Simplify (20a)/b-(9b)/5

$\frac{20 a}{b} - \frac{9 b}{5}$

Step 1

To write $\frac{20 a}{b}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{20 a}{b} \cdot \frac{5}{5} - \frac{9 b}{5}$

Step 2

To write $- \frac{9 b}{5}$ as a fraction with a common denominator, multiply by $\frac{b}{b}$ .

$\frac{20 a}{b} \cdot \frac{5}{5} - \frac{9 b}{5} \cdot \frac{b}{b}$

Step 3

Write each expression with a common denominator of $b \cdot 5$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{20 a}{b}$ by $\frac{5}{5}$ .

$\frac{20 a \cdot 5}{b \cdot 5} - \frac{9 b}{5} \cdot \frac{b}{b}$

Multiply $\frac{9 b}{5}$ by $\frac{b}{b}$ .

$\frac{20 a \cdot 5}{b \cdot 5} - \frac{9 b \cdot b}{5 b}$

Reorder the factors of $b \cdot 5$ .

$\frac{20 a \cdot 5}{5 b} - \frac{9 b \cdot b}{5 b}$

Step 4

Combine the numerators over the common denominator.

$\frac{20 a \cdot 5 - 9 b \cdot b}{5 b}$

Step 5

Simplify the numerator.

Multiply $5$ by $20$ .

$\frac{100 a - 9 b \cdot b}{5 b}$

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

$\frac{100 a - 9 (b \cdot b)}{5 b}$

Multiply $b$ by $b$ .

$\frac{100 a - 9 b^{2}}{5 b}$