Basic Math Examples

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

Step 1

Find the common denominator.

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Step 1.1

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

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

Step 1.2

Multiply $\frac{1}{1}$ by $\frac{6}{6}$ .

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

Step 1.3

Multiply $\frac{1}{1}$ by $\frac{6}{6}$ .

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

Step 1.4

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

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

Step 1.5

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

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

Step 1.6

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

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

Step 1.7

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

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

Step 1.8

Write $- (1 - \frac{1}{2} - \frac{4}{3})$ as a fraction with denominator $1$ .

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

Step 1.9

Multiply $\frac{- (1 - \frac{1}{2} - \frac{4}{3})}{1}$ by $\frac{6}{6}$ .

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

Step 1.10

Multiply $\frac{- (1 - \frac{1}{2} - \frac{4}{3})}{1}$ by $\frac{6}{6}$ .

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

Step 1.11

Multiply $2$ by $3$ .

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

Step 1.12

Reorder the factors of $3 \cdot 2$ .

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

Step 1.13

Multiply $2$ by $3$ .

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Simplify each term.

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Step 3.1

Find the common denominator.

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Step 3.1.1

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

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

Step 3.1.2

Multiply $\frac{1}{1}$ by $\frac{6}{6}$ .

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

Step 3.1.3

Multiply $\frac{1}{1}$ by $\frac{6}{6}$ .

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

Step 3.1.4

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

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

Step 3.1.5

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

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

Step 3.1.6

Multiply $\frac{4}{3}$ by $\frac{2}{2}$ .

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

Step 3.1.7

Multiply $\frac{4}{3}$ by $\frac{2}{2}$ .

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

Step 3.1.8

Multiply $2$ by $3$ .

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

Step 3.1.9

Reorder the factors of $3 \cdot 2$ .

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

Step 3.1.10

Multiply $2$ by $3$ .

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

Step 3.2

Combine the numerators over the common denominator.

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

Step 3.3

Multiply $- 4$ by $2$ .

$\frac{6 + 3 + 2 - \frac{6 - 3 - 8}{6} \cdot 6}{6}$

Step 3.4

Subtract $3$ from $6$ .

$\frac{6 + 3 + 2 - \frac{3 - 8}{6} \cdot 6}{6}$

Step 3.5

Subtract $8$ from $3$ .

$\frac{6 + 3 + 2 - \frac{- 5}{6} \cdot 6}{6}$

Step 3.6

Cancel the common factor of $6$ .

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Step 3.6.1

Move the leading negative in $- \frac{- 5}{6}$ into the numerator.

$\frac{6 + 3 + 2 + \frac{5}{6} \cdot 6}{6}$

Step 3.6.2

Cancel the common factor.

$\frac{6 + 3 + 2 + \frac{5}{6} \cdot 6}{6}$

Step 3.6.3

Rewrite the expression.

$\frac{6 + 3 + 2 + 5}{6}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Add $6$ and $3$ .

$\frac{9 + 2 + 5}{6}$

Step 4.2

Simplify by adding numbers.

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Step 4.2.1

Add $9$ and $2$ .

$\frac{11 + 5}{6}$

Step 4.2.2

Add $11$ and $5$ .

$\frac{16}{6}$

Step 4.3

Cancel the common factor of $16$ and $6$ .

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Step 4.3.1

Factor $2$ out of $16$ .

$\frac{2 (8)}{6}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $2$ out of $6$ .

$\frac{2 \cdot 8}{2 \cdot 3}$

Step 4.3.2.2

Cancel the common factor.

$\frac{2 \cdot 8}{2 \cdot 3}$

Step 4.3.2.3

Rewrite the expression.

$\frac{8}{3}$