Basic Math Examples

$i = \frac{q}{t}$

Step 1

Rewrite the equation as $\frac{q}{t} = i$ .

$\frac{q}{t} = i$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$t, 1$

Step 2.2

The LCM of one and any expression is the expression.

$t$

Step 3

Multiply each term in $\frac{q}{t} = i$ by $t$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{q}{t} = i$ by $t$ .

$\frac{q}{t} t = i t$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $t$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{q}{t} t = i t$

Step 3.2.1.2

Rewrite the expression.

$q = i t$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $i t = q$ .

$i t = q$

Step 4.2

Divide each term in $i t = q$ by $i$ and simplify.

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Step 4.2.1

Divide each term in $i t = q$ by $i$ .

$\frac{i t}{i} = \frac{q}{i}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $i$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{i t}{i} = \frac{q}{i}$

Step 4.2.2.1.2

Divide $t$ by $1$ .

$t = \frac{q}{i}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Multiply the numerator and denominator of $\frac{q}{i}$ by the conjugate of $i$ to make the denominator real.

$t = \frac{q}{i} \cdot \frac{i}{i}$

Step 4.2.3.2

Multiply.

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Step 4.2.3.2.1

Combine.

$t = \frac{q i}{i i}$

Step 4.2.3.2.2

Simplify the denominator.

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Step 4.2.3.2.2.1

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

$t = \frac{q i}{i^{1} i}$

Step 4.2.3.2.2.2

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

$t = \frac{q i}{i^{1} i^{1}}$

Step 4.2.3.2.2.3

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

$t = \frac{q i}{i^{1 + 1}}$

Step 4.2.3.2.2.4

Add $1$ and $1$ .

$t = \frac{q i}{i^{2}}$

Step 4.2.3.2.2.5

Rewrite $i^{2}$ as $- 1$ .

$t = \frac{q i}{- 1}$

Step 4.2.3.3

Move the negative one from the denominator of $\frac{q i}{- 1}$ .

$t = - 1 \cdot (q i)$

Step 4.2.3.4

Rewrite $- 1 \cdot (q i)$ as $- (q i)$ .

$t = - q i$