Pre-Algebra Examples

$\frac{3}{4} \cdot \frac{1}{2} + \frac{2}{3} - \frac{5}{6} \div \frac{30}{12}$

Step 1

Simplify each term.

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Step 1.1

Multiply $\frac{3}{4} \cdot \frac{1}{2}$ .

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Step 1.1.1

Multiply $\frac{3}{4}$ by $\frac{1}{2}$ .

$\frac{3}{4 \cdot 2} + \frac{2}{3} - \frac{5}{6} \div \frac{30}{12}$

Step 1.1.2

Multiply $4$ by $2$ .

$\frac{3}{8} + \frac{2}{3} - \frac{5}{6} \div \frac{30}{12}$

Step 1.2

To divide by a fraction, multiply by its reciprocal.

$\frac{3}{8} + \frac{2}{3} - (\frac{5}{6} \cdot \frac{12}{30})$

Step 1.3

Cancel the common factor of $5$ .

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Step 1.3.1

Factor $5$ out of $30$ .

$\frac{3}{8} + \frac{2}{3} - (\frac{5}{6} \cdot \frac{12}{5 (6)})$

Step 1.3.2

Cancel the common factor.

$\frac{3}{8} + \frac{2}{3} - (\frac{5}{6} \cdot \frac{12}{5 \cdot 6})$

Step 1.3.3

Rewrite the expression.

$\frac{3}{8} + \frac{2}{3} - (\frac{1}{6} \cdot \frac{12}{6})$

Step 1.4

Cancel the common factor of $6$ .

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Step 1.4.1

Factor $6$ out of $12$ .

$\frac{3}{8} + \frac{2}{3} - (\frac{1}{6} \cdot \frac{6 (2)}{6})$

Step 1.4.2

Cancel the common factor.

$\frac{3}{8} + \frac{2}{3} - (\frac{1}{6} \cdot \frac{6 \cdot 2}{6})$

Step 1.4.3

Rewrite the expression.

$\frac{3}{8} + \frac{2}{3} - \frac{2}{6}$

Step 1.5

Cancel the common factor of $2$ and $6$ .

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Step 1.5.1

Factor $2$ out of $2$ .

$\frac{3}{8} + \frac{2}{3} - \frac{2 (1)}{6}$

Step 1.5.2

Cancel the common factors.

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Step 1.5.2.1

Factor $2$ out of $6$ .

$\frac{3}{8} + \frac{2}{3} - \frac{2 \cdot 1}{2 \cdot 3}$

Step 1.5.2.2

Cancel the common factor.

$\frac{3}{8} + \frac{2}{3} - \frac{2 \cdot 1}{2 \cdot 3}$

Step 1.5.2.3

Rewrite the expression.

$\frac{3}{8} + \frac{2}{3} - \frac{1}{3}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{3}{8} + \frac{2 - 1}{3}$

Step 2.2

Subtract $1$ from $2$ .

$\frac{3}{8} + \frac{1}{3}$

Step 3

To write $\frac{3}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3}{8} \cdot \frac{3}{3} + \frac{1}{3}$

Step 4

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{3}{8} \cdot \frac{3}{3} + \frac{1}{3} \cdot \frac{8}{8}$

Step 5

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{3}{8}$ by $\frac{3}{3}$ .

$\frac{3 \cdot 3}{8 \cdot 3} + \frac{1}{3} \cdot \frac{8}{8}$

Step 5.2

Multiply $8$ by $3$ .

$\frac{3 \cdot 3}{24} + \frac{1}{3} \cdot \frac{8}{8}$

Step 5.3

Multiply $\frac{1}{3}$ by $\frac{8}{8}$ .

$\frac{3 \cdot 3}{24} + \frac{8}{3 \cdot 8}$

Step 5.4

Multiply $3$ by $8$ .

$\frac{3 \cdot 3}{24} + \frac{8}{24}$

Step 6

Combine the numerators over the common denominator.

$\frac{3 \cdot 3 + 8}{24}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $3$ by $3$ .

$\frac{9 + 8}{24}$

Step 7.2

Add $9$ and $8$ .

$\frac{17}{24}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{17}{24}$

Decimal Form:

$0.708\overline{3}$