Basic Math Examples

$(243 - \frac{243}{5}) - (243 + \frac{- 243}{5})$

Step 1

Find the common denominator.

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Step 1.1

Write $243$ as a fraction with denominator $1$ .

$\frac{243}{1} - \frac{243}{5} - (243 + \frac{- 243}{5})$

Step 1.2

Multiply $\frac{243}{1}$ by $\frac{5}{5}$ .

$\frac{243}{1} \cdot \frac{5}{5} - \frac{243}{5} - (243 + \frac{- 243}{5})$

Step 1.3

Multiply $\frac{243}{1}$ by $\frac{5}{5}$ .

$\frac{243 \cdot 5}{5} - \frac{243}{5} - (243 + \frac{- 243}{5})$

Step 1.4

Write $- (243 + \frac{- 243}{5})$ as a fraction with denominator $1$ .

$\frac{243 \cdot 5}{5} - \frac{243}{5} + \frac{- (243 + \frac{- 243}{5})}{1}$

Step 1.5

Multiply $\frac{- (243 + \frac{- 243}{5})}{1}$ by $\frac{5}{5}$ .

$\frac{243 \cdot 5}{5} - \frac{243}{5} + \frac{- (243 + \frac{- 243}{5})}{1} \cdot \frac{5}{5}$

Step 1.6

Multiply $\frac{- (243 + \frac{- 243}{5})}{1}$ by $\frac{5}{5}$ .

$\frac{243 \cdot 5}{5} - \frac{243}{5} + \frac{- (243 + \frac{- 243}{5}) \cdot 5}{5}$

Step 2

Combine the numerators over the common denominator.

$\frac{243 \cdot 5 - 243 - (243 + \frac{- 243}{5}) \cdot 5}{5}$

Step 3

Simplify each term.

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Step 3.1

Multiply $243$ by $5$ .

$\frac{1215 - 243 - (243 + \frac{- 243}{5}) \cdot 5}{5}$

Step 3.2

Move the negative in front of the fraction.

$\frac{1215 - 243 - (243 - \frac{243}{5}) \cdot 5}{5}$

Step 3.3

To write $243$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{1215 - 243 - (243 \cdot \frac{5}{5} - \frac{243}{5}) \cdot 5}{5}$

Step 3.4

Combine $243$ and $\frac{5}{5}$ .

$\frac{1215 - 243 - (\frac{243 \cdot 5}{5} - \frac{243}{5}) \cdot 5}{5}$

Step 3.5

Combine the numerators over the common denominator.

$\frac{1215 - 243 - \frac{243 \cdot 5 - 243}{5} \cdot 5}{5}$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Multiply $243$ by $5$ .

$\frac{1215 - 243 - \frac{1215 - 243}{5} \cdot 5}{5}$

Step 3.6.2

Subtract $243$ from $1215$ .

$\frac{1215 - 243 - \frac{972}{5} \cdot 5}{5}$

Step 3.7

Cancel the common factor of $5$ .

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Step 3.7.1

Move the leading negative in $- \frac{972}{5}$ into the numerator.

$\frac{1215 - 243 + \frac{- 972}{5} \cdot 5}{5}$

Step 3.7.2

Cancel the common factor.

$\frac{1215 - 243 + \frac{- 972}{5} \cdot 5}{5}$

Step 3.7.3

Rewrite the expression.

$\frac{1215 - 243 - 972}{5}$

Step 4

Simplify the expression.

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Step 4.1

Subtract $243$ from $1215$ .

$\frac{972 - 972}{5}$

Step 4.2

Subtract $972$ from $972$ .

$\frac{0}{5}$

Step 4.3

Divide $0$ by $5$ .

$0$