Pre-Algebra Examples

$51.88 \cdot 665$

Step 1

Multiply $5$ by $8$ . Place the ones digit $(0)$ in the result line and carry the tens digit $(4)$ . There is one result line for each digit in $665$ .

			$4$
	$5$	$1$	. $8$	$8$
$⨯$		$6$	$6$	$5$
				$0$

Step 2

Multiply $5$ by $8$ and add the carried $4$ . Place the ones digit $(4)$ in the result line and carry the tens digit $(4)$ . There is one result line for each digit in the $665$ .

		$4$	$4$
	$5$	$1$	. $8$	$8$
$⨯$		$6$	$6$	$5$
			$4$	$0$

Step 3

Multiply $5$ by $1$ and add the carried $4$ . Place the result in the next column in the result line. There is one result line for each digit in $665$ .

		$4$	$4$
	$5$	$1$	. $8$	$8$
$⨯$		$6$	$6$	$5$
		$9$	$4$	$0$

Step 4

Multiply $5$ by $5$ . Place the ones digit $(5)$ in the result line and carry the tens digit $(2)$ . There is one result line for each digit in $665$ .


	$5$	$1$	. $8$	$8$
$⨯$		$6$	$6$	$5$
$2$	$5$	$9$	$4$	$0$

Step 5

Multiply $6$ by $8$ . Place the ones digit $(8)$ in the result line and carry the tens digit $(4)$ . There is one result line for each digit in $665$ .

			$4$
	$5$	$1$	. $8$	$8$
$⨯$		$6$	$6$	$5$
$2$	$5$	$9$	$4$	$0$
			$8$

Step 6

Multiply $6$ by $8$ and add the carried $4$ . Place the ones digit $(2)$ in the result line and carry the tens digit $(5)$ . There is one result line for each digit in the $665$ .

		$5$	$4$
	$5$	$1$	. $8$	$8$
$⨯$		$6$	$6$	$5$
$2$	$5$	$9$	$4$	$0$
		$2$	$8$

Step 7

Multiply $6$ by $1$ and add the carried $5$ . Place the ones digit $(1)$ in the result line and carry the tens digit $(1)$ . There is one result line for each digit in the $665$ .

	$1$	$5$	$4$
	$5$	$1$	. $8$	$8$
$⨯$		$6$	$6$	$5$
$2$	$5$	$9$	$4$	$0$
	$1$	$2$	$8$

Step 8

Multiply $6$ by $5$ and add the carried $1$ . Place the ones digit $(1)$ in the result line and carry the tens digit $(3)$ . There is one result line for each digit in the $665$ .


		$5$	$1$	. $8$	$8$
	$⨯$		$6$	$6$	$5$
	$2$	$5$	$9$	$4$	$0$
$3$	$1$	$1$	$2$	$8$

Step 9

Multiply $6$ by $8$ . Place the ones digit $(8)$ in the result line and carry the tens digit $(4)$ . There is one result line for each digit in $665$ .

				$4$
		$5$	$1$	. $8$	$8$
	$⨯$		$6$	$6$	$5$
	$2$	$5$	$9$	$4$	$0$
$3$	$1$	$1$	$2$	$8$
			$8$

Step 10

Multiply $6$ by $8$ and add the carried $4$ . Place the ones digit $(2)$ in the result line and carry the tens digit $(5)$ . There is one result line for each digit in the $665$ .

			$5$	$4$
		$5$	$1$	. $8$	$8$
	$⨯$		$6$	$6$	$5$
	$2$	$5$	$9$	$4$	$0$
$3$	$1$	$1$	$2$	$8$
		$2$	$8$

Step 11

Multiply $6$ by $1$ and add the carried $5$ . Place the ones digit $(1)$ in the result line and carry the tens digit $(1)$ . There is one result line for each digit in the $665$ .

		$1$	$5$	$4$
		$5$	$1$	. $8$	$8$
	$⨯$		$6$	$6$	$5$
	$2$	$5$	$9$	$4$	$0$
$3$	$1$	$1$	$2$	$8$
	$1$	$2$	$8$

Step 12

Multiply $6$ by $5$ and add the carried $1$ . Place the ones digit $(1)$ in the result line and carry the tens digit $(3)$ . There is one result line for each digit in the $665$ .


			$5$	$1$	. $8$	$8$
		$⨯$		$6$	$6$	$5$
		$2$	$5$	$9$	$4$	$0$
	$3$	$1$	$1$	$2$	$8$
$3$	$1$	$1$	$2$	$8$

Step 13

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


			$5$	$1$	. $8$	$8$
		$⨯$		$6$	$6$	$5$
		$2$	$5$	$9$	$4$	$0$
	$3$	$1$	$1$	$2$	$8$
$3$	$1$	$1$	$2$	$8$
						$0$

Step 14

Add the numbers in each column. In this case, add $4 + 8 + 0$ , then place the $2$ in the result line and carry the $1$ .


			$5$	$1$	. $8$	$8$
		$⨯$		$6$	$6$	$5$
		$2$	$5$	$9$	$4$	$0$
	$3$	$1$	$1$	$2$	$8$
$3$	$1$	$1$	$2$	$8$
					$2$	$0$

Step 15

Add the numbers in each column. In this case, add $9 + 2 + 8 + 1$ , then place the $0$ in the result line and carry the $2$ .


			$5$	$1$	. $8$	$8$
		$⨯$		$6$	$6$	$5$
		$2$	$5$	$9$	$4$	$0$
	$3$	$1$	$1$	$2$	$8$
$3$	$1$	$1$	$2$	$8$
				$0$	$2$	$0$

Step 16

Add the numbers in each column. In this case, add $5 + 1 + 2 + 2$ , then place the $0$ in the result line and carry the $1$ .


			$5$	$1$	. $8$	$8$
		$⨯$		$6$	$6$	$5$
		$2$	$5$	$9$	$4$	$0$
	$3$	$1$	$1$	$2$	$8$
$3$	$1$	$1$	$2$	$8$
			$0$	$0$	$2$	$0$

Step 17

Add the numbers in each column. In this case, add $2 + 1 + 1 + 1$ , then place the $5$ in the result line.


			$5$	$1$	. $8$	$8$
		$⨯$		$6$	$6$	$5$
		$2$	$5$	$9$	$4$	$0$
	$3$	$1$	$1$	$2$	$8$
$3$	$1$	$1$	$2$	$8$
		$5$	$0$	$0$	$2$	$0$

Step 18

Add the numbers in each column. In this case, add $0 + 3 + 1$ , then place the $4$ in the result line.


			$5$	$1$	. $8$	$8$
		$⨯$		$6$	$6$	$5$
		$2$	$5$	$9$	$4$	$0$
	$3$	$1$	$1$	$2$	$8$
$3$	$1$	$1$	$2$	$8$
	$4$	$5$	$0$	$0$	$2$	$0$

Step 19

Add the numbers in each column. In this case, add $0 + 0 + 3$ , then place the $3$ in the result line.


			$5$	$1$	. $8$	$8$
		$⨯$		$6$	$6$	$5$
		$2$	$5$	$9$	$4$	$0$
	$3$	$1$	$1$	$2$	$8$
$3$	$1$	$1$	$2$	$8$
$3$	$4$	$5$	$0$	$0$	$2$	$0$

Step 20

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.

$34500.2$