Basic Math Examples

$- \frac{7}{2} = - \frac{3}{2} p - \frac{1}{4}$

Step 1

Rewrite the equation as $- \frac{3}{2} p - \frac{1}{4} = - \frac{7}{2}$ .

$- \frac{3}{2} p - \frac{1}{4} = - \frac{7}{2}$

Step 2

Simplify each term.

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Step 2.1

Combine $p$ and $\frac{3}{2}$ .

$- \frac{p \cdot 3}{2} - \frac{1}{4} = - \frac{7}{2}$

Step 2.2

Move $3$ to the left of $p$ .

$- \frac{3 p}{2} - \frac{1}{4} = - \frac{7}{2}$

Step 3

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

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Step 3.1

Add $\frac{1}{4}$ to both sides of the equation.

$- \frac{3 p}{2} = - \frac{7}{2} + \frac{1}{4}$

Step 3.2

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

$- \frac{3 p}{2} = - \frac{7}{2} \cdot \frac{2}{2} + \frac{1}{4}$

Step 3.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

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

$- \frac{3 p}{2} = - \frac{7 \cdot 2}{2 \cdot 2} + \frac{1}{4}$

Step 3.3.2

Multiply $2$ by $2$ .

$- \frac{3 p}{2} = - \frac{7 \cdot 2}{4} + \frac{1}{4}$

Step 3.4

Combine the numerators over the common denominator.

$- \frac{3 p}{2} = \frac{- 7 \cdot 2 + 1}{4}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 7$ by $2$ .

$- \frac{3 p}{2} = \frac{- 14 + 1}{4}$

Step 3.5.2

Add $- 14$ and $1$ .

$- \frac{3 p}{2} = \frac{- 13}{4}$

Step 3.6

Move the negative in front of the fraction.

$- \frac{3 p}{2} = - \frac{13}{4}$

Step 4

Multiply both sides of the equation by $- \frac{2}{3}$ .

$- \frac{2}{3} (- \frac{3 p}{2}) = - \frac{2}{3} (- \frac{13}{4})$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $- \frac{2}{3} (- \frac{3 p}{2})$ .

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Step 5.1.1.1

Cancel the common factor of $2$ .

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Step 5.1.1.1.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$\frac{- 2}{3} (- \frac{3 p}{2}) = - \frac{2}{3} (- \frac{13}{4})$

Step 5.1.1.1.2

Move the leading negative in $- \frac{3 p}{2}$ into the numerator.

$\frac{- 2}{3} \cdot \frac{- 3 p}{2} = - \frac{2}{3} (- \frac{13}{4})$

Step 5.1.1.1.3

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{3} \cdot \frac{- 3 p}{2} = - \frac{2}{3} (- \frac{13}{4})$

Step 5.1.1.1.4

Cancel the common factor.

$\frac{2 \cdot - 1}{3} \cdot \frac{- 3 p}{2} = - \frac{2}{3} (- \frac{13}{4})$

Step 5.1.1.1.5

Rewrite the expression.

$\frac{- 1}{3} (- 3 p) = - \frac{2}{3} (- \frac{13}{4})$

Step 5.1.1.2

Cancel the common factor of $3$ .

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Step 5.1.1.2.1

Factor $3$ out of $- 3 p$ .

$\frac{- 1}{3} (3 (- p)) = - \frac{2}{3} (- \frac{13}{4})$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{- 1}{3} (3 (- p)) = - \frac{2}{3} (- \frac{13}{4})$

Step 5.1.1.2.3

Rewrite the expression.

$- - p = - \frac{2}{3} (- \frac{13}{4})$

Step 5.1.1.3

Multiply.

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Step 5.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 p = - \frac{2}{3} (- \frac{13}{4})$

Step 5.1.1.3.2

Multiply $p$ by $1$ .

$p = - \frac{2}{3} (- \frac{13}{4})$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $- \frac{2}{3} (- \frac{13}{4})$ .

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Step 5.2.1.1

Cancel the common factor of $2$ .

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Step 5.2.1.1.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$p = \frac{- 2}{3} (- \frac{13}{4})$

Step 5.2.1.1.2

Move the leading negative in $- \frac{13}{4}$ into the numerator.

$p = \frac{- 2}{3} \cdot \frac{- 13}{4}$

Step 5.2.1.1.3

Factor $2$ out of $- 2$ .

$p = \frac{2 (- 1)}{3} \cdot \frac{- 13}{4}$

Step 5.2.1.1.4

Factor $2$ out of $4$ .

$p = \frac{2 \cdot - 1}{3} \cdot \frac{- 13}{2 \cdot 2}$

Step 5.2.1.1.5

Cancel the common factor.

$p = \frac{2 \cdot - 1}{3} \cdot \frac{- 13}{2 \cdot 2}$

Step 5.2.1.1.6

Rewrite the expression.

$p = \frac{- 1}{3} \cdot \frac{- 13}{2}$

Step 5.2.1.2

Multiply $\frac{- 1}{3}$ by $\frac{- 13}{2}$ .

$p = \frac{- - 13}{3 \cdot 2}$

Step 5.2.1.3

Multiply.

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Step 5.2.1.3.1

Multiply $- 1$ by $- 13$ .

$p = \frac{13}{3 \cdot 2}$

Step 5.2.1.3.2

Multiply $3$ by $2$ .

$p = \frac{13}{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$p = \frac{13}{6}$

Decimal Form:

$p = 2.1\overline{6}$

Mixed Number Form:

$p = 2 \frac{1}{6}$