Pre-Algebra Examples

$\frac{7 a^{2} b (a - 3 b)}{21 a b}$

Step 1

Cancel the common factor of $7$ and $21$ .

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Step 1.1

Factor $7$ out of $7 a^{2} b (a - 3 b)$ .

$\frac{7 (a^{2} b (a - 3 b))}{21 a b}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $7$ out of $21 a b$ .

$\frac{7 (a^{2} b (a - 3 b))}{7 (3 a b)}$

Step 1.2.2

Cancel the common factor.

$\frac{7 (a^{2} b (a - 3 b))}{7 (3 a b)}$

Step 1.2.3

Rewrite the expression.

$\frac{a^{2} b (a - 3 b)}{3 a b}$

$\frac{a^{2} b (a - 3 b)}{3 a b}$

$\frac{a^{2} b (a - 3 b)}{3 a b}$

Step 2

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

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Step 2.1

Factor $a$ out of $a^{2} b (a - 3 b)$ .

$\frac{a (a b (a - 3 b))}{3 a b}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $a$ out of $3 a b$ .

$\frac{a (a b (a - 3 b))}{a (3 b)}$

Step 2.2.2

Cancel the common factor.

$\frac{a (a b (a - 3 b))}{a (3 b)}$

Step 2.2.3

Rewrite the expression.

$\frac{a b (a - 3 b)}{3 b}$

$\frac{a b (a - 3 b)}{3 b}$

$\frac{a b (a - 3 b)}{3 b}$

Step 3

Cancel the common factor of $b$ .

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Step 3.1

Cancel the common factor.

$\frac{a b (a - 3 b)}{3 b}$

Step 3.2

Rewrite the expression.

$\frac{a (a - 3 b)}{3}$

$\frac{a (a - 3 b)}{3}$

Step 4

Apply the distributive property.

$\frac{a \cdot a + a (- 3 b)}{3}$

Step 5

Multiply $a$ by $a$ .

$\frac{a^{2} + a (- 3 b)}{3}$

Step 6

Rewrite using the commutative property of multiplication.

$\frac{a^{2} - 3 a b}{3}$

Step 7

Split the fraction $\frac{a^{2} - 3 a b}{3}$ into two fractions.

$\frac{a^{2}}{3} + \frac{- 3 a b}{3}$

Step 8

Cancel the common factor of $- 3$ and $3$ .

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Step 8.1

Factor $3$ out of $- 3 a b$ .

$\frac{a^{2}}{3} + \frac{3 (- a b)}{3}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $3$ out of $3$ .

$\frac{a^{2}}{3} + \frac{3 (- a b)}{3 (1)}$

Step 8.2.2

Cancel the common factor.

$\frac{a^{2}}{3} + \frac{3 (- a b)}{3 \cdot 1}$

Step 8.2.3

Rewrite the expression.

$\frac{a^{2}}{3} + \frac{- a b}{1}$

Step 8.2.4

Divide $- a b$ by $1$ .

$\frac{a^{2}}{3} - a b$

$\frac{a^{2}}{3} - a b$

$\frac{a^{2}}{3} - a b$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$