Pre-Algebra Examples

$a \div \frac{b}{2} = 2 \cdot a \div b$

Step 1

Multiply both sides by $\frac{b}{2}$ .

$a \div \frac{b}{2} \cdot \frac{b}{2} = 2 \cdot a \div b \cdot \frac{b}{2}$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $a \div \frac{b}{2} \cdot \frac{b}{2}$ .

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Step 2.1.1.1

To divide by a fraction, multiply by its reciprocal.

$a \frac{2}{b} \frac{b}{2} = 2 \cdot a \div b \cdot \frac{b}{2}$

Step 2.1.1.2

Combine $a$ and $\frac{2}{b}$ .

$\frac{a \cdot 2}{b} \cdot \frac{b}{2} = 2 \cdot a \div b \cdot \frac{b}{2}$

Step 2.1.1.3

Cancel the common factor of $2$ .

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Step 2.1.1.3.1

Factor $2$ out of $a \cdot 2$ .

$\frac{2 \cdot a}{b} \cdot \frac{b}{2} = 2 \cdot a \div b \cdot \frac{b}{2}$

Step 2.1.1.3.2

Cancel the common factor.

$\frac{2 \cdot a}{b} \cdot \frac{b}{2} = 2 \cdot a \div b \cdot \frac{b}{2}$

Step 2.1.1.3.3

Rewrite the expression.

$\frac{a}{b} b = 2 \cdot a \div b \cdot \frac{b}{2}$

Step 2.1.1.4

Cancel the common factor of $b$ .

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Step 2.1.1.4.1

Cancel the common factor.

$\frac{a}{b} b = 2 \cdot a \div b \cdot \frac{b}{2}$

Step 2.1.1.4.2

Rewrite the expression.

$a = 2 \cdot a \div b \cdot \frac{b}{2}$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $2 \cdot a \div b \cdot \frac{b}{2}$ .

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Step 2.2.1.1

Rewrite the division as a fraction.

$a = \frac{2 \cdot a}{b} \cdot \frac{b}{2}$

Step 2.2.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.2.1

Factor $2$ out of $2 \cdot a$ .

$a = \frac{2 (a)}{b} \cdot \frac{b}{2}$

Step 2.2.1.2.2

Cancel the common factor.

$a = \frac{2 a}{b} \cdot \frac{b}{2}$

Step 2.2.1.2.3

Rewrite the expression.

$a = \frac{a}{b} b$

Step 2.2.1.3

Cancel the common factor of $b$ .

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Step 2.2.1.3.1

Cancel the common factor.

$a = \frac{a}{b} b$

Step 2.2.1.3.2

Rewrite the expression.

$a = a$

Step 3

Solve for $a$ .

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Step 3.1

Move all terms containing $a$ to the left side of the equation.

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Step 3.1.1

Subtract $a$ from both sides of the equation.

$a - a = 0$

Step 3.1.2

Subtract $a$ from $a$ .

$0 = 0$

Step 3.2

Since $0 = 0$ , the equation will always be true.

Always true

Step 4

The result can be shown in multiple forms.

Always true

Interval Notation:

$(- \infty, \infty)$