Algebra Examples

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

Step 1

Find the common denominator.

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Step 1.1

Write $3$ as a fraction with denominator $1$ .

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

Write $- (2 + \frac{1}{6})$ as a fraction with denominator $1$ .

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

Step 1.5

Multiply $\frac{- (2 + \frac{1}{6})}{1}$ by $\frac{4}{4}$ .

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

Step 1.6

Multiply $\frac{- (2 + \frac{1}{6})}{1}$ by $\frac{4}{4}$ .

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Simplify each term.

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Step 3.1

Multiply $3$ by $4$ .

$\frac{12 + 1 - (2 + \frac{1}{6}) \cdot 4}{4}$

Step 3.2

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

$\frac{12 + 1 - (2 \cdot \frac{6}{6} + \frac{1}{6}) \cdot 4}{4}$

Step 3.3

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

$\frac{12 + 1 - (\frac{2 \cdot 6}{6} + \frac{1}{6}) \cdot 4}{4}$

Step 3.4

Combine the numerators over the common denominator.

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

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $2$ by $6$ .

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

Step 3.5.2

Add $12$ and $1$ .

$\frac{12 + 1 - \frac{13}{6} \cdot 4}{4}$

Step 3.6

Cancel the common factor of $2$ .

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Step 3.6.1

Move the leading negative in $- \frac{13}{6}$ into the numerator.

$\frac{12 + 1 + \frac{- 13}{6} \cdot 4}{4}$

Step 3.6.2

Factor $2$ out of $6$ .

$\frac{12 + 1 + \frac{- 13}{2 (3)} \cdot 4}{4}$

Step 3.6.3

Factor $2$ out of $4$ .

$\frac{12 + 1 + \frac{- 13}{2 \cdot 3} \cdot (2 \cdot 2)}{4}$

Step 3.6.4

Cancel the common factor.

$\frac{12 + 1 + \frac{- 13}{2 \cdot 3} \cdot (2 \cdot 2)}{4}$

Step 3.6.5

Rewrite the expression.

$\frac{12 + 1 + \frac{- 13}{3} \cdot 2}{4}$

Step 3.7

Combine $\frac{- 13}{3}$ and $2$ .

$\frac{12 + 1 + \frac{- 13 \cdot 2}{3}}{4}$

Step 3.8

Multiply $- 13$ by $2$ .

$\frac{12 + 1 + \frac{- 26}{3}}{4}$

Step 3.9

Move the negative in front of the fraction.

$\frac{12 + 1 - \frac{26}{3}}{4}$

Step 4

Find the common denominator.

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Step 4.1

Write $12$ as a fraction with denominator $1$ .

$\frac{\frac{12}{1} + 1 - \frac{26}{3}}{4}$

Step 4.2

Multiply $\frac{12}{1}$ by $\frac{3}{3}$ .

$\frac{\frac{12}{1} \cdot \frac{3}{3} + 1 - \frac{26}{3}}{4}$

Step 4.3

Multiply $\frac{12}{1}$ by $\frac{3}{3}$ .

$\frac{\frac{12 \cdot 3}{3} + 1 - \frac{26}{3}}{4}$

Step 4.4

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

$\frac{\frac{12 \cdot 3}{3} + \frac{1}{1} - \frac{26}{3}}{4}$

Step 4.5

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

$\frac{\frac{12 \cdot 3}{3} + \frac{1}{1} \cdot \frac{3}{3} - \frac{26}{3}}{4}$

Step 4.6

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

$\frac{\frac{12 \cdot 3}{3} + \frac{3}{3} - \frac{26}{3}}{4}$

Step 5

Combine the numerators over the common denominator.

$\frac{\frac{12 \cdot 3 + 3 - 26}{3}}{4}$

Step 6

Simplify the expression.

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Step 6.1

Multiply $12$ by $3$ .

$\frac{\frac{36 + 3 - 26}{3}}{4}$

Step 6.2

Add $36$ and $3$ .

$\frac{\frac{39 - 26}{3}}{4}$

Step 6.3

Subtract $26$ from $39$ .

$\frac{\frac{13}{3}}{4}$

Step 7

Multiply the numerator by the reciprocal of the denominator.

$\frac{13}{3} \cdot \frac{1}{4}$

Step 8

Multiply $\frac{13}{3} \cdot \frac{1}{4}$ .

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Step 8.1

Multiply $\frac{13}{3}$ by $\frac{1}{4}$ .

$\frac{13}{3 \cdot 4}$

Step 8.2

Multiply $3$ by $4$ .

$\frac{13}{12}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{13}{12}$

Decimal Form:

$1.08\overline{3}$

Mixed Number Form:

$1 \frac{1}{12}$