Basic Math Examples

$\frac{3}{5 w^{3} y^{2}} - \frac{7}{2 w^{2} y}$

Step 1

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

$\frac{3}{5 w^{3} y^{2}} \cdot \frac{2}{2} - \frac{7}{2 w^{2} y}$

Step 2

To write $- \frac{7}{2 w^{2} y}$ as a fraction with a common denominator, multiply by $\frac{5 w y}{5 w y}$ .

$\frac{3}{5 w^{3} y^{2}} \cdot \frac{2}{2} - \frac{7}{2 w^{2} y} \cdot \frac{5 w y}{5 w y}$

Step 3

Write each expression with a common denominator of $10 w^{3} y^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{3}{5 w^{3} y^{2}}$ by $\frac{2}{2}$ .

$\frac{3 \cdot 2}{5 w^{3} y^{2} \cdot 2} - \frac{7}{2 w^{2} y} \cdot \frac{5 w y}{5 w y}$

Step 3.2

Multiply $2$ by $5$ .

$\frac{3 \cdot 2}{10 w^{3} y^{2}} - \frac{7}{2 w^{2} y} \cdot \frac{5 w y}{5 w y}$

Step 3.3

Multiply $\frac{7}{2 w^{2} y}$ by $\frac{5 w y}{5 w y}$ .

$\frac{3 \cdot 2}{10 w^{3} y^{2}} - \frac{7 (5 w y)}{2 w^{2} y (5 w y)}$

Step 3.4

Multiply $5$ by $2$ .

$\frac{3 \cdot 2}{10 w^{3} y^{2}} - \frac{7 (5 w y)}{10 w^{2} y (w y)}$

Step 3.5

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

$\frac{3 \cdot 2}{10 w^{3} y^{2}} - \frac{7 (5 w y)}{10 (w^{1} w^{2}) y \cdot y}$

Step 3.6

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

$\frac{3 \cdot 2}{10 w^{3} y^{2}} - \frac{7 (5 w y)}{10 w^{1 + 2} y \cdot y}$

Step 3.7

Add $1$ and $2$ .

$\frac{3 \cdot 2}{10 w^{3} y^{2}} - \frac{7 (5 w y)}{10 w^{3} y \cdot y}$

Step 3.8

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

$\frac{3 \cdot 2}{10 w^{3} y^{2}} - \frac{7 (5 w y)}{10 w^{3} (y^{1} y)}$

Step 3.9

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

$\frac{3 \cdot 2}{10 w^{3} y^{2}} - \frac{7 (5 w y)}{10 w^{3} (y^{1} y^{1})}$

Step 3.10

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

$\frac{3 \cdot 2}{10 w^{3} y^{2}} - \frac{7 (5 w y)}{10 w^{3} y^{1 + 1}}$

Step 3.11

Add $1$ and $1$ .

$\frac{3 \cdot 2}{10 w^{3} y^{2}} - \frac{7 (5 w y)}{10 w^{3} y^{2}}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 \cdot 2 - 7 (5 w y)}{10 w^{3} y^{2}}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $3$ by $2$ .

$\frac{6 - 7 \cdot 5 w y}{10 w^{3} y^{2}}$

Step 5.2

Multiply $- 7$ by $5$ .

$\frac{6 - 35 w y}{10 w^{3} y^{2}}$