Basic Math Examples

$\frac{5 w}{3 b c^{2}} + \frac{b^{3} y^{3}}{6 c^{3} d^{2}}$

Step 1

To write $\frac{5 w}{3 b c^{2}}$ as a fraction with a common denominator, multiply by $\frac{2 c d^{2}}{2 c d^{2}}$ .

$\frac{5 w}{3 b c^{2}} \cdot \frac{2 c d^{2}}{2 c d^{2}} + \frac{b^{3} y^{3}}{6 c^{3} d^{2}}$

Step 2

To write $\frac{b^{3} y^{3}}{6 c^{3} d^{2}}$ as a fraction with a common denominator, multiply by $\frac{b}{b}$ .

$\frac{5 w}{3 b c^{2}} \cdot \frac{2 c d^{2}}{2 c d^{2}} + \frac{b^{3} y^{3}}{6 c^{3} d^{2}} \cdot \frac{b}{b}$

Step 3

Write each expression with a common denominator of $6 b c^{3} d^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{5 w}{3 b c^{2}}$ by $\frac{2 c d^{2}}{2 c d^{2}}$ .

$\frac{5 w (2 c d^{2})}{3 b c^{2} (2 c d^{2})} + \frac{b^{3} y^{3}}{6 c^{3} d^{2}} \cdot \frac{b}{b}$

Step 3.2

Multiply $2$ by $3$ .

$\frac{5 w (2 c d^{2})}{6 b c^{2} (c d^{2})} + \frac{b^{3} y^{3}}{6 c^{3} d^{2}} \cdot \frac{b}{b}$

Step 3.3

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

$\frac{5 w (2 c d^{2})}{6 b (c^{1} c^{2}) d^{2}} + \frac{b^{3} y^{3}}{6 c^{3} d^{2}} \cdot \frac{b}{b}$

Step 3.4

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

$\frac{5 w (2 c d^{2})}{6 b c^{1 + 2} d^{2}} + \frac{b^{3} y^{3}}{6 c^{3} d^{2}} \cdot \frac{b}{b}$

Step 3.5

Add $1$ and $2$ .

$\frac{5 w (2 c d^{2})}{6 b c^{3} d^{2}} + \frac{b^{3} y^{3}}{6 c^{3} d^{2}} \cdot \frac{b}{b}$

Step 3.6

Multiply $\frac{b^{3} y^{3}}{6 c^{3} d^{2}}$ by $\frac{b}{b}$ .

$\frac{5 w (2 c d^{2})}{6 b c^{3} d^{2}} + \frac{b^{3} y^{3} b}{6 c^{3} d^{2} b}$

Step 3.7

Reorder the factors of $6 b c^{3} d^{2}$ .

$\frac{5 w (2 c d^{2})}{6 c^{3} d^{2} b} + \frac{b^{3} y^{3} b}{6 c^{3} d^{2} b}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 w (2 c d^{2}) + b^{3} y^{3} b}{6 c^{3} d^{2} b}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $2$ by $5$ .

$\frac{10 w c d^{2} + b^{3} y^{3} b}{6 c^{3} d^{2} b}$

Step 5.2

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

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Step 5.2.1

Move $b$ .

$\frac{10 w c d^{2} + b \cdot b^{3} y^{3}}{6 c^{3} d^{2} b}$

Step 5.2.2

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

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Step 5.2.2.1

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

$\frac{10 w c d^{2} + b^{1} b^{3} y^{3}}{6 c^{3} d^{2} b}$

Step 5.2.2.2

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

$\frac{10 w c d^{2} + b^{1 + 3} y^{3}}{6 c^{3} d^{2} b}$

Step 5.2.3

Add $1$ and $3$ .

$\frac{10 w c d^{2} + b^{4} y^{3}}{6 c^{3} d^{2} b}$