Pre-Algebra Examples

$\frac{5}{6} - \frac{2}{3} \cdot (6 - \frac{1}{2}) + \frac{3}{4}$

Step 1

Simplify each term.

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Step 1.1

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

$\frac{5}{6} - \frac{2}{3} \cdot (6 \cdot \frac{2}{2} - \frac{1}{2}) + \frac{3}{4}$

Step 1.2

Combine $6$ and $\frac{2}{2}$ .

$\frac{5}{6} - \frac{2}{3} \cdot (\frac{6 \cdot 2}{2} - \frac{1}{2}) + \frac{3}{4}$

Step 1.3

Combine the numerators over the common denominator.

$\frac{5}{6} - \frac{2}{3} \cdot \frac{6 \cdot 2 - 1}{2} + \frac{3}{4}$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Multiply $6$ by $2$ .

$\frac{5}{6} - \frac{2}{3} \cdot \frac{12 - 1}{2} + \frac{3}{4}$

Step 1.4.2

Subtract $1$ from $12$ .

$\frac{5}{6} - \frac{2}{3} \cdot \frac{11}{2} + \frac{3}{4}$

Step 1.5

Cancel the common factor of $2$ .

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Step 1.5.1

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

$\frac{5}{6} + \frac{- 2}{3} \cdot \frac{11}{2} + \frac{3}{4}$

Step 1.5.2

Factor $2$ out of $- 2$ .

$\frac{5}{6} + \frac{2 (- 1)}{3} \cdot \frac{11}{2} + \frac{3}{4}$

Step 1.5.3

Cancel the common factor.

$\frac{5}{6} + \frac{2 \cdot - 1}{3} \cdot \frac{11}{2} + \frac{3}{4}$

Step 1.5.4

Rewrite the expression.

$\frac{5}{6} + \frac{- 1}{3} \cdot 11 + \frac{3}{4}$

Step 1.6

Combine $\frac{- 1}{3}$ and $11$ .

$\frac{5}{6} + \frac{- 1 \cdot 11}{3} + \frac{3}{4}$

Step 1.7

Multiply $- 1$ by $11$ .

$\frac{5}{6} + \frac{- 11}{3} + \frac{3}{4}$

Step 1.8

Move the negative in front of the fraction.

$\frac{5}{6} - \frac{11}{3} + \frac{3}{4}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{5}{6}$ by $\frac{2}{2}$ .

$\frac{5}{6} \cdot \frac{2}{2} - \frac{11}{3} + \frac{3}{4}$

Step 2.2

Multiply $\frac{5}{6}$ by $\frac{2}{2}$ .

$\frac{5 \cdot 2}{6 \cdot 2} - \frac{11}{3} + \frac{3}{4}$

Step 2.3

Multiply $\frac{11}{3}$ by $\frac{4}{4}$ .

$\frac{5 \cdot 2}{6 \cdot 2} - (\frac{11}{3} \cdot \frac{4}{4}) + \frac{3}{4}$

Step 2.4

Multiply $\frac{11}{3}$ by $\frac{4}{4}$ .

$\frac{5 \cdot 2}{6 \cdot 2} - \frac{11 \cdot 4}{3 \cdot 4} + \frac{3}{4}$

Step 2.5

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

$\frac{5 \cdot 2}{6 \cdot 2} - \frac{11 \cdot 4}{3 \cdot 4} + \frac{3}{4} \cdot \frac{3}{3}$

Step 2.6

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

$\frac{5 \cdot 2}{6 \cdot 2} - \frac{11 \cdot 4}{3 \cdot 4} + \frac{3 \cdot 3}{4 \cdot 3}$

Step 2.7

Reorder the factors of $6 \cdot 2$ .

$\frac{5 \cdot 2}{2 \cdot 6} - \frac{11 \cdot 4}{3 \cdot 4} + \frac{3 \cdot 3}{4 \cdot 3}$

Step 2.8

Multiply $2$ by $6$ .

$\frac{5 \cdot 2}{12} - \frac{11 \cdot 4}{3 \cdot 4} + \frac{3 \cdot 3}{4 \cdot 3}$

Step 2.9

Multiply $3$ by $4$ .

$\frac{5 \cdot 2}{12} - \frac{11 \cdot 4}{12} + \frac{3 \cdot 3}{4 \cdot 3}$

Step 2.10

Reorder the factors of $4 \cdot 3$ .

$\frac{5 \cdot 2}{12} - \frac{11 \cdot 4}{12} + \frac{3 \cdot 3}{3 \cdot 4}$

Step 2.11

Multiply $3$ by $4$ .

$\frac{5 \cdot 2}{12} - \frac{11 \cdot 4}{12} + \frac{3 \cdot 3}{12}$

Step 3

Combine the numerators over the common denominator.

$\frac{5 \cdot 2 - 11 \cdot 4 + 3 \cdot 3}{12}$

Step 4

Simplify each term.

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Step 4.1

Multiply $5$ by $2$ .

$\frac{10 - 11 \cdot 4 + 3 \cdot 3}{12}$

Step 4.2

Multiply $- 11$ by $4$ .

$\frac{10 - 44 + 3 \cdot 3}{12}$

Step 4.3

Multiply $3$ by $3$ .

$\frac{10 - 44 + 9}{12}$

Step 5

Simplify the expression.

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Step 5.1

Subtract $44$ from $10$ .

$\frac{- 34 + 9}{12}$

Step 5.2

Add $- 34$ and $9$ .

$\frac{- 25}{12}$

Step 5.3

Move the negative in front of the fraction.

$- \frac{25}{12}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{25}{12}$

Decimal Form:

$- 2.08\overline{3}$

Mixed Number Form:

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