Basic Math Examples

$\frac{6}{9 y^{2}} - \frac{5}{27 y}$

Step 1

Cancel the common factor of $6$ and $9$ .

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Step 1.1

Factor $3$ out of $6$ .

$\frac{3 (2)}{9 y^{2}} - \frac{5}{27 y}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $3$ out of $9 y^{2}$ .

$\frac{3 (2)}{3 (3 y^{2})} - \frac{5}{27 y}$

Step 1.2.2

Cancel the common factor.

$\frac{3 \cdot 2}{3 (3 y^{2})} - \frac{5}{27 y}$

Step 1.2.3

Rewrite the expression.

$\frac{2}{3 y^{2}} - \frac{5}{27 y}$

Step 2

To write $\frac{2}{3 y^{2}}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{2}{3 y^{2}} \cdot \frac{9}{9} - \frac{5}{27 y}$

Step 3

To write $- \frac{5}{27 y}$ as a fraction with a common denominator, multiply by $\frac{y}{y}$ .

$\frac{2}{3 y^{2}} \cdot \frac{9}{9} - \frac{5}{27 y} \cdot \frac{y}{y}$

Step 4

Write each expression with a common denominator of $27 y^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{2}{3 y^{2}}$ by $\frac{9}{9}$ .

$\frac{2 \cdot 9}{3 y^{2} \cdot 9} - \frac{5}{27 y} \cdot \frac{y}{y}$

Step 4.2

Multiply $9$ by $3$ .

$\frac{2 \cdot 9}{27 y^{2}} - \frac{5}{27 y} \cdot \frac{y}{y}$

Step 4.3

Multiply $\frac{5}{27 y}$ by $\frac{y}{y}$ .

$\frac{2 \cdot 9}{27 y^{2}} - \frac{5 y}{27 y \cdot y}$

Step 4.4

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

$\frac{2 \cdot 9}{27 y^{2}} - \frac{5 y}{27 (y^{1} y)}$

Step 4.5

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

$\frac{2 \cdot 9}{27 y^{2}} - \frac{5 y}{27 (y^{1} y^{1})}$

Step 4.6

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

$\frac{2 \cdot 9}{27 y^{2}} - \frac{5 y}{27 y^{1 + 1}}$

Step 4.7

Add $1$ and $1$ .

$\frac{2 \cdot 9}{27 y^{2}} - \frac{5 y}{27 y^{2}}$

Step 5

Combine the numerators over the common denominator.

$\frac{2 \cdot 9 - 5 y}{27 y^{2}}$

Step 6

Multiply $2$ by $9$ .

$\frac{18 - 5 y}{27 y^{2}}$