Basic Math Examples

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

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

Step 1

To write

\frac{c y^{3}}{12 d^{3} k^{3}}

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

\frac{3 c}{3 c}

$\frac{3 c}{3 c}$ .

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

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

Step 2

To write

- \frac{4 w}{9 c d^{2}}

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

\frac{4 d k^{3}}{4 d k^{3}}

$\frac{4 d k^{3}}{4 d k^{3}}$ .

\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}}

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

Step 3

Write each expression with a common denominator of

36 c d^{3} k^{3}

$36 c d^{3} k^{3}$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{c y^{3}}{12 d^{3} k^{3}}

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

\frac{3 c}{3 c}

$\frac{3 c}{3 c}$ .

\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}}

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

Step 3.2

Multiply

3

$3$ by

12

$12$ .

\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}}

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

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

$- 4$ .

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