Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

Combine the numerators over the common denominator.

$\frac{1}{3} - 2 \frac{4 - 1}{4}$

Step 1.3

Subtract $1$ from $4$ .

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

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Factor $2$ out of $- 2$ .

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

Step 1.4.2

Factor $2$ out of $4$ .

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

Step 1.4.3

Cancel the common factor.

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

Step 1.4.4

Rewrite the expression.

$\frac{1}{3} - 1 (\frac{3}{2})$

Step 1.5

Rewrite $- 1 (\frac{3}{2})$ as $- (\frac{3}{2})$ .

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

Step 2

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 3

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

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

Step 4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

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

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

Step 4.2

Multiply $3$ by $2$ .

$\frac{2}{6} - \frac{3}{2} \cdot \frac{3}{3}$

Step 4.3

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

$\frac{2}{6} - \frac{3 \cdot 3}{2 \cdot 3}$

Step 4.4

Multiply $2$ by $3$ .

$\frac{2}{6} - \frac{3 \cdot 3}{6}$

Step 5

Combine the numerators over the common denominator.

$\frac{2 - 3 \cdot 3}{6}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 3$ by $3$ .

$\frac{2 - 9}{6}$

Step 6.2

Subtract $9$ from $2$ .

$\frac{- 7}{6}$

Step 7

Move the negative in front of the fraction.

$- \frac{7}{6}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{7}{6}$

Decimal Form:

$- 1.1\overline{6}$

Mixed Number Form:

$- 1 \frac{1}{6}$