Pre-Algebra Examples

$\frac{2}{15} - \frac{\frac{1}{10}}{\frac{1}{6}}$

Step 1

Simplify each term.

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Step 1.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{2}{15} - (\frac{1}{10} \cdot 6)$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Factor $2$ out of $10$ .

$\frac{2}{15} - (\frac{1}{2 (5)} \cdot 6)$

Step 1.2.2

Factor $2$ out of $6$ .

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

Step 1.2.3

Cancel the common factor.

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

Step 1.2.4

Rewrite the expression.

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

Step 1.3

Combine $\frac{1}{5}$ and $3$ .

$\frac{2}{15} - \frac{3}{5}$

Step 2

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

$\frac{2}{15} - \frac{3}{5} \cdot \frac{3}{3}$

Step 3

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

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Step 3.1

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

$\frac{2}{15} - \frac{3 \cdot 3}{5 \cdot 3}$

Step 3.2

Multiply $5$ by $3$ .

$\frac{2}{15} - \frac{3 \cdot 3}{15}$

Step 4

Combine the numerators over the common denominator.

$\frac{2 - 3 \cdot 3}{15}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 3$ by $3$ .

$\frac{2 - 9}{15}$

Step 5.2

Subtract $9$ from $2$ .

$\frac{- 7}{15}$

Step 6

Move the negative in front of the fraction.

$- \frac{7}{15}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{7}{15}$

Decimal Form:

$- 0.4\overline{6}$