Pre-Algebra Examples

$\frac{16 x m n^{2} + 10 x m^{2} \cdot (20 x^{2} m n)}{4 x m^{2} n}$

Step 1

Simplify the numerator.

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Step 1.1

Factor $2 x m n$ out of $16 x m n^{2} + 10 x m^{2} \cdot (20 x^{2} m n)$ .

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Step 1.1.1

Factor $2 x m n$ out of $16 x m n^{2}$ .

$\frac{2 x m n (8 n) + 10 x m^{2} \cdot (20 x^{2} m n)}{4 x m^{2} n}$

Step 1.1.2

Factor $2 x m n$ out of $10 x m^{2} \cdot (20 x^{2} m n)$ .

$\frac{2 x m n (8 n) + 2 x m n (5 m \cdot (20 x^{2} m))}{4 x m^{2} n}$

Step 1.1.3

Factor $2 x m n$ out of $2 x m n (8 n) + 2 x m n (5 m \cdot (20 x^{2} m))$ .

$\frac{2 x m n (8 n + 5 m \cdot (20 x^{2} m))}{4 x m^{2} n}$

Step 1.2

Combine exponents.

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Step 1.2.1

Multiply $20$ by $5$ .

$\frac{2 x m n (8 n + 100 m \cdot (x^{2} m))}{4 x m^{2} n}$

Step 1.2.2

Raise $m$ to the power of $1$ .

$\frac{2 x m n (8 n + 100 (m^{1} m) \cdot x^{2})}{4 x m^{2} n}$

Step 1.2.3

Raise $m$ to the power of $1$ .

$\frac{2 x m n (8 n + 100 (m^{1} m^{1}) \cdot x^{2})}{4 x m^{2} n}$

Step 1.2.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2 x m n (8 n + 100 m^{1 + 1} \cdot x^{2})}{4 x m^{2} n}$

Step 1.2.5

Add $1$ and $1$ .

$\frac{2 x m n (8 n + 100 m^{2} \cdot x^{2})}{4 x m^{2} n}$

Step 1.3

Factor $4$ out of $8 n + 100 m^{2} x^{2}$ .

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Step 1.3.1

Factor $4$ out of $8 n$ .

$\frac{2 x m n (4 (2 n) + 100 m^{2} x^{2})}{4 x m^{2} n}$

Step 1.3.2

Factor $4$ out of $100 m^{2} x^{2}$ .

$\frac{2 x m n (4 (2 n) + 4 (25 m^{2} x^{2}))}{4 x m^{2} n}$

Step 1.3.3

Factor $4$ out of $4 (2 n) + 4 (25 m^{2} x^{2})$ .

$\frac{2 x m n (4 (2 n + 25 m^{2} x^{2}))}{4 x m^{2} n}$

$\frac{2 x m n \cdot 4 (2 n + 25 m^{2} x^{2})}{4 x m^{2} n}$

Step 1.4

Multiply $4$ by $2$ .

$\frac{8 x m n (2 n + 25 m^{2} x^{2})}{4 x m^{2} n}$

Step 2

Cancel the common factor of $8$ and $4$ .

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Step 2.1

Factor $4$ out of $8 x m n (2 n + 25 m^{2} x^{2})$ .

$\frac{4 (2 x m n (2 n + 25 m^{2} x^{2}))}{4 x m^{2} n}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $4$ out of $4 x m^{2} n$ .

$\frac{4 (2 x m n (2 n + 25 m^{2} x^{2}))}{4 (x m^{2} n)}$

Step 2.2.2

Cancel the common factor.

$\frac{4 (2 x m n (2 n + 25 m^{2} x^{2}))}{4 (x m^{2} n)}$

Step 2.2.3

Rewrite the expression.

$\frac{2 x m n (2 n + 25 m^{2} x^{2})}{x m^{2} n}$

Step 3

Cancel the common factor of $x$ .

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Step 3.1

Cancel the common factor.

$\frac{2 x m n (2 n + 25 m^{2} x^{2})}{x m^{2} n}$

Step 3.2

Rewrite the expression.

$\frac{2 m n (2 n + 25 m^{2} x^{2})}{m^{2} n}$

Step 4

Cancel the common factor of $m$ and $m^{2}$ .

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Step 4.1

Factor $m$ out of $2 m n (2 n + 25 m^{2} x^{2})$ .

$\frac{m (2 n (2 n + 25 m^{2} x^{2}))}{m^{2} n}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $m$ out of $m^{2} n$ .

$\frac{m (2 n (2 n + 25 m^{2} x^{2}))}{m (m n)}$

Step 4.2.2

Cancel the common factor.

$\frac{m (2 n (2 n + 25 m^{2} x^{2}))}{m (m n)}$

Step 4.2.3

Rewrite the expression.

$\frac{2 n (2 n + 25 m^{2} x^{2})}{m n}$

Step 5

Cancel the common factor of $n$ .

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Step 5.1

Cancel the common factor.

$\frac{2 n (2 n + 25 m^{2} x^{2})}{m n}$

Step 5.2

Rewrite the expression.

$\frac{2 (2 n + 25 m^{2} x^{2})}{m}$

Step 6

Apply the distributive property.

$\frac{2 (2 n) + 2 (25 m^{2} x^{2})}{m}$

Step 7

Multiply $2$ by $2$ .

$\frac{4 n + 2 (25 m^{2} x^{2})}{m}$

Step 8

Multiply $25$ by $2$ .

$\frac{4 n + 50 m^{2} x^{2}}{m}$

Step 9

Split the fraction $\frac{4 n + 50 m^{2} x^{2}}{m}$ into two fractions.

$\frac{4 n}{m} + \frac{50 m^{2} x^{2}}{m}$

Step 10

Cancel the common factor of $m^{2}$ and $m$ .

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Step 10.1

Factor $m$ out of $50 m^{2} x^{2}$ .

$\frac{4 n}{m} + \frac{m (50 m x^{2})}{m}$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Raise $m$ to the power of $1$ .

$\frac{4 n}{m} + \frac{m (50 m x^{2})}{m^{1}}$

Step 10.2.2

Factor $m$ out of $m^{1}$ .

$\frac{4 n}{m} + \frac{m (50 m x^{2})}{m \cdot 1}$

Step 10.2.3

Cancel the common factor.

$\frac{4 n}{m} + \frac{m (50 m x^{2})}{m \cdot 1}$

Step 10.2.4

Rewrite the expression.

$\frac{4 n}{m} + \frac{50 m x^{2}}{1}$

Step 10.2.5

Divide $50 m x^{2}$ by $1$ .

$\frac{4 n}{m} + 50 m x^{2}$