Basic Math Examples

$\frac{10 (5 - 1)}{2 (5) + 10}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Cancel the common factor of $10$ and $2 (5) + 10$ .

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Step 1.1.1

Factor $- 1$ out of $2 (5)$ .

$\frac{10 (5 - 1)}{- (- 2 \cdot 5) + 10}$

Step 1.1.2

Rewrite $10$ as $- 1 (- 10)$ .

$\frac{10 (5 - 1)}{- (- 2 \cdot 5) - 1 (- 10)}$

Step 1.1.3

Factor $- 1$ out of $- (- 2 \cdot 5) - 1 (- 10)$ .

$\frac{10 (5 - 1)}{- (- 2 \cdot 5 - 10)}$

Step 1.1.4

Rewrite $- (- 2 \cdot 5 - 10)$ as $- 1 (- 2 \cdot 5 - 10)$ .

$\frac{10 (5 - 1)}{- 1 (- 2 \cdot 5 - 10)}$

Step 1.1.5

Reorder terms.

$\frac{10 (5 - 1)}{- 1 (- 10 - 2 \cdot 5)}$

Step 1.1.6

Factor $2$ out of $10 (5 - 1)$ .

$\frac{2 (5 (5 - 1))}{- 1 (- 10 - 2 \cdot 5)}$

Step 1.1.7

Cancel the common factors.

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Step 1.1.7.1

Factor $2$ out of $- 1 (- 10 - 2 \cdot 5)$ .

$\frac{2 (5 (5 - 1))}{2 (- 1 (- 5 - 1 \cdot 5))}$

Step 1.1.7.2

Cancel the common factor.

$\frac{2 (5 (5 - 1))}{2 (- 1 (- 5 - 1 \cdot 5))}$

Step 1.1.7.3

Rewrite the expression.

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

Step 1.2

Cancel the common factor of $5$ and $- 5 - 1 \cdot 5$ .

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Step 1.2.1

Rewrite $- 5$ as $- 1 (5)$ .

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

Step 1.2.2

Factor $- 1$ out of $- 1 \cdot 5$ .

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

Step 1.2.3

Factor $- 1$ out of $- 1 (5) - 1 (5)$ .

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

Step 1.2.4

Cancel the common factors.

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Step 1.2.4.1

Factor $5$ out of $- 1 (- 1 (5 + 5))$ .

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

Step 1.2.4.2

Cancel the common factor.

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

Step 1.2.4.3

Rewrite the expression.

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

Step 1.3

Subtract $1$ from $5$ .

$\frac{4}{- 1 (- 1 (1 + 1))}$

Step 2

Simplify the denominator.

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Step 2.1

Multiply $- 1$ by $- 1$ .

$\frac{4}{1 (1 + 1)}$

Step 2.2

Multiply $1 + 1$ by $1$ .

$\frac{4}{1 + 1}$

Step 3

Simplify the expression.

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Step 3.1

Add $1$ and $1$ .

$\frac{4}{2}$

Step 3.2

Divide $4$ by $2$ .

$2$