Pre-Algebra Examples

$p - \frac{1}{7} = - \frac{2}{4}$

Step 1

Cancel the common factor of $2$ and $4$ .

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Step 1.1

Factor $2$ out of $2$ .

$p - \frac{1}{7} = - \frac{2 (1)}{4}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $4$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

$p - \frac{1}{7} = - \frac{1}{2}$

Step 2

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

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Step 2.1

Add $\frac{1}{7}$ to both sides of the equation.

$p = - \frac{1}{2} + \frac{1}{7}$

Step 2.2

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

$p = - \frac{1}{2} \cdot \frac{7}{7} + \frac{1}{7}$

Step 2.3

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

$p = - \frac{1}{2} \cdot \frac{7}{7} + \frac{1}{7} \cdot \frac{2}{2}$

Step 2.4

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

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Step 2.4.1

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

$p = - \frac{7}{2 \cdot 7} + \frac{1}{7} \cdot \frac{2}{2}$

Step 2.4.2

Multiply $2$ by $7$ .

$p = - \frac{7}{14} + \frac{1}{7} \cdot \frac{2}{2}$

Step 2.4.3

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

$p = - \frac{7}{14} + \frac{2}{7 \cdot 2}$

Step 2.4.4

Multiply $7$ by $2$ .

$p = - \frac{7}{14} + \frac{2}{14}$

Step 2.5

Combine the numerators over the common denominator.

$p = \frac{- 7 + 2}{14}$

Step 2.6

Add $- 7$ and $2$ .

$p = \frac{- 5}{14}$

Step 2.7

Move the negative in front of the fraction.

$p = - \frac{5}{14}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$p = - \frac{5}{14}$

Decimal Form:

$p = - 0.3\overline{571428}$