Algebra Examples

$- 2 \frac{3}{4} + (- \frac{1}{2})$

Step 1

Remove parentheses.

$- 2 \frac{3}{4} - \frac{1}{2}$

Step 2

Convert $2 \frac{3}{4}$ to an improper fraction.

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Step 2.1

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

$- (2 + \frac{3}{4}) - \frac{1}{2}$

Step 2.2

Add $2$ and $\frac{3}{4}$ .

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Step 2.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- (2 \cdot \frac{4}{4} + \frac{3}{4}) - \frac{1}{2}$

Step 2.2.2

Combine $2$ and $\frac{4}{4}$ .

$- (\frac{2 \cdot 4}{4} + \frac{3}{4}) - \frac{1}{2}$

Step 2.2.3

Combine the numerators over the common denominator.

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

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $4$ .

$- \frac{8 + 3}{4} - \frac{1}{2}$

Step 2.2.4.2

Add $8$ and $3$ .

$- \frac{11}{4} - \frac{1}{2}$

Step 3

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

$- \frac{11}{4} - \frac{1}{2} \cdot \frac{2}{2}$

Step 4

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

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Step 4.1

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

$- \frac{11}{4} - \frac{2}{2 \cdot 2}$

Step 4.2

Multiply $2$ by $2$ .

$- \frac{11}{4} - \frac{2}{4}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 11 - 2}{4}$

Step 6

Subtract $2$ from $- 11$ .

$\frac{- 13}{4}$

Step 7

Move the negative in front of the fraction.

$- \frac{13}{4}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{13}{4}$

Decimal Form:

$- 3.25$

Mixed Number Form:

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