Divide Using Long Polynomial Division (32a3/7)÷(40a2/5)

$(32 a \frac{3}{7}) \div (40 a \frac{2}{5})$

Step 1

Combine $32 a$ and $\frac{3}{7}$ .

$\frac{\frac{32 a \cdot 3}{7}}{40 a (\frac{2}{5})}$

Step 2

Combine $40 a$ and $\frac{2}{5}$ .

$\frac{\frac{32 a \cdot 3}{7}}{\frac{40 a \cdot 2}{5}}$

Step 3

Turn the denominator into a polynomial.

Start expanding.

$40 a (\frac{2}{5})$

Combine $40 a$ and $\frac{2}{5}$ .

$\frac{40 a \cdot 2}{5}$

Multiply $2$ by $40$ .

$\frac{80 a}{5}$

Step 4

Turn the numerator into a polynomial.

Start expanding.

$32 a (\frac{3}{7})$

Combine $32 a$ and $\frac{3}{7}$ .

$\frac{32 a \cdot 3}{7}$

Multiply $3$ by $32$ .

$\frac{96 a}{7}$

Step 5

Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of $0$ .

$\frac{80 a}{5}$

$0$

$\frac{96 a}{7}$

$0$

Step 6

Divide the highest order term in the dividend $\frac{96 a}{7}$ by the highest order term in divisor $\frac{80 a}{5}$ .

					$\frac{6}{7}$
	$\frac{80 a}{5}$	+	$0$		$\frac{96 a}{7}$	+	$0$

Step 7

Multiply the new quotient term by the divisor.

Step 8

The expression needs to be subtracted from the dividend, so change all the signs in $\frac{96 a}{7} + 0$

Step 9

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

Step 10

Since the remander is $0$ , the final answer is the quotient.

$\frac{6}{7}$