Pre-Algebra Examples

$- \frac{5}{12} - \frac{1}{4} + \frac{3}{12}$

Step 1

Combine fractions.

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Step 1.1

Combine the numerators over the common denominator.

$\frac{- 5 + 3}{12} + \frac{- 1}{4}$

Step 1.2

Add $- 5$ and $3$ .

$\frac{- 2}{12} + \frac{- 1}{4}$

Step 2

Simplify each term.

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Step 2.1

Cancel the common factor of $- 2$ and $12$ .

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Step 2.1.1

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{12} + \frac{- 1}{4}$

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $2$ out of $12$ .

$\frac{2 \cdot - 1}{2 \cdot 6} + \frac{- 1}{4}$

Step 2.1.2.2

Cancel the common factor.

$\frac{2 \cdot - 1}{2 \cdot 6} + \frac{- 1}{4}$

Step 2.1.2.3

Rewrite the expression.

$\frac{- 1}{6} + \frac{- 1}{4}$

Step 2.2

Move the negative in front of the fraction.

$- \frac{1}{6} + \frac{- 1}{4}$

Step 2.3

Move the negative in front of the fraction.

$- \frac{1}{6} - \frac{1}{4}$

Step 3

To write $- \frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{1}{6} \cdot \frac{2}{2} - \frac{1}{4}$

Step 4

To write $- \frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{1}{6} \cdot \frac{2}{2} - \frac{1}{4} \cdot \frac{3}{3}$

Step 5

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{1}{6}$ by $\frac{2}{2}$ .

$- \frac{2}{6 \cdot 2} - \frac{1}{4} \cdot \frac{3}{3}$

Step 5.2

Multiply $6$ by $2$ .

$- \frac{2}{12} - \frac{1}{4} \cdot \frac{3}{3}$

Step 5.3

Multiply $\frac{1}{4}$ by $\frac{3}{3}$ .

$- \frac{2}{12} - \frac{3}{4 \cdot 3}$

Step 5.4

Multiply $4$ by $3$ .

$- \frac{2}{12} - \frac{3}{12}$

Step 6

Combine the numerators over the common denominator.

$\frac{- 2 - 3}{12}$

Step 7

Subtract $3$ from $- 2$ .

$\frac{- 5}{12}$

Step 8

Move the negative in front of the fraction.

$- \frac{5}{12}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{5}{12}$

Decimal Form:

$- 0.41\overline{6}$