Algebra Examples

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

Step 1

Convert $1 \frac{1}{4}$ to an improper fraction.

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Step 1.1

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

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

Step 1.2

Add $1$ and $\frac{1}{4}$ .

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Step 1.2.1

Write $1$ as a fraction with a common denominator.

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

Step 1.2.2

Combine the numerators over the common denominator.

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

Step 1.2.3

Add $4$ and $1$ .

$- \frac{5}{4} - (- \frac{1}{2})$

Step 2

Multiply $- (- \frac{1}{2})$ .

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Step 2.1

Multiply $- 1$ by $- 1$ .

$- \frac{5}{4} + 1 (\frac{1}{2})$

Step 2.2

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

$- \frac{5}{4} + \frac{1}{2}$

Step 3

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

$- \frac{5}{4} + \frac{1}{2} \cdot \frac{2}{2}$

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 $\frac{2}{2}$ .

$- \frac{5}{4} + \frac{2}{2 \cdot 2}$

Step 4.2

Multiply $2$ by $2$ .

$- \frac{5}{4} + \frac{2}{4}$

Step 5

Combine the numerators over the common denominator.

$\frac{- 5 + 2}{4}$

Step 6

Add $- 5$ and $2$ .

$\frac{- 3}{4}$

Step 7

Move the negative in front of the fraction.

$- \frac{3}{4}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{3}{4}$

Decimal Form:

$- 0.75$