Basic Math Examples

$3 \cdot (12 y i) = 27 + 36 i$

Step 1

Simplify.

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Step 1.1

Multiply $12$ by $3$ .

$36 \cdot (y i) = 27 + 36 i$

Step 1.2

Remove parentheses.

$36 \cdot y i = 27 + 36 i$

Step 2

Divide each term in $36 \cdot (y i) = 27 + 36 i$ by $36 i$ and simplify.

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Step 2.1

Divide each term in $36 \cdot (y i) = 27 + 36 i$ by $36 i$ .

$\frac{36 \cdot (y i)}{36 i} = \frac{27}{36 i} + \frac{36 i}{36 i}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $36$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{36 \cdot (y i)}{36 i} = \frac{27}{36 i} + \frac{36 i}{36 i}$

Step 2.2.1.2

Rewrite the expression.

$\frac{y i}{i} = \frac{27}{36 i} + \frac{36 i}{36 i}$

Step 2.2.2

Cancel the common factor of $i$ .

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Step 2.2.2.1

Cancel the common factor.

$\frac{y i}{i} = \frac{27}{36 i} + \frac{36 i}{36 i}$

Step 2.2.2.2

Divide $y$ by $1$ .

$y = \frac{27}{36 i} + \frac{36 i}{36 i}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Cancel the common factor of $27$ and $36$ .

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Step 2.3.1.1.1

Factor $9$ out of $27$ .

$y = \frac{9 (3)}{36 i} + \frac{36 i}{36 i}$

Step 2.3.1.1.2

Cancel the common factors.

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Step 2.3.1.1.2.1

Factor $9$ out of $36 i$ .

$y = \frac{9 (3)}{9 (4 i)} + \frac{36 i}{36 i}$

Step 2.3.1.1.2.2

Cancel the common factor.

$y = \frac{9 \cdot 3}{9 (4 i)} + \frac{36 i}{36 i}$

Step 2.3.1.1.2.3

Rewrite the expression.

$y = \frac{3}{4 i} + \frac{36 i}{36 i}$

Step 2.3.1.2

Multiply the numerator and denominator of $\frac{3}{4 i}$ by the conjugate of $4 i$ to make the denominator real.

$y = \frac{3}{4 i} \cdot \frac{i}{i} + \frac{36 i}{36 i}$

Step 2.3.1.3

Multiply.

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Step 2.3.1.3.1

Combine.

$y = \frac{3 i}{4 i i} + \frac{36 i}{36 i}$

Step 2.3.1.3.2

Simplify the denominator.

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Step 2.3.1.3.2.1

Add parentheses.

$y = \frac{3 i}{4 (i i)} + \frac{36 i}{36 i}$

Step 2.3.1.3.2.2

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

$y = \frac{3 i}{4 (i^{1} i)} + \frac{36 i}{36 i}$

Step 2.3.1.3.2.3

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

$y = \frac{3 i}{4 (i^{1} i^{1})} + \frac{36 i}{36 i}$

Step 2.3.1.3.2.4

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

$y = \frac{3 i}{4 i^{1 + 1}} + \frac{36 i}{36 i}$

Step 2.3.1.3.2.5

Add $1$ and $1$ .

$y = \frac{3 i}{4 i^{2}} + \frac{36 i}{36 i}$

Step 2.3.1.3.2.6

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

$y = \frac{3 i}{4 \cdot - 1} + \frac{36 i}{36 i}$

Step 2.3.1.4

Multiply $4$ by $- 1$ .

$y = \frac{3 i}{- 4} + \frac{36 i}{36 i}$

Step 2.3.1.5

Move the negative in front of the fraction.

$y = - \frac{3 i}{4} + \frac{36 i}{36 i}$

Step 2.3.1.6

Cancel the common factor of $36$ .

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Step 2.3.1.6.1

Cancel the common factor.

$y = - \frac{3 i}{4} + \frac{36 i}{36 i}$

Step 2.3.1.6.2

Rewrite the expression.

$y = - \frac{3 i}{4} + \frac{i}{i}$

Step 2.3.1.7

Cancel the common factor of $i$ .

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Step 2.3.1.7.1

Cancel the common factor.

$y = - \frac{3 i}{4} + \frac{i}{i}$

Step 2.3.1.7.2

Rewrite the expression.

$y = - \frac{3 i}{4} + 1$

Step 2.3.2

Reorder $- \frac{3 i}{4}$ and $1$ .

$y = 1 - \frac{3 i}{4}$