Basic Math Examples

$\frac{2}{7} - \frac{1}{2} \cdot \frac{4}{14} - (\frac{1}{2} - \frac{3}{4})$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $2$ .

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Step 1.1.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$\frac{2}{7} + \frac{- 1}{2} \cdot \frac{4}{14} - (\frac{1}{2} - \frac{3}{4})$

Step 1.1.2

Factor $2$ out of $4$ .

$\frac{2}{7} + \frac{- 1}{2} \cdot \frac{2 (2)}{14} - (\frac{1}{2} - \frac{3}{4})$

Step 1.1.3

Cancel the common factor.

$\frac{2}{7} + \frac{- 1}{2} \cdot \frac{2 \cdot 2}{14} - (\frac{1}{2} - \frac{3}{4})$

Step 1.1.4

Rewrite the expression.

$\frac{2}{7} - 1 \cdot \frac{2}{14} - (\frac{1}{2} - \frac{3}{4})$

Step 1.2

Cancel the common factor of $2$ and $14$ .

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Step 1.2.1

Factor $2$ out of $2$ .

$\frac{2}{7} - 1 \cdot \frac{2 (1)}{14} - (\frac{1}{2} - \frac{3}{4})$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $2$ out of $14$ .

$\frac{2}{7} - 1 \cdot \frac{2 \cdot 1}{2 \cdot 7} - (\frac{1}{2} - \frac{3}{4})$

Step 1.2.2.2

Cancel the common factor.

$\frac{2}{7} - 1 \cdot \frac{2 \cdot 1}{2 \cdot 7} - (\frac{1}{2} - \frac{3}{4})$

Step 1.2.2.3

Rewrite the expression.

$\frac{2}{7} - 1 \cdot \frac{1}{7} - (\frac{1}{2} - \frac{3}{4})$

Step 1.3

Rewrite $- 1 (\frac{1}{7})$ as $- (\frac{1}{7})$ .

$\frac{2}{7} - (\frac{1}{7}) - (\frac{1}{2} - \frac{3}{4})$

Step 1.4

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

$\frac{2}{7} - \frac{1}{7} - (\frac{1}{2} \cdot \frac{2}{2} - \frac{3}{4})$

Step 1.5

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.5.1

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

$\frac{2}{7} - \frac{1}{7} - (\frac{2}{2 \cdot 2} - \frac{3}{4})$

Step 1.5.2

Multiply $2$ by $2$ .

$\frac{2}{7} - \frac{1}{7} - (\frac{2}{4} - \frac{3}{4})$

Step 1.6

Combine the numerators over the common denominator.

$\frac{2}{7} - \frac{1}{7} - \frac{2 - 3}{4}$

Step 1.7

Subtract $3$ from $2$ .

$\frac{2}{7} - \frac{1}{7} - \frac{- 1}{4}$

Step 1.8

Move the negative in front of the fraction.

$\frac{2}{7} - \frac{1}{7} - - \frac{1}{4}$

Step 1.9

Multiply $- - \frac{1}{4}$ .

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Step 1.9.1

Multiply $- 1$ by $- 1$ .

$\frac{2}{7} - \frac{1}{7} + 1 (\frac{1}{4})$

Step 1.9.2

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

$\frac{2}{7} - \frac{1}{7} + \frac{1}{4}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{2 - 1}{7} + \frac{1}{4}$

Step 2.2

Subtract $1$ from $2$ .

$\frac{1}{7} + \frac{1}{4}$

Step 3

To write $\frac{1}{7}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{1}{7} \cdot \frac{4}{4} + \frac{1}{4}$

Step 4

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{1}{7} \cdot \frac{4}{4} + \frac{1}{4} \cdot \frac{7}{7}$

Step 5

Write each expression with a common denominator of $28$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{1}{7}$ by $\frac{4}{4}$ .

$\frac{4}{7 \cdot 4} + \frac{1}{4} \cdot \frac{7}{7}$

Step 5.2

Multiply $7$ by $4$ .

$\frac{4}{28} + \frac{1}{4} \cdot \frac{7}{7}$

Step 5.3

Multiply $\frac{1}{4}$ by $\frac{7}{7}$ .

$\frac{4}{28} + \frac{7}{4 \cdot 7}$

Step 5.4

Multiply $4$ by $7$ .

$\frac{4}{28} + \frac{7}{28}$

Step 6

Combine the numerators over the common denominator.

$\frac{4 + 7}{28}$

Step 7

Add $4$ and $7$ .

$\frac{11}{28}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{11}{28}$

Decimal Form:

$0.39285714 \dots$