Pre-Algebra Examples

$- \frac{1}{2} d = - 5 \frac{1}{2}$

Step 1

Simplify the left side.

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Step 1.1

Combine $d$ and $\frac{1}{2}$ .

$- \frac{d}{2} = - 5 \frac{1}{2}$

Step 2

Simplify the right side.

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Step 2.1

Convert $5 \frac{1}{2}$ to an improper fraction.

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Step 2.1.1

A mixed number is an addition of its whole and fractional parts.

$- \frac{d}{2} = - (5 + \frac{1}{2})$

Step 2.1.2

Add $5$ and $\frac{1}{2}$ .

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Step 2.1.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{d}{2} = - (5 \cdot \frac{2}{2} + \frac{1}{2})$

Step 2.1.2.2

Combine $5$ and $\frac{2}{2}$ .

$- \frac{d}{2} = - (\frac{5 \cdot 2}{2} + \frac{1}{2})$

Step 2.1.2.3

Combine the numerators over the common denominator.

$- \frac{d}{2} = - \frac{5 \cdot 2 + 1}{2}$

Step 2.1.2.4

Simplify the numerator.

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Step 2.1.2.4.1

Multiply $5$ by $2$ .

$- \frac{d}{2} = - \frac{10 + 1}{2}$

Step 2.1.2.4.2

Add $10$ and $1$ .

$- \frac{d}{2} = - \frac{11}{2}$

Step 3

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

$- d = - 11$

Step 4

Divide each term in $- d = - 11$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- d = - 11$ by $- 1$ .

$\frac{- d}{- 1} = \frac{- 11}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{d}{1} = \frac{- 11}{- 1}$

Step 4.2.2

Divide $d$ by $1$ .

$d = \frac{- 11}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 11$ by $- 1$ .

$d = 11$