Basic Math Examples

$\frac{1}{2} + \frac{r}{7} = \frac{5}{14}$

Step 1

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

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Step 1.1

Subtract $\frac{1}{2}$ from both sides of the equation.

$\frac{r}{7} = \frac{5}{14} - \frac{1}{2}$

Step 1.2

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{r}{7} = \frac{5}{14} - \frac{1}{2} \cdot \frac{7}{7}$

Step 1.3

Write each expression with a common denominator of $14$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{1}{2}$ by $\frac{7}{7}$ .

$\frac{r}{7} = \frac{5}{14} - \frac{7}{2 \cdot 7}$

Step 1.3.2

Multiply $2$ by $7$ .

$\frac{r}{7} = \frac{5}{14} - \frac{7}{14}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{r}{7} = \frac{5 - 7}{14}$

Step 1.5

Subtract $7$ from $5$ .

$\frac{r}{7} = \frac{- 2}{14}$

Step 1.6

Cancel the common factor of $- 2$ and $14$ .

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Step 1.6.1

Factor $2$ out of $- 2$ .

$\frac{r}{7} = \frac{2 (- 1)}{14}$

Step 1.6.2

Cancel the common factors.

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Step 1.6.2.1

Factor $2$ out of $14$ .

$\frac{r}{7} = \frac{2 \cdot - 1}{2 \cdot 7}$

Step 1.6.2.2

Cancel the common factor.

$\frac{r}{7} = \frac{2 \cdot - 1}{2 \cdot 7}$

Step 1.6.2.3

Rewrite the expression.

$\frac{r}{7} = \frac{- 1}{7}$

Step 1.7

Move the negative in front of the fraction.

$\frac{r}{7} = - \frac{1}{7}$

Step 2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$r = - 1$