Pre-Algebra Examples

$\frac{3}{10} - \frac{1}{4} \cdot (\frac{2}{6} \cdot \frac{4}{5} + \frac{2}{3})$

Step 1

Simplify each term.

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Step 1.1

Simplify each term.

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Step 1.1.1

Cancel the common factor of $2$ .

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Step 1.1.1.1

Factor $2$ out of $6$ .

$\frac{3}{10} - \frac{1}{4} \cdot (\frac{2}{2 (3)} \cdot \frac{4}{5} + \frac{2}{3})$

Step 1.1.1.2

Factor $2$ out of $4$ .

$\frac{3}{10} - \frac{1}{4} \cdot (\frac{2}{2 \cdot 3} \cdot \frac{2 \cdot 2}{5} + \frac{2}{3})$

Step 1.1.1.3

Cancel the common factor.

$\frac{3}{10} - \frac{1}{4} \cdot (\frac{2}{2 \cdot 3} \cdot \frac{2 \cdot 2}{5} + \frac{2}{3})$

Step 1.1.1.4

Rewrite the expression.

$\frac{3}{10} - \frac{1}{4} \cdot (\frac{2}{3} \cdot \frac{2}{5} + \frac{2}{3})$

Step 1.1.2

Multiply $\frac{2}{3}$ by $\frac{2}{5}$ .

$\frac{3}{10} - \frac{1}{4} \cdot (\frac{2 \cdot 2}{3 \cdot 5} + \frac{2}{3})$

Step 1.1.3

Multiply $2$ by $2$ .

$\frac{3}{10} - \frac{1}{4} \cdot (\frac{4}{3 \cdot 5} + \frac{2}{3})$

Step 1.1.4

Multiply $3$ by $5$ .

$\frac{3}{10} - \frac{1}{4} \cdot (\frac{4}{15} + \frac{2}{3})$

Step 1.2

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{3}{10} - \frac{1}{4} \cdot (\frac{4}{15} + \frac{2}{3} \cdot \frac{5}{5})$

Step 1.3

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{2}{3}$ by $\frac{5}{5}$ .

$\frac{3}{10} - \frac{1}{4} \cdot (\frac{4}{15} + \frac{2 \cdot 5}{3 \cdot 5})$

Step 1.3.2

Multiply $3$ by $5$ .

$\frac{3}{10} - \frac{1}{4} \cdot (\frac{4}{15} + \frac{2 \cdot 5}{15})$

Step 1.4

Combine the numerators over the common denominator.

$\frac{3}{10} - \frac{1}{4} \cdot \frac{4 + 2 \cdot 5}{15}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $2$ by $5$ .

$\frac{3}{10} - \frac{1}{4} \cdot \frac{4 + 10}{15}$

Step 1.5.2

Add $4$ and $10$ .

$\frac{3}{10} - \frac{1}{4} \cdot \frac{14}{15}$

Step 1.6

Cancel the common factor of $2$ .

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Step 1.6.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$\frac{3}{10} + \frac{- 1}{4} \cdot \frac{14}{15}$

Step 1.6.2

Factor $2$ out of $4$ .

$\frac{3}{10} + \frac{- 1}{2 (2)} \cdot \frac{14}{15}$

Step 1.6.3

Factor $2$ out of $14$ .

$\frac{3}{10} + \frac{- 1}{2 \cdot 2} \cdot \frac{2 \cdot 7}{15}$

Step 1.6.4

Cancel the common factor.

$\frac{3}{10} + \frac{- 1}{2 \cdot 2} \cdot \frac{2 \cdot 7}{15}$

Step 1.6.5

Rewrite the expression.

$\frac{3}{10} + \frac{- 1}{2} \cdot \frac{7}{15}$

Step 1.7

Multiply $\frac{- 1}{2}$ by $\frac{7}{15}$ .

$\frac{3}{10} + \frac{- 1 \cdot 7}{2 \cdot 15}$

Step 1.8

Multiply $- 1$ by $7$ .

$\frac{3}{10} + \frac{- 7}{2 \cdot 15}$

Step 1.9

Multiply $2$ by $15$ .

$\frac{3}{10} + \frac{- 7}{30}$

Step 1.10

Move the negative in front of the fraction.

$\frac{3}{10} - \frac{7}{30}$

Step 2

To write $\frac{3}{10}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3}{10} \cdot \frac{3}{3} - \frac{7}{30}$

Step 3

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{3}{10}$ by $\frac{3}{3}$ .

$\frac{3 \cdot 3}{10 \cdot 3} - \frac{7}{30}$

Step 3.2

Multiply $10$ by $3$ .

$\frac{3 \cdot 3}{30} - \frac{7}{30}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 \cdot 3 - 7}{30}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $3$ by $3$ .

$\frac{9 - 7}{30}$

Step 5.2

Subtract $7$ from $9$ .

$\frac{2}{30}$

Step 6

Cancel the common factor of $2$ and $30$ .

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Step 6.1

Factor $2$ out of $2$ .

$\frac{2 (1)}{30}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $30$ .

$\frac{2 \cdot 1}{2 \cdot 15}$

Step 6.2.2

Cancel the common factor.

$\frac{2 \cdot 1}{2 \cdot 15}$

Step 6.2.3

Rewrite the expression.

$\frac{1}{15}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{15}$

Decimal Form:

$0.0\overline{6}$