Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

To divide by a fraction, multiply by its reciprocal.

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

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Factor $2$ out of $\frac{5}{6} \cdot 6$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

Step 1.3

Combine $\frac{5}{6}$ and $3$ .

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

Step 1.4

Multiply $5$ by $3$ .

$\frac{3}{4} + \frac{1}{3} + \frac{15}{6}$

Step 1.5

Cancel the common factor of $15$ and $6$ .

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Step 1.5.1

Factor $3$ out of $15$ .

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

Step 1.5.2

Cancel the common factors.

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Step 1.5.2.1

Factor $3$ out of $6$ .

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

Step 1.5.2.2

Cancel the common factor.

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

Step 1.5.2.3

Rewrite the expression.

$\frac{3}{4} + \frac{1}{3} + \frac{5}{2}$

Step 2

Find the common denominator.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

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

$\frac{3 \cdot 3}{4 \cdot 3} + \frac{4}{3 \cdot 4} + \frac{5}{2}$

Step 2.5

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

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

Step 2.6

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

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

Step 2.7

Reorder the factors of $4 \cdot 3$ .

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

Step 2.8

Multiply $3$ by $4$ .

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

Step 2.9

Multiply $3$ by $4$ .

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

Step 2.10

Multiply $2$ by $6$ .

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify each term.

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Step 4.1

Multiply $3$ by $3$ .

$\frac{9 + 4 + 5 \cdot 6}{12}$

Step 4.2

Multiply $5$ by $6$ .

$\frac{9 + 4 + 30}{12}$

Step 5

Simplify by adding numbers.

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Step 5.1

Add $9$ and $4$ .

$\frac{13 + 30}{12}$

Step 5.2

Add $13$ and $30$ .

$\frac{43}{12}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{43}{12}$

Decimal Form:

$3.58\overline{3}$

Mixed Number Form:

$3 \frac{7}{12}$