Basic Math Examples

$\frac{42 - 54 (176 + \frac{17 (\frac{8}{76})}{54}) - 32}{193}$

Step 1

Simplify terms.

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Step 1.1

Cancel the common factor of $8$ and $76$ .

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Step 1.1.1

Factor $4$ out of $8$ .

$\frac{42 - 54 (176 + \frac{17 \frac{4 (2)}{76}}{54}) - 32}{193}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $4$ out of $76$ .

$\frac{42 - 54 (176 + \frac{17 \frac{4 \cdot 2}{4 \cdot 19}}{54}) - 32}{193}$

Step 1.1.2.2

Cancel the common factor.

$\frac{42 - 54 (176 + \frac{17 \frac{4 \cdot 2}{4 \cdot 19}}{54}) - 32}{193}$

Step 1.1.2.3

Rewrite the expression.

$\frac{42 - 54 (176 + \frac{17 (\frac{2}{19})}{54}) - 32}{193}$

Step 1.2

Combine $17$ and $\frac{2}{19}$ .

$\frac{42 - 54 (176 + \frac{\frac{17 \cdot 2}{19}}{54}) - 32}{193}$

Step 1.3

Multiply $17$ by $2$ .

$\frac{42 - 54 (176 + \frac{\frac{34}{19}}{54}) - 32}{193}$

Step 2

Simplify the numerator.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{42 - 54 (176 + \frac{34}{19} \cdot \frac{1}{54}) - 32}{193}$

Step 2.1.2

Cancel the common factor of $2$ .

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Step 2.1.2.1

Factor $2$ out of $34$ .

$\frac{42 - 54 (176 + \frac{2 (17)}{19} \cdot \frac{1}{54}) - 32}{193}$

Step 2.1.2.2

Factor $2$ out of $54$ .

$\frac{42 - 54 (176 + \frac{2 \cdot 17}{19} \cdot \frac{1}{2 \cdot 27}) - 32}{193}$

Step 2.1.2.3

Cancel the common factor.

$\frac{42 - 54 (176 + \frac{2 \cdot 17}{19} \cdot \frac{1}{2 \cdot 27}) - 32}{193}$

Step 2.1.2.4

Rewrite the expression.

$\frac{42 - 54 (176 + \frac{17}{19} \cdot \frac{1}{27}) - 32}{193}$

Step 2.1.3

Multiply $\frac{17}{19}$ by $\frac{1}{27}$ .

$\frac{42 - 54 (176 + \frac{17}{19 \cdot 27}) - 32}{193}$

Step 2.1.4

Multiply $19$ by $27$ .

$\frac{42 - 54 (176 + \frac{17}{513}) - 32}{193}$

Step 2.2

To write $176$ as a fraction with a common denominator, multiply by $\frac{513}{513}$ .

$\frac{42 - 54 (176 \cdot \frac{513}{513} + \frac{17}{513}) - 32}{193}$

Step 2.3

Combine $176$ and $\frac{513}{513}$ .

$\frac{42 - 54 (\frac{176 \cdot 513}{513} + \frac{17}{513}) - 32}{193}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{42 - 54 \frac{176 \cdot 513 + 17}{513} - 32}{193}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $176$ by $513$ .

$\frac{42 - 54 \frac{90288 + 17}{513} - 32}{193}$

Step 2.5.2

Add $90288$ and $17$ .

$\frac{42 - 54 (\frac{90305}{513}) - 32}{193}$

Step 2.6

Cancel the common factor of $27$ .

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Step 2.6.1

Factor $27$ out of $- 54$ .

$\frac{42 + 27 (- 2) \frac{90305}{513} - 32}{193}$

Step 2.6.2

Factor $27$ out of $513$ .

$\frac{42 + 27 \cdot - 2 \frac{90305}{27 \cdot 19} - 32}{193}$

Step 2.6.3

Cancel the common factor.

$\frac{42 + 27 \cdot - 2 \frac{90305}{27 \cdot 19} - 32}{193}$

Step 2.6.4

Rewrite the expression.

$\frac{42 - 2 (\frac{90305}{19}) - 32}{193}$

Step 2.7

Combine $- 2$ and $\frac{90305}{19}$ .

$\frac{42 + \frac{- 2 \cdot 90305}{19} - 32}{193}$

Step 2.8

Multiply $- 2$ by $90305$ .

$\frac{42 + \frac{- 180610}{19} - 32}{193}$

Step 2.9

Move the negative in front of the fraction.

$\frac{42 - \frac{180610}{19} - 32}{193}$

Step 2.10

To write $42$ as a fraction with a common denominator, multiply by $\frac{19}{19}$ .

$\frac{42 \cdot \frac{19}{19} - \frac{180610}{19} - 32}{193}$

Step 2.11

Combine $42$ and $\frac{19}{19}$ .

$\frac{\frac{42 \cdot 19}{19} - \frac{180610}{19} - 32}{193}$

Step 2.12

Combine the numerators over the common denominator.

$\frac{\frac{42 \cdot 19 - 180610}{19} - 32}{193}$

Step 2.13

Simplify the numerator.

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Step 2.13.1

Multiply $42$ by $19$ .

$\frac{\frac{798 - 180610}{19} - 32}{193}$

Step 2.13.2

Subtract $180610$ from $798$ .

$\frac{\frac{- 179812}{19} - 32}{193}$

Step 2.14

To write $- 32$ as a fraction with a common denominator, multiply by $\frac{19}{19}$ .

$\frac{\frac{- 179812}{19} - 32 \cdot \frac{19}{19}}{193}$

Step 2.15

Combine $- 32$ and $\frac{19}{19}$ .

$\frac{\frac{- 179812}{19} + \frac{- 32 \cdot 19}{19}}{193}$

Step 2.16

Combine the numerators over the common denominator.

$\frac{\frac{- 179812 - 32 \cdot 19}{19}}{193}$

Step 2.17

Simplify the numerator.

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Step 2.17.1

Multiply $- 32$ by $19$ .

$\frac{\frac{- 179812 - 608}{19}}{193}$

Step 2.17.2

Subtract $608$ from $- 179812$ .

$\frac{\frac{- 180420}{19}}{193}$

Step 2.18

Move the negative in front of the fraction.

$\frac{- \frac{180420}{19}}{193}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$- \frac{180420}{19} \cdot \frac{1}{193}$

Step 4

Multiply $- \frac{180420}{19} \cdot \frac{1}{193}$ .

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Step 4.1

Multiply $\frac{1}{193}$ by $\frac{180420}{19}$ .

$- \frac{180420}{193 \cdot 19}$

Step 4.2

Multiply $193$ by $19$ .

$- \frac{180420}{3667}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{180420}{3667}$

Decimal Form:

$- 49.20098172 \dots$

Mixed Number Form:

$- 49 \frac{737}{3667}$