Basic Math Examples

$(81 - \frac{81}{3} + 1) - (- 81 - \frac{18}{3} - 1)$

Step 1

Find the common denominator.

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Step 1.1

Write $81$ as a fraction with denominator $1$ .

$\frac{81}{1} - \frac{81}{3} + 1 - (- 81 - \frac{18}{3} - 1)$

Step 1.2

Multiply $\frac{81}{1}$ by $\frac{3}{3}$ .

$\frac{81}{1} \cdot \frac{3}{3} - \frac{81}{3} + 1 - (- 81 - \frac{18}{3} - 1)$

Step 1.3

Multiply $\frac{81}{1}$ by $\frac{3}{3}$ .

$\frac{81 \cdot 3}{3} - \frac{81}{3} + 1 - (- 81 - \frac{18}{3} - 1)$

Step 1.4

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

$\frac{81 \cdot 3}{3} - \frac{81}{3} + \frac{1}{1} - (- 81 - \frac{18}{3} - 1)$

Step 1.5

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

$\frac{81 \cdot 3}{3} - \frac{81}{3} + \frac{1}{1} \cdot \frac{3}{3} - (- 81 - \frac{18}{3} - 1)$

Step 1.6

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

$\frac{81 \cdot 3}{3} - \frac{81}{3} + \frac{3}{3} - (- 81 - \frac{18}{3} - 1)$

Step 1.7

Write $- (- 81 - \frac{18}{3} - 1)$ as a fraction with denominator $1$ .

$\frac{81 \cdot 3}{3} - \frac{81}{3} + \frac{3}{3} + \frac{- (- 81 - \frac{18}{3} - 1)}{1}$

Step 1.8

Multiply $\frac{- (- 81 - \frac{18}{3} - 1)}{1}$ by $\frac{3}{3}$ .

$\frac{81 \cdot 3}{3} - \frac{81}{3} + \frac{3}{3} + \frac{- (- 81 - \frac{18}{3} - 1)}{1} \cdot \frac{3}{3}$

Step 1.9

Multiply $\frac{- (- 81 - \frac{18}{3} - 1)}{1}$ by $\frac{3}{3}$ .

$\frac{81 \cdot 3}{3} - \frac{81}{3} + \frac{3}{3} + \frac{- (- 81 - \frac{18}{3} - 1) \cdot 3}{3}$

Step 2

Combine the numerators over the common denominator.

$\frac{81 \cdot 3 - 81 + 3 - (- 81 - \frac{18}{3} - 1) \cdot 3}{3}$

Step 3

Simplify each term.

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Step 3.1

Multiply $81$ by $3$ .

$\frac{243 - 81 + 3 - (- 81 - \frac{18}{3} - 1) \cdot 3}{3}$

Step 3.2

Find the common denominator.

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Step 3.2.1

Write $- 81$ as a fraction with denominator $1$ .

$\frac{243 - 81 + 3 - (\frac{- 81}{1} - \frac{18}{3} - 1) \cdot 3}{3}$

Step 3.2.2

Multiply $\frac{- 81}{1}$ by $\frac{3}{3}$ .

$\frac{243 - 81 + 3 - (\frac{- 81}{1} \cdot \frac{3}{3} - \frac{18}{3} - 1) \cdot 3}{3}$

Step 3.2.3

Multiply $\frac{- 81}{1}$ by $\frac{3}{3}$ .

$\frac{243 - 81 + 3 - (\frac{- 81 \cdot 3}{3} - \frac{18}{3} - 1) \cdot 3}{3}$

Step 3.2.4

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

$\frac{243 - 81 + 3 - (\frac{- 81 \cdot 3}{3} - \frac{18}{3} + \frac{- 1}{1}) \cdot 3}{3}$

Step 3.2.5

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

$\frac{243 - 81 + 3 - (\frac{- 81 \cdot 3}{3} - \frac{18}{3} + \frac{- 1}{1} \cdot \frac{3}{3}) \cdot 3}{3}$

Step 3.2.6

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

$\frac{243 - 81 + 3 - (\frac{- 81 \cdot 3}{3} - \frac{18}{3} + \frac{- 1 \cdot 3}{3}) \cdot 3}{3}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{243 - 81 + 3 - \frac{- 81 \cdot 3 - 18 - 1 \cdot 3}{3} \cdot 3}{3}$

Step 3.4

Simplify each term.

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Step 3.4.1

Multiply $- 81$ by $3$ .

$\frac{243 - 81 + 3 - \frac{- 243 - 18 - 1 \cdot 3}{3} \cdot 3}{3}$

Step 3.4.2

Multiply $- 1$ by $3$ .

$\frac{243 - 81 + 3 - \frac{- 243 - 18 - 3}{3} \cdot 3}{3}$

Step 3.5

Subtract $18$ from $- 243$ .

$\frac{243 - 81 + 3 - \frac{- 261 - 3}{3} \cdot 3}{3}$

Step 3.6

Subtract $3$ from $- 261$ .

$\frac{243 - 81 + 3 - \frac{- 264}{3} \cdot 3}{3}$

Step 3.7

Cancel the common factor of $3$ .

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Step 3.7.1

Move the leading negative in $- \frac{- 264}{3}$ into the numerator.

$\frac{243 - 81 + 3 + \frac{264}{3} \cdot 3}{3}$

Step 3.7.2

Cancel the common factor.

$\frac{243 - 81 + 3 + \frac{264}{3} \cdot 3}{3}$

Step 3.7.3

Rewrite the expression.

$\frac{243 - 81 + 3 + 264}{3}$

Step 4

Simplify the expression.

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Step 4.1

Subtract $81$ from $243$ .

$\frac{162 + 3 + 264}{3}$

Step 4.2

Add $162$ and $3$ .

$\frac{165 + 264}{3}$

Step 4.3

Add $165$ and $264$ .

$\frac{429}{3}$

Step 4.4

Divide $429$ by $3$ .

$143$