Basic Math Examples

$a \div b = b \div a$

Step 1

Simplify both sides.

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Step 1.1

Rewrite the division as a fraction.

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

Step 1.2

Rewrite the division as a fraction.

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

Step 2

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$a \cdot a = b \cdot b$

Step 3

Solve the equation for $b$ .

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Step 3.1

Rewrite the equation as $b \cdot b = a \cdot a$ .

$b \cdot b = a \cdot a$

Step 3.2

Multiply $b$ by $b$ .

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

Step 3.3

Multiply $a$ by $a$ .

$b^{2} = a^{2}$

Step 3.4

Since the exponents are equal, the bases of the exponents on both sides of the equation must be equal.

$| b | = | a |$

Step 3.5

Solve for $b$ .

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Step 3.5.1

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$b = \pm | a |$

Step 3.5.2

The complete solution is the result of both the positive and negative portions of the solution.

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Step 3.5.2.1

First, use the positive value of the $\pm$ to find the first solution.

$b = | a |$

Step 3.5.2.2

Next, use the negative value of the $\pm$ to find the second solution.

$b = - | a |$

Step 3.5.2.3

The complete solution is the result of both the positive and negative portions of the solution.

$b = | a |$

$b = - | a |$

$b = | a |$

$b = - | a |$

$b = | a |$

$b = - | a |$

$b = | a |$

$b = - | a |$