Basic Math Examples

$| (- (\frac{12}{34} - \frac{36}{34}) + (\frac{12}{4} - \frac{3}{4})) \cdot ((\frac{2}{3} - \frac{5}{4}) - (\frac{6}{4} \cdot \frac{4}{3})) |$

Step 1

Combine fractions.

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Step 1.1

Combine the numerators over the common denominator.

$| (- (\frac{12}{34} - \frac{36}{34}) + \frac{12 - 3}{4}) \cdot ((\frac{2}{3} - \frac{5}{4}) - (\frac{6}{4} \cdot \frac{4}{3})) |$

Step 1.2

Subtract $3$ from $12$ .

$| (- (\frac{12}{34} - \frac{36}{34}) + \frac{9}{4}) \cdot ((\frac{2}{3} - \frac{5}{4}) - (\frac{6}{4} \cdot \frac{4}{3})) |$

Step 2

Simplify each term.

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Step 2.1

Combine the numerators over the common denominator.

$| (- \frac{12 - 36}{34} + \frac{9}{4}) \cdot ((\frac{2}{3} - \frac{5}{4}) - (\frac{6}{4} \cdot \frac{4}{3})) |$

Step 2.2

Subtract $36$ from $12$ .

$| (- \frac{- 24}{34} + \frac{9}{4}) \cdot ((\frac{2}{3} - \frac{5}{4}) - (\frac{6}{4} \cdot \frac{4}{3})) |$

Step 2.3

Cancel the common factor of $- 24$ and $34$ .

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Step 2.3.1

Factor $2$ out of $- 24$ .

$| (- \frac{2 (- 12)}{34} + \frac{9}{4}) \cdot ((\frac{2}{3} - \frac{5}{4}) - (\frac{6}{4} \cdot \frac{4}{3})) |$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $2$ out of $34$ .

$| (- \frac{2 \cdot - 12}{2 \cdot 17} + \frac{9}{4}) \cdot ((\frac{2}{3} - \frac{5}{4}) - (\frac{6}{4} \cdot \frac{4}{3})) |$

Step 2.3.2.2

Cancel the common factor.

$| (- \frac{2 \cdot - 12}{2 \cdot 17} + \frac{9}{4}) \cdot ((\frac{2}{3} - \frac{5}{4}) - (\frac{6}{4} \cdot \frac{4}{3})) |$

Step 2.3.2.3

Rewrite the expression.

$| (- \frac{- 12}{17} + \frac{9}{4}) \cdot ((\frac{2}{3} - \frac{5}{4}) - (\frac{6}{4} \cdot \frac{4}{3})) |$

Step 2.4

Move the negative in front of the fraction.

$| (- - \frac{12}{17} + \frac{9}{4}) \cdot ((\frac{2}{3} - \frac{5}{4}) - (\frac{6}{4} \cdot \frac{4}{3})) |$

Step 2.5

Multiply $- - \frac{12}{17}$ .

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Step 2.5.1

Multiply $- 1$ by $- 1$ .

$| (1 (\frac{12}{17}) + \frac{9}{4}) \cdot ((\frac{2}{3} - \frac{5}{4}) - (\frac{6}{4} \cdot \frac{4}{3})) |$

Step 2.5.2

Multiply $\frac{12}{17}$ by $1$ .

$| (\frac{12}{17} + \frac{9}{4}) \cdot ((\frac{2}{3} - \frac{5}{4}) - (\frac{6}{4} \cdot \frac{4}{3})) |$

Step 3

To write $\frac{12}{17}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$| (\frac{12}{17} \cdot \frac{4}{4} + \frac{9}{4}) \cdot ((\frac{2}{3} - \frac{5}{4}) - (\frac{6}{4} \cdot \frac{4}{3})) |$

Step 4

To write $\frac{9}{4}$ as a fraction with a common denominator, multiply by $\frac{17}{17}$ .

$| (\frac{12}{17} \cdot \frac{4}{4} + \frac{9}{4} \cdot \frac{17}{17}) \cdot ((\frac{2}{3} - \frac{5}{4}) - (\frac{6}{4} \cdot \frac{4}{3})) |$

Step 5

Write each expression with a common denominator of $68$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{12}{17}$ by $\frac{4}{4}$ .

$| (\frac{12 \cdot 4}{17 \cdot 4} + \frac{9}{4} \cdot \frac{17}{17}) \cdot ((\frac{2}{3} - \frac{5}{4}) - (\frac{6}{4} \cdot \frac{4}{3})) |$

Step 5.2

Multiply $17$ by $4$ .

$| (\frac{12 \cdot 4}{68} + \frac{9}{4} \cdot \frac{17}{17}) \cdot ((\frac{2}{3} - \frac{5}{4}) - (\frac{6}{4} \cdot \frac{4}{3})) |$

Step 5.3

Multiply $\frac{9}{4}$ by $\frac{17}{17}$ .

$| (\frac{12 \cdot 4}{68} + \frac{9 \cdot 17}{4 \cdot 17}) \cdot ((\frac{2}{3} - \frac{5}{4}) - (\frac{6}{4} \cdot \frac{4}{3})) |$

Step 5.4

Multiply $4$ by $17$ .

$| (\frac{12 \cdot 4}{68} + \frac{9 \cdot 17}{68}) \cdot ((\frac{2}{3} - \frac{5}{4}) - (\frac{6}{4} \cdot \frac{4}{3})) |$

Step 6

Combine the numerators over the common denominator.

$| \frac{12 \cdot 4 + 9 \cdot 17}{68} \cdot ((\frac{2}{3} - \frac{5}{4}) - (\frac{6}{4} \cdot \frac{4}{3})) |$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $12$ by $4$ .

$| \frac{48 + 9 \cdot 17}{68} \cdot ((\frac{2}{3} - \frac{5}{4}) - (\frac{6}{4} \cdot \frac{4}{3})) |$

Step 7.2

Multiply $9$ by $17$ .

$| \frac{48 + 153}{68} \cdot ((\frac{2}{3} - \frac{5}{4}) - (\frac{6}{4} \cdot \frac{4}{3})) |$

Step 7.3

Add $48$ and $153$ .

$| \frac{201}{68} \cdot ((\frac{2}{3} - \frac{5}{4}) - (\frac{6}{4} \cdot \frac{4}{3})) |$

Step 8

Simplify each term.

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Step 8.1

Cancel the common factor of $3$ .

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Step 8.1.1

Factor $3$ out of $6$ .

$| \frac{201}{68} \cdot (\frac{2}{3} - \frac{5}{4} - (\frac{3 (2)}{4} \cdot \frac{4}{3})) |$

Step 8.1.2

Cancel the common factor.

$| \frac{201}{68} \cdot (\frac{2}{3} - \frac{5}{4} - (\frac{3 \cdot 2}{4} \cdot \frac{4}{3})) |$

Step 8.1.3

Rewrite the expression.

$| \frac{201}{68} \cdot (\frac{2}{3} - \frac{5}{4} - (\frac{2}{4} \cdot 4)) |$

Step 8.2

Cancel the common factor of $4$ .

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Step 8.2.1

Cancel the common factor.

$| \frac{201}{68} \cdot (\frac{2}{3} - \frac{5}{4} - (\frac{2}{4} \cdot 4)) |$

Step 8.2.2

Rewrite the expression.

$| \frac{201}{68} \cdot (\frac{2}{3} - \frac{5}{4} - 1 \cdot 2) |$

Step 8.3

Multiply $- 1$ by $2$ .

$| \frac{201}{68} \cdot (\frac{2}{3} - \frac{5}{4} - 2) |$

Step 9

Find the common denominator.

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Step 9.1

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

$| \frac{201}{68} \cdot (\frac{2}{3} \cdot \frac{4}{4} - \frac{5}{4} - 2) |$

Step 9.2

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

$| \frac{201}{68} \cdot (\frac{2 \cdot 4}{3 \cdot 4} - \frac{5}{4} - 2) |$

Step 9.3

Multiply $\frac{5}{4}$ by $\frac{3}{3}$ .

$| \frac{201}{68} \cdot (\frac{2 \cdot 4}{3 \cdot 4} - (\frac{5}{4} \cdot \frac{3}{3}) - 2) |$

Step 9.4

Multiply $\frac{5}{4}$ by $\frac{3}{3}$ .

$| \frac{201}{68} \cdot (\frac{2 \cdot 4}{3 \cdot 4} - \frac{5 \cdot 3}{4 \cdot 3} - 2) |$

Step 9.5

Write $- 2$ as a fraction with denominator $1$ .

$| \frac{201}{68} \cdot (\frac{2 \cdot 4}{3 \cdot 4} - \frac{5 \cdot 3}{4 \cdot 3} + \frac{- 2}{1}) |$

Step 9.6

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

$| \frac{201}{68} \cdot (\frac{2 \cdot 4}{3 \cdot 4} - \frac{5 \cdot 3}{4 \cdot 3} + \frac{- 2}{1} \cdot \frac{12}{12}) |$

Step 9.7

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

$| \frac{201}{68} \cdot (\frac{2 \cdot 4}{3 \cdot 4} - \frac{5 \cdot 3}{4 \cdot 3} + \frac{- 2 \cdot 12}{12}) |$

Step 9.8

Multiply $3$ by $4$ .

$| \frac{201}{68} \cdot (\frac{2 \cdot 4}{12} - \frac{5 \cdot 3}{4 \cdot 3} + \frac{- 2 \cdot 12}{12}) |$

Step 9.9

Reorder the factors of $4 \cdot 3$ .

$| \frac{201}{68} \cdot (\frac{2 \cdot 4}{12} - \frac{5 \cdot 3}{3 \cdot 4} + \frac{- 2 \cdot 12}{12}) |$

Step 9.10

Multiply $3$ by $4$ .

$| \frac{201}{68} \cdot (\frac{2 \cdot 4}{12} - \frac{5 \cdot 3}{12} + \frac{- 2 \cdot 12}{12}) |$

Step 10

Combine the numerators over the common denominator.

$| \frac{201}{68} \cdot \frac{2 \cdot 4 - 5 \cdot 3 - 2 \cdot 12}{12} |$

Step 11

Simplify each term.

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Step 11.1

Multiply $2$ by $4$ .

$| \frac{201}{68} \cdot \frac{8 - 5 \cdot 3 - 2 \cdot 12}{12} |$

Step 11.2

Multiply $- 5$ by $3$ .

$| \frac{201}{68} \cdot \frac{8 - 15 - 2 \cdot 12}{12} |$

Step 11.3

Multiply $- 2$ by $12$ .

$| \frac{201}{68} \cdot \frac{8 - 15 - 24}{12} |$

Step 12

Simplify terms.

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Step 12.1

Subtract $15$ from $8$ .

$| \frac{201}{68} \cdot \frac{- 7 - 24}{12} |$

Step 12.2

Subtract $24$ from $- 7$ .

$| \frac{201}{68} \cdot \frac{- 31}{12} |$

Step 12.3

Cancel the common factor of $3$ .

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Step 12.3.1

Factor $3$ out of $201$ .

$| \frac{3 (67)}{68} \cdot \frac{- 31}{12} |$

Step 12.3.2

Factor $3$ out of $12$ .

$| \frac{3 \cdot 67}{68} \cdot \frac{- 31}{3 \cdot 4} |$

Step 12.3.3

Cancel the common factor.

$| \frac{3 \cdot 67}{68} \cdot \frac{- 31}{3 \cdot 4} |$

Step 12.3.4

Rewrite the expression.

$| \frac{67}{68} \cdot \frac{- 31}{4} |$

Step 12.4

Multiply $\frac{67}{68}$ by $\frac{- 31}{4}$ .

$| \frac{67 \cdot - 31}{68 \cdot 4} |$

Step 12.5

Simplify the expression.

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Step 12.5.1

Multiply $67$ by $- 31$ .

$| \frac{- 2077}{68 \cdot 4} |$

Step 12.5.2

Multiply $68$ by $4$ .

$| \frac{- 2077}{272} |$

Step 12.5.3

Move the negative in front of the fraction.

$| - \frac{2077}{272} |$

Step 13

$- \frac{2077}{272}$ is approximately $- 7.63602941$ which is negative so negate $- \frac{2077}{272}$ and remove the absolute value

$\frac{2077}{272}$

Step 14

The result can be shown in multiple forms.

Exact Form:

$\frac{2077}{272}$

Decimal Form:

$7.63602941 \dots$

Mixed Number Form:

$7 \frac{173}{272}$