Basic Math Examples

$(3 + \frac{1}{4}) - (2 + \frac{1}{6}) \cdot (\frac{7}{2} - 2)$

Step 1

Find the common denominator.

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Step 1.1

Write $3$ as a fraction with denominator $1$ .

$\frac{3}{1} + \frac{1}{4} - (2 + \frac{1}{6}) \cdot (\frac{7}{2} - 2)$

Step 1.2

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

$\frac{3}{1} \cdot \frac{4}{4} + \frac{1}{4} - (2 + \frac{1}{6}) \cdot (\frac{7}{2} - 2)$

Step 1.3

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

$\frac{3 \cdot 4}{4} + \frac{1}{4} - (2 + \frac{1}{6}) \cdot (\frac{7}{2} - 2)$

Step 1.4

Write $- (2 + \frac{1}{6}) \cdot (\frac{7}{2} - 2)$ as a fraction with denominator $1$ .

$\frac{3 \cdot 4}{4} + \frac{1}{4} + \frac{- (2 + \frac{1}{6}) \cdot (\frac{7}{2} - 2)}{1}$

Step 1.5

Multiply $\frac{- (2 + \frac{1}{6}) \cdot (\frac{7}{2} - 2)}{1}$ by $\frac{4}{4}$ .

$\frac{3 \cdot 4}{4} + \frac{1}{4} + \frac{- (2 + \frac{1}{6}) \cdot (\frac{7}{2} - 2)}{1} \cdot \frac{4}{4}$

Step 1.6

Multiply $\frac{- (2 + \frac{1}{6}) \cdot (\frac{7}{2} - 2)}{1}$ by $\frac{4}{4}$ .

$\frac{3 \cdot 4}{4} + \frac{1}{4} + \frac{- (2 + \frac{1}{6}) \cdot (\frac{7}{2} - 2) \cdot 4}{4}$

Step 2

Combine the numerators over the common denominator.

$\frac{3 \cdot 4 + 1 - (2 + \frac{1}{6}) \cdot (\frac{7}{2} - 2) \cdot 4}{4}$

Step 3

Simplify each term.

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Step 3.1

Multiply $3$ by $4$ .

$\frac{12 + 1 - (2 + \frac{1}{6}) \cdot (\frac{7}{2} - 2) \cdot 4}{4}$

Step 3.2

To write $2$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{12 + 1 - (2 \cdot \frac{6}{6} + \frac{1}{6}) \cdot (\frac{7}{2} - 2) \cdot 4}{4}$

Step 3.3

Combine $2$ and $\frac{6}{6}$ .

$\frac{12 + 1 - (\frac{2 \cdot 6}{6} + \frac{1}{6}) \cdot (\frac{7}{2} - 2) \cdot 4}{4}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{12 + 1 - \frac{2 \cdot 6 + 1}{6} \cdot (\frac{7}{2} - 2) \cdot 4}{4}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $2$ by $6$ .

$\frac{12 + 1 - \frac{12 + 1}{6} \cdot (\frac{7}{2} - 2) \cdot 4}{4}$

Step 3.5.2

Add $12$ and $1$ .

$\frac{12 + 1 - \frac{13}{6} \cdot (\frac{7}{2} - 2) \cdot 4}{4}$

Step 3.6

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

$\frac{12 + 1 - \frac{13}{6} \cdot (\frac{7}{2} - 2 \cdot \frac{2}{2}) \cdot 4}{4}$

Step 3.7

Combine $- 2$ and $\frac{2}{2}$ .

$\frac{12 + 1 - \frac{13}{6} \cdot (\frac{7}{2} + \frac{- 2 \cdot 2}{2}) \cdot 4}{4}$

Step 3.8

Combine the numerators over the common denominator.

$\frac{12 + 1 - \frac{13}{6} \cdot \frac{7 - 2 \cdot 2}{2} \cdot 4}{4}$

Step 3.9

Simplify the numerator.

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Step 3.9.1

Multiply $- 2$ by $2$ .

$\frac{12 + 1 - \frac{13}{6} \cdot \frac{7 - 4}{2} \cdot 4}{4}$

Step 3.9.2

Subtract $4$ from $7$ .

$\frac{12 + 1 - \frac{13}{6} \cdot \frac{3}{2} \cdot 4}{4}$

Step 3.10

Cancel the common factor of $3$ .

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Step 3.10.1

Move the leading negative in $- \frac{13}{6}$ into the numerator.

$\frac{12 + 1 + \frac{- 13}{6} \cdot \frac{3}{2} \cdot 4}{4}$

Step 3.10.2

Factor $3$ out of $6$ .

$\frac{12 + 1 + \frac{- 13}{3 (2)} \cdot \frac{3}{2} \cdot 4}{4}$

Step 3.10.3

Cancel the common factor.

$\frac{12 + 1 + \frac{- 13}{3 \cdot 2} \cdot \frac{3}{2} \cdot 4}{4}$

Step 3.10.4

Rewrite the expression.

$\frac{12 + 1 + \frac{- 13}{2} \cdot \frac{1}{2} \cdot 4}{4}$

Step 3.11

Multiply $\frac{- 13}{2}$ by $\frac{1}{2}$ .

$\frac{12 + 1 + \frac{- 13}{2 \cdot 2} \cdot 4}{4}$

Step 3.12

Multiply $2$ by $2$ .

$\frac{12 + 1 + \frac{- 13}{4} \cdot 4}{4}$

Step 3.13

Cancel the common factor of $4$ .

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Step 3.13.1

Cancel the common factor.

$\frac{12 + 1 + \frac{- 13}{4} \cdot 4}{4}$

Step 3.13.2

Rewrite the expression.

$\frac{12 + 1 - 13}{4}$

Step 4

Simplify the expression.

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Step 4.1

Add $12$ and $1$ .

$\frac{13 - 13}{4}$

Step 4.2

Subtract $13$ from $13$ .

$\frac{0}{4}$

Step 4.3

Divide $0$ by $4$ .

$0$