Basic Math Examples

$((\frac{1}{2} + \frac{1}{3}) + \frac{1}{4} - (\frac{1}{1} - \frac{5}{8})) + \frac{2}{3}$

Step 1

Combine the numerators over the common denominator.

$- (\frac{1}{1} - \frac{5}{8}) + \frac{1}{2} + \frac{1 + 2}{3} + \frac{1}{4}$

Step 2

Add $1$ and $2$ .

$- (\frac{1}{1} - \frac{5}{8}) + \frac{1}{2} + \frac{3}{3} + \frac{1}{4}$

Step 3

Find the common denominator.

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Step 3.1

Write $- (\frac{1}{1} - \frac{5}{8})$ as a fraction with denominator $1$ .

$\frac{- (\frac{1}{1} - \frac{5}{8})}{1} + \frac{1}{2} + \frac{3}{3} + \frac{1}{4}$

Step 3.2

Multiply $\frac{- (\frac{1}{1} - \frac{5}{8})}{1}$ by $\frac{12}{12}$ .

$\frac{- (\frac{1}{1} - \frac{5}{8})}{1} \cdot \frac{12}{12} + \frac{1}{2} + \frac{3}{3} + \frac{1}{4}$

Step 3.3

Multiply $\frac{- (\frac{1}{1} - \frac{5}{8})}{1}$ by $\frac{12}{12}$ .

$\frac{- (\frac{1}{1} - \frac{5}{8}) \cdot 12}{12} + \frac{1}{2} + \frac{3}{3} + \frac{1}{4}$

Step 3.4

Multiply $\frac{1}{2}$ by $\frac{6}{6}$ .

$\frac{- (\frac{1}{1} - \frac{5}{8}) \cdot 12}{12} + \frac{1}{2} \cdot \frac{6}{6} + \frac{3}{3} + \frac{1}{4}$

Step 3.5

Multiply $\frac{1}{2}$ by $\frac{6}{6}$ .

$\frac{- (\frac{1}{1} - \frac{5}{8}) \cdot 12}{12} + \frac{6}{2 \cdot 6} + \frac{3}{3} + \frac{1}{4}$

Step 3.6

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

$\frac{- (\frac{1}{1} - \frac{5}{8}) \cdot 12}{12} + \frac{6}{2 \cdot 6} + \frac{3}{3} \cdot \frac{4}{4} + \frac{1}{4}$

Step 3.7

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

$\frac{- (\frac{1}{1} - \frac{5}{8}) \cdot 12}{12} + \frac{6}{2 \cdot 6} + \frac{3 \cdot 4}{3 \cdot 4} + \frac{1}{4}$

Step 3.8

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

$\frac{- (\frac{1}{1} - \frac{5}{8}) \cdot 12}{12} + \frac{6}{2 \cdot 6} + \frac{3 \cdot 4}{3 \cdot 4} + \frac{1}{4} \cdot \frac{3}{3}$

Step 3.9

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

$\frac{- (\frac{1}{1} - \frac{5}{8}) \cdot 12}{12} + \frac{6}{2 \cdot 6} + \frac{3 \cdot 4}{3 \cdot 4} + \frac{3}{4 \cdot 3}$

Step 3.10

Multiply $2$ by $6$ .

$\frac{- (\frac{1}{1} - \frac{5}{8}) \cdot 12}{12} + \frac{6}{12} + \frac{3 \cdot 4}{3 \cdot 4} + \frac{3}{4 \cdot 3}$

Step 3.11

Multiply $3$ by $4$ .

$\frac{- (\frac{1}{1} - \frac{5}{8}) \cdot 12}{12} + \frac{6}{12} + \frac{3 \cdot 4}{12} + \frac{3}{4 \cdot 3}$

Step 3.12

Reorder the factors of $4 \cdot 3$ .

$\frac{- (\frac{1}{1} - \frac{5}{8}) \cdot 12}{12} + \frac{6}{12} + \frac{3 \cdot 4}{12} + \frac{3}{3 \cdot 4}$

Step 3.13

Multiply $3$ by $4$ .

$\frac{- (\frac{1}{1} - \frac{5}{8}) \cdot 12}{12} + \frac{6}{12} + \frac{3 \cdot 4}{12} + \frac{3}{12}$

Step 4

Combine the numerators over the common denominator.

$\frac{- (\frac{1}{1} - \frac{5}{8}) \cdot 12 + 6 + 3 \cdot 4 + 3}{12}$

Step 5

Simplify each term.

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Step 5.1

Divide $1$ by $1$ .

$\frac{- (1 - \frac{5}{8}) \cdot 12 + 6 + 3 \cdot 4 + 3}{12}$

Step 5.2

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

$\frac{- (\frac{8}{8} - \frac{5}{8}) \cdot 12 + 6 + 3 \cdot 4 + 3}{12}$

Step 5.3

Combine the numerators over the common denominator.

$\frac{- \frac{8 - 5}{8} \cdot 12 + 6 + 3 \cdot 4 + 3}{12}$

Step 5.4

Subtract $5$ from $8$ .

$\frac{- \frac{3}{8} \cdot 12 + 6 + 3 \cdot 4 + 3}{12}$

Step 5.5

Cancel the common factor of $4$ .

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Step 5.5.1

Move the leading negative in $- \frac{3}{8}$ into the numerator.

$\frac{\frac{- 3}{8} \cdot 12 + 6 + 3 \cdot 4 + 3}{12}$

Step 5.5.2

Factor $4$ out of $8$ .

$\frac{\frac{- 3}{4 (2)} \cdot 12 + 6 + 3 \cdot 4 + 3}{12}$

Step 5.5.3

Factor $4$ out of $12$ .

$\frac{\frac{- 3}{4 \cdot 2} \cdot (4 \cdot 3) + 6 + 3 \cdot 4 + 3}{12}$

Step 5.5.4

Cancel the common factor.

$\frac{\frac{- 3}{4 \cdot 2} \cdot (4 \cdot 3) + 6 + 3 \cdot 4 + 3}{12}$

Step 5.5.5

Rewrite the expression.

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

Step 5.6

Combine $\frac{- 3}{2}$ and $3$ .

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

Step 5.7

Multiply $- 3$ by $3$ .

$\frac{\frac{- 9}{2} + 6 + 3 \cdot 4 + 3}{12}$

Step 5.8

Move the negative in front of the fraction.

$\frac{- \frac{9}{2} + 6 + 3 \cdot 4 + 3}{12}$

Step 5.9

Multiply $3$ by $4$ .

$\frac{- \frac{9}{2} + 6 + 12 + 3}{12}$

Step 6

Find the common denominator.

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Step 6.1

Write $6$ as a fraction with denominator $1$ .

$\frac{- \frac{9}{2} + \frac{6}{1} + 12 + 3}{12}$

Step 6.2

Multiply $\frac{6}{1}$ by $\frac{2}{2}$ .

$\frac{- \frac{9}{2} + \frac{6}{1} \cdot \frac{2}{2} + 12 + 3}{12}$

Step 6.3

Multiply $\frac{6}{1}$ by $\frac{2}{2}$ .

$\frac{- \frac{9}{2} + \frac{6 \cdot 2}{2} + 12 + 3}{12}$

Step 6.4

Write $12$ as a fraction with denominator $1$ .

$\frac{- \frac{9}{2} + \frac{6 \cdot 2}{2} + \frac{12}{1} + 3}{12}$

Step 6.5

Multiply $\frac{12}{1}$ by $\frac{2}{2}$ .

$\frac{- \frac{9}{2} + \frac{6 \cdot 2}{2} + \frac{12}{1} \cdot \frac{2}{2} + 3}{12}$

Step 6.6

Multiply $\frac{12}{1}$ by $\frac{2}{2}$ .

$\frac{- \frac{9}{2} + \frac{6 \cdot 2}{2} + \frac{12 \cdot 2}{2} + 3}{12}$

Step 6.7

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

$\frac{- \frac{9}{2} + \frac{6 \cdot 2}{2} + \frac{12 \cdot 2}{2} + \frac{3}{1}}{12}$

Step 6.8

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

$\frac{- \frac{9}{2} + \frac{6 \cdot 2}{2} + \frac{12 \cdot 2}{2} + \frac{3}{1} \cdot \frac{2}{2}}{12}$

Step 6.9

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

$\frac{- \frac{9}{2} + \frac{6 \cdot 2}{2} + \frac{12 \cdot 2}{2} + \frac{3 \cdot 2}{2}}{12}$

Step 7

Combine the numerators over the common denominator.

$\frac{\frac{- 9 + 6 \cdot 2 + 12 \cdot 2 + 3 \cdot 2}{2}}{12}$

Step 8

Simplify each term.

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Step 8.1

Multiply $6$ by $2$ .

$\frac{\frac{- 9 + 12 + 12 \cdot 2 + 3 \cdot 2}{2}}{12}$

Step 8.2

Multiply $12$ by $2$ .

$\frac{\frac{- 9 + 12 + 24 + 3 \cdot 2}{2}}{12}$

Step 8.3

Multiply $3$ by $2$ .

$\frac{\frac{- 9 + 12 + 24 + 6}{2}}{12}$

Step 9

Simplify by adding numbers.

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Step 9.1

Add $- 9$ and $12$ .

$\frac{\frac{3 + 24 + 6}{2}}{12}$

Step 9.2

Add $3$ and $24$ .

$\frac{\frac{27 + 6}{2}}{12}$

Step 9.3

Add $27$ and $6$ .

$\frac{\frac{33}{2}}{12}$

Step 10

Multiply the numerator by the reciprocal of the denominator.

$\frac{33}{2} \cdot \frac{1}{12}$

Step 11

Cancel the common factor of $3$ .

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Step 11.1

Factor $3$ out of $33$ .

$\frac{3 (11)}{2} \cdot \frac{1}{12}$

Step 11.2

Factor $3$ out of $12$ .

$\frac{3 \cdot 11}{2} \cdot \frac{1}{3 \cdot 4}$

Step 11.3

Cancel the common factor.

$\frac{3 \cdot 11}{2} \cdot \frac{1}{3 \cdot 4}$

Step 11.4

Rewrite the expression.

$\frac{11}{2} \cdot \frac{1}{4}$

Step 12

Multiply $\frac{11}{2}$ by $\frac{1}{4}$ .

$\frac{11}{2 \cdot 4}$

Step 13

Multiply $2$ by $4$ .

$\frac{11}{8}$

Step 14

The result can be shown in multiple forms.

Exact Form:

$\frac{11}{8}$

Decimal Form:

$1.375$

Mixed Number Form:

$1 \frac{3}{8}$