Basic Math Examples

$\frac{c y^{3}}{12 d^{3} k^{3}} - \frac{4 w}{9 c d^{2}}$

Step 1

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

$\frac{c y^{3}}{12 d^{3} k^{3}} \cdot \frac{3 c}{3 c} - \frac{4 w}{9 c d^{2}}$

Step 2

To write $- \frac{4 w}{9 c d^{2}}$ as a fraction with a common denominator, multiply by $\frac{4 d k^{3}}{4 d k^{3}}$ .

$\frac{c y^{3}}{12 d^{3} k^{3}} \cdot \frac{3 c}{3 c} - \frac{4 w}{9 c d^{2}} \cdot \frac{4 d k^{3}}{4 d k^{3}}$

Step 3

Write each expression with a common denominator of $36 c d^{3} k^{3}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{c y^{3}}{12 d^{3} k^{3}}$ by $\frac{3 c}{3 c}$ .

$\frac{c y^{3} (3 c)}{12 d^{3} k^{3} (3 c)} - \frac{4 w}{9 c d^{2}} \cdot \frac{4 d k^{3}}{4 d k^{3}}$

Step 3.2

Multiply $3$ by $12$ .

$\frac{c y^{3} (3 c)}{36 d^{3} k^{3} c} - \frac{4 w}{9 c d^{2}} \cdot \frac{4 d k^{3}}{4 d k^{3}}$

Step 3.3

Multiply $\frac{4 w}{9 c d^{2}}$ by $\frac{4 d k^{3}}{4 d k^{3}}$ .

$\frac{c y^{3} (3 c)}{36 d^{3} k^{3} c} - \frac{4 w (4 d k^{3})}{9 c d^{2} (4 d k^{3})}$

Step 3.4

Multiply $4$ by $9$ .

$\frac{c y^{3} (3 c)}{36 d^{3} k^{3} c} - \frac{4 w (4 d k^{3})}{36 c d^{2} (d k^{3})}$

Step 3.5

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

$\frac{c y^{3} (3 c)}{36 d^{3} k^{3} c} - \frac{4 w (4 d k^{3})}{36 c (d^{1} d^{2}) k^{3}}$

Step 3.6

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

$\frac{c y^{3} (3 c)}{36 d^{3} k^{3} c} - \frac{4 w (4 d k^{3})}{36 c d^{1 + 2} k^{3}}$

Step 3.7

Add $1$ and $2$ .

$\frac{c y^{3} (3 c)}{36 d^{3} k^{3} c} - \frac{4 w (4 d k^{3})}{36 c d^{3} k^{3}}$

Step 3.8

Reorder the factors of $36 c d^{3} k^{3}$ .

$\frac{c y^{3} (3 c)}{36 d^{3} k^{3} c} - \frac{4 w (4 d k^{3})}{36 d^{3} k^{3} c}$

Step 4

Combine the numerators over the common denominator.

$\frac{c y^{3} (3 c) - 4 w (4 d k^{3})}{36 d^{3} k^{3} c}$

Step 5

Simplify the numerator.

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Step 5.1

Rewrite using the commutative property of multiplication.

$\frac{3 c y^{3} c - 4 w \cdot 4 d k^{3}}{36 d^{3} k^{3} c}$

Step 5.2

Multiply $c$ by $c$ by adding the exponents.

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Step 5.2.1

Move $c$ .

$\frac{3 (c \cdot c) y^{3} - 4 w \cdot 4 d k^{3}}{36 d^{3} k^{3} c}$

Step 5.2.2

Multiply $c$ by $c$ .

$\frac{3 c^{2} y^{3} - 4 w \cdot 4 d k^{3}}{36 d^{3} k^{3} c}$

Step 5.3

Multiply $4$ by $- 4$ .

$\frac{3 c^{2} y^{3} - 16 w d k^{3}}{36 d^{3} k^{3} c}$