Basic Math Examples

$\frac{y^{2}}{12 b k^{3}} + \frac{3 b^{3} w}{4 a^{2} k^{2}}$

Step 1

To write $\frac{y^{2}}{12 b k^{3}}$ as a fraction with a common denominator, multiply by $\frac{a^{2}}{a^{2}}$ .

$\frac{y^{2}}{12 b k^{3}} \cdot \frac{a^{2}}{a^{2}} + \frac{3 b^{3} w}{4 a^{2} k^{2}}$

Step 2

To write $\frac{3 b^{3} w}{4 a^{2} k^{2}}$ as a fraction with a common denominator, multiply by $\frac{3 b k}{3 b k}$ .

$\frac{y^{2}}{12 b k^{3}} \cdot \frac{a^{2}}{a^{2}} + \frac{3 b^{3} w}{4 a^{2} k^{2}} \cdot \frac{3 b k}{3 b k}$

Step 3

Write each expression with a common denominator of $12 b k^{3} a^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{y^{2}}{12 b k^{3}}$ by $\frac{a^{2}}{a^{2}}$ .

$\frac{y^{2} a^{2}}{12 b k^{3} a^{2}} + \frac{3 b^{3} w}{4 a^{2} k^{2}} \cdot \frac{3 b k}{3 b k}$

Step 3.2

Multiply $\frac{3 b^{3} w}{4 a^{2} k^{2}}$ by $\frac{3 b k}{3 b k}$ .

$\frac{y^{2} a^{2}}{12 b k^{3} a^{2}} + \frac{3 b^{3} w (3 b k)}{4 a^{2} k^{2} (3 b k)}$

Step 3.3

Multiply $3$ by $4$ .

$\frac{y^{2} a^{2}}{12 b k^{3} a^{2}} + \frac{3 b^{3} w (3 b k)}{12 a^{2} k^{2} (b k)}$

Step 3.4

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

$\frac{y^{2} a^{2}}{12 b k^{3} a^{2}} + \frac{3 b^{3} w (3 b k)}{12 a^{2} (b (k^{2} k^{1}))}$

Step 3.5

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

$\frac{y^{2} a^{2}}{12 b k^{3} a^{2}} + \frac{3 b^{3} w (3 b k)}{12 a^{2} (b k^{2 + 1})}$

Step 3.6

Add $2$ and $1$ .

$\frac{y^{2} a^{2}}{12 b k^{3} a^{2}} + \frac{3 b^{3} w (3 b k)}{12 a^{2} (b k^{3})}$

Step 3.7

Reorder the factors of $12 b k^{3} a^{2}$ .

$\frac{y^{2} a^{2}}{12 k^{3} a^{2} b} + \frac{3 b^{3} w (3 b k)}{12 a^{2} (b k^{3})}$

Step 3.8

Reorder the factors of $12 a^{2} (b k^{3})$ .

$\frac{y^{2} a^{2}}{12 k^{3} a^{2} b} + \frac{3 b^{3} w (3 b k)}{12 k^{3} a^{2} b}$

Step 4

Combine the numerators over the common denominator.

$\frac{y^{2} a^{2} + 3 b^{3} w (3 b k)}{12 k^{3} a^{2} b}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $b^{3}$ by $b$ by adding the exponents.

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Step 5.1.1

Move $b$ .

$\frac{y^{2} a^{2} + 3 (b \cdot b^{3}) w (3 k)}{12 k^{3} a^{2} b}$

Step 5.1.2

Multiply $b$ by $b^{3}$ .

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Step 5.1.2.1

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

$\frac{y^{2} a^{2} + 3 (b^{1} b^{3}) w (3 k)}{12 k^{3} a^{2} b}$

Step 5.1.2.2

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

$\frac{y^{2} a^{2} + 3 b^{1 + 3} w (3 k)}{12 k^{3} a^{2} b}$

Step 5.1.3

Add $1$ and $3$ .

$\frac{y^{2} a^{2} + 3 b^{4} w (3 k)}{12 k^{3} a^{2} b}$

Step 5.2

Multiply $3$ by $3$ .

$\frac{y^{2} a^{2} + 9 b^{4} w k}{12 k^{3} a^{2} b}$