{11} \cdot \frac{3}{3} - \frac{1}{3} \cdot \frac{11}{11}$

Step 2.4

Write each expression with a common denominator of $33$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.4.1

Multiply $\frac{3}{11}$ by $\frac{3}{3}$ .

$r = - \frac{3 \cdot 3}{11 \cdot 3} - \frac{1}{3} \cdot \frac{11}{11}$

Step 2.4.2

Multiply $11$ by $3$ .

$r = - \frac{3 \cdot 3}{33} - \frac{1}{3} \cdot \frac{11}{11}$

Step 2.4.3

Multiply $\frac{1}{3}$ by $\frac{11}{11}$ .

$r = - \frac{3 \cdot 3}{33} - \frac{11}{3 \cdot 11}$

Step 2.4.4

Multiply $3$ by $11$ .

$r = - \frac{3 \cdot 3}{33} - \frac{11}{33}$

Step 2.5

Combine the numerators over the common denominator.

$r = \frac{- 3 \cdot 3 - 11}{33}$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $- 3$ by $3$ .

$r = \frac{- 9 - 11}{33}$

Step 2.6.2

Subtract $11$ from $- 9$ .

$r = \frac{- 20}{33}$

Step 2.7

Move the negative in front of the fraction.

$r = - \frac{20}{33}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$r = - \frac{20}{33}$

Decimal Form:

$r = - 0.\overline{60}$