Basic Math Examples

$\frac{10^{2} - 3 (5 (\frac{2 + 2 \cdot 4}{6 - \frac{3}{3}} \cdot 4 + 2))}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 1

Cancel the common factor of $3$ .

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Step 1.1

Cancel the common factor.

$\frac{10^{2} - 3 (5 (\frac{2 + 2 \cdot 4}{6 - \frac{3}{3}} \cdot 4 + 2))}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 1.2

Rewrite the expression.

$\frac{10^{2} - 3 (5 (\frac{2 + 2 \cdot 4}{6 - 1 \cdot 1} \cdot 4 + 2))}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 2

Simplify the numerator.

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Step 2.1

Multiply $2$ by $4$ .

$\frac{10^{2} - 3 \cdot 5 (\frac{2 + 8}{6 - 1 \cdot 1} \cdot 4 + 2)}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 2.2

Add $2$ and $8$ .

$\frac{10^{2} - 3 \cdot 5 (\frac{10}{6 - 1 \cdot 1} \cdot 4 + 2)}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 3

Simplify the denominator.

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Step 3.1

Multiply $- 1$ by $1$ .

$\frac{10^{2} - 3 \cdot 5 (\frac{10}{6 - 1} \cdot 4 + 2)}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 3.2

Subtract $1$ from $6$ .

$\frac{10^{2} - 3 \cdot 5 (\frac{10}{5} \cdot 4 + 2)}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 4

Simplify the numerator.

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Step 4.1

Raise $10$ to the power of $2$ .

$\frac{100 - 3 \cdot 5 (\frac{10}{5} \cdot 4 + 2)}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 4.2

Multiply $- 3$ by $5$ .

$\frac{100 - 15 (\frac{10}{5} \cdot 4 + 2)}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 4.3

Simplify each term.

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Step 4.3.1

Divide $10$ by $5$ .

$\frac{100 - 15 (2 \cdot 4 + 2)}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 4.3.2

Multiply $2$ by $4$ .

$\frac{100 - 15 (8 + 2)}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 4.4

Add $8$ and $2$ .

$\frac{100 - 15 \cdot 10}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 4.5

Multiply $- 15$ by $10$ .

$\frac{100 - 150}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 4.6

Subtract $150$ from $100$ .

$\frac{- 50}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 5

Simplify the denominator.

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Step 5.1

Add $3$ and $4$ .

$\frac{- 50}{{(7 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 5.2

Subtract $2$ from $7$ .

$\frac{- 50}{5^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 5.3

Raise $5$ to the power of $2$ .

$\frac{- 50}{25 - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 5.4

Raise $2$ to the power of $2$ .

$\frac{- 50}{25 - 1 \cdot 4 (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 5.5

Multiply $- 1$ by $4$ .

$\frac{- 50}{25 - 4 (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 5.6

Simplify each term.

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Step 5.6.1

Multiply $12$ by $2$ .

$\frac{- 50}{25 - 4 (24 - 4 \cdot 5) \cdot 1^{8}}$

Step 5.6.2

Multiply $- 4$ by $5$ .

$\frac{- 50}{25 - 4 (24 - 20) \cdot 1^{8}}$

Step 5.7

Subtract $20$ from $24$ .

$\frac{- 50}{25 - 4 \cdot 4 \cdot 1^{8}}$

Step 5.8

Multiply $- 4$ by $4$ .

$\frac{- 50}{25 - 16 \cdot 1^{8}}$

Step 5.9

One to any power is one.

$\frac{- 50}{25 - 16 \cdot 1}$

Step 5.10

Multiply $- 16$ by $1$ .

$\frac{- 50}{25 - 16}$

Step 5.11

Subtract $16$ from $25$ .

$\frac{- 50}{9}$

Step 6

Move the negative in front of the fraction.

$- \frac{50}{9}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{50}{9}$

Decimal Form:

$- 5.\overline{5}$

Mixed Number Form:

$- 5 \frac{5}{9}$