Basic Math Examples

$\frac{5 w^{2}}{9 b d^{2}} - \frac{d^{3} y}{6 b^{2} k}$

Step 1

To write $\frac{5 w^{2}}{9 b d^{2}}$ as a fraction with a common denominator, multiply by $\frac{2 k b}{2 k b}$ .

$\frac{5 w^{2}}{9 b d^{2}} \cdot \frac{2 k b}{2 k b} - \frac{d^{3} y}{6 b^{2} k}$

Step 2

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

$\frac{5 w^{2}}{9 b d^{2}} \cdot \frac{2 k b}{2 k b} - \frac{d^{3} y}{6 b^{2} k} \cdot \frac{3 d^{2}}{3 d^{2}}$

Step 3

Write each expression with a common denominator of $18 k b^{2} d^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{5 w^{2}}{9 b d^{2}}$ by $\frac{2 k b}{2 k b}$ .

$\frac{5 w^{2} (2 k b)}{9 b d^{2} (2 k b)} - \frac{d^{3} y}{6 b^{2} k} \cdot \frac{3 d^{2}}{3 d^{2}}$

Step 3.2

Multiply $2$ by $9$ .

$\frac{5 w^{2} (2 k b)}{18 b d^{2} (k b)} - \frac{d^{3} y}{6 b^{2} k} \cdot \frac{3 d^{2}}{3 d^{2}}$

Step 3.3

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

$\frac{5 w^{2} (2 k b)}{18 (b^{1} b) d^{2} k} - \frac{d^{3} y}{6 b^{2} k} \cdot \frac{3 d^{2}}{3 d^{2}}$

Step 3.4

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

$\frac{5 w^{2} (2 k b)}{18 (b^{1} b^{1}) d^{2} k} - \frac{d^{3} y}{6 b^{2} k} \cdot \frac{3 d^{2}}{3 d^{2}}$

Step 3.5

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

$\frac{5 w^{2} (2 k b)}{18 b^{1 + 1} d^{2} k} - \frac{d^{3} y}{6 b^{2} k} \cdot \frac{3 d^{2}}{3 d^{2}}$

Step 3.6

Add $1$ and $1$ .

$\frac{5 w^{2} (2 k b)}{18 b^{2} d^{2} k} - \frac{d^{3} y}{6 b^{2} k} \cdot \frac{3 d^{2}}{3 d^{2}}$

Step 3.7

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

$\frac{5 w^{2} (2 k b)}{18 b^{2} d^{2} k} - \frac{d^{3} y (3 d^{2})}{6 b^{2} k (3 d^{2})}$

Step 3.8

Multiply $3$ by $6$ .

$\frac{5 w^{2} (2 k b)}{18 b^{2} d^{2} k} - \frac{d^{3} y (3 d^{2})}{18 b^{2} k d^{2}}$

Step 3.9

Reorder the factors of $18 b^{2} k d^{2}$ .

$\frac{5 w^{2} (2 k b)}{18 b^{2} d^{2} k} - \frac{d^{3} y (3 d^{2})}{18 b^{2} d^{2} k}$

Step 4

Combine the numerators over the common denominator.

$\frac{5 w^{2} (2 k b) - d^{3} y (3 d^{2})}{18 b^{2} d^{2} k}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $2$ by $5$ .

$\frac{10 w^{2} k b - d^{3} y (3 d^{2})}{18 b^{2} d^{2} k}$

Step 5.2

Multiply $d^{3}$ by $d^{2}$ by adding the exponents.

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Step 5.2.1

Move $d^{2}$ .

$\frac{10 w^{2} k b - (d^{2} d^{3}) y \cdot 3}{18 b^{2} d^{2} k}$

Step 5.2.2

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

$\frac{10 w^{2} k b - d^{2 + 3} y \cdot 3}{18 b^{2} d^{2} k}$

Step 5.2.3

Add $2$ and $3$ .

$\frac{10 w^{2} k b - d^{5} y \cdot 3}{18 b^{2} d^{2} k}$

Step 5.3

Multiply $3$ by $- 1$ .

$\frac{10 w^{2} k b - 3 d^{5} y}{18 b^{2} d^{2} k}$