Algebra Examples

$3.14 \cdot 36$

Step 1

Multiply using long multiplication.

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Step 1.1

Multiply $6$ by $4$ . Place the ones digit $(4)$ in the result line and carry the tens digit $(2)$ . There is one result line for each digit in $36$ .

		$2$
	$3$	. $1$	$4$
$⨯$		$3$	$6$
			$4$

Step 1.2

Multiply $6$ by $1$ and add the carried $2$ . Place the result in the next column in the result line. There is one result line for each digit in $36$ .

		$2$
	$3$	. $1$	$4$
$⨯$		$3$	$6$
		$8$	$4$

Step 1.3

Multiply $6$ by $3$ . Place the ones digit $(8)$ in the result line and carry the tens digit $(1)$ . There is one result line for each digit in $36$ .


	$3$	. $1$	$4$
$⨯$		$3$	$6$
$1$	$8$	$8$	$4$

Step 1.4

Multiply $3$ by $4$ . Place the ones digit $(2)$ in the result line and carry the tens digit $(1)$ . There is one result line for each digit in $36$ .

		$1$
	$3$	. $1$	$4$
$⨯$		$3$	$6$
$1$	$8$	$8$	$4$
		$2$

Step 1.5

Multiply $3$ by $1$ and add the carried $1$ . Place the result in the next column in the result line. There is one result line for each digit in $36$ .

		$1$
	$3$	. $1$	$4$
$⨯$		$3$	$6$
$1$	$8$	$8$	$4$
	$4$	$2$

Step 1.6

Multiply $3$ by $3$ . Place the result in the next column in the result line. There is one result line for each digit in $36$ .


	$3$	. $1$	$4$
$⨯$		$3$	$6$
$1$	$8$	$8$	$4$
$9$	$4$	$2$

Step 1.7

Add the numbers in each column. In this case, add $4 + 0$ , then place the $4$ in the result line.


	$3$	. $1$	$4$
$⨯$		$3$	$6$
$1$	$8$	$8$	$4$
$9$	$4$	$2$
			$4$

Step 1.8

Add the numbers in each column. In this case, add $8 + 2$ , then place the $0$ in the result line and carry the $1$ .


	$3$	. $1$	$4$
$⨯$		$3$	$6$
$1$	$8$	$8$	$4$
$9$	$4$	$2$
		$0$	$4$

Step 1.9

Add the numbers in each column. In this case, add $8 + 4 + 1$ , then place the $3$ in the result line and carry the $1$ .


	$3$	. $1$	$4$
$⨯$		$3$	$6$
$1$	$8$	$8$	$4$
$9$	$4$	$2$
	$3$	$0$	$4$

Step 1.10

Add the numbers in each column. In this case, add $1 + 9 + 1$ , then place the $1$ in the result line and carry the $1$ .


		$3$	. $1$	$4$
	$⨯$		$3$	$6$
	$1$	$8$	$8$	$4$
	$9$	$4$	$2$
$1$	$1$	$3$	$0$	$4$


		$3$	. $1$	$4$
	$⨯$		$3$	$6$
	$1$	$8$	$8$	$4$
	$9$	$4$	$2$
$1$	$1$	$3$	$0$	$4$

Step 2

To find the number of decimal places needed in the answer, add the number of decimal places in the multiplier and multiplicand. In this case, there is a total of $2$ , so the answer must have $2$ decimal places as well.

$113.04$