Algebra Examples

$- \frac{1}{3} = r - \frac{3}{4}$

Step 1

Rewrite the equation as $r - \frac{3}{4} = - \frac{1}{3}$ .

$r - \frac{3}{4} = - \frac{1}{3}$

Step 2

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

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Step 2.1

Add $\frac{3}{4}$ to both sides of the equation.

$r = - \frac{1}{3} + \frac{3}{4}$

Step 2.2

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$r = - \frac{1}{3} \cdot \frac{4}{4} + \frac{3}{4}$

Step 2.3

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

$r = - \frac{1}{3} \cdot \frac{4}{4} + \frac{3}{4} \cdot \frac{3}{3}$

Step 2.4

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

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Step 2.4.1

Multiply $\frac{1}{3}$ by $\frac{4}{4}$ .

$r = - \frac{4}{3 \cdot 4} + \frac{3}{4} \cdot \frac{3}{3}$

Step 2.4.2

Multiply $3$ by $4$ .

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

Step 2.4.3

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

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

Step 2.4.4

Multiply $4$ by $3$ .

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

Step 2.5

Combine the numerators over the common denominator.

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

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $3$ by $3$ .

$r = \frac{- 4 + 9}{12}$

Step 2.6.2

Add $- 4$ and $9$ .

$r = \frac{5}{12}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$r = \frac{5}{12}$

Decimal Form:

$r = 0.41\overline{6}$