Pre-Algebra Examples

$15.6 \cdot 7.123$

Step 1

Multiply $3$ by $6$ . Place the ones digit $(8)$ in the result line and carry the tens digit $(1)$ . There is one result line for each digit in $7.123$ .

			$1$
		$1$	$5$	. $6$
$⨯$	$7$	. $1$	$2$	$3$
				$8$

Step 2

Multiply $3$ by $5$ and add the carried $1$ . Place the ones digit $(6)$ in the result line and carry the tens digit $(1)$ . There is one result line for each digit in the $7.123$ .

		$1$	$1$
		$1$	$5$	. $6$
$⨯$	$7$	. $1$	$2$	$3$
			$6$	$8$

Step 3

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 $7.123$ .


		$1$	$5$	. $6$
$⨯$	$7$	. $1$	$2$	$3$
		$4$	$6$	$8$

Step 4

Multiply $2$ by $6$ . Place the ones digit $(2)$ in the result line and carry the tens digit $(1)$ . There is one result line for each digit in $7.123$ .

			$1$
		$1$	$5$	. $6$
$⨯$	$7$	. $1$	$2$	$3$
		$4$	$6$	$8$
			$2$

Step 5

Multiply $2$ by $5$ and add the carried $1$ . 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 $7.123$ .

		$1$	$1$
		$1$	$5$	. $6$
$⨯$	$7$	. $1$	$2$	$3$
		$4$	$6$	$8$
		$1$	$2$

Step 6

Multiply $2$ 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 $7.123$ .


		$1$	$5$	. $6$
$⨯$	$7$	. $1$	$2$	$3$
		$4$	$6$	$8$
	$3$	$1$	$2$

Step 7

Multiply $1$ by $6$ . Place the result in the next column in the result line. There is one result line for each digit in $7.123$ .


		$1$	$5$	. $6$
$⨯$	$7$	. $1$	$2$	$3$
		$4$	$6$	$8$
	$3$	$1$	$2$
		$6$

Step 8

Multiply $1$ by $5$ . Place the result in the next column in the result line. There is one result line for each digit in $7.123$ .


		$1$	$5$	. $6$
$⨯$	$7$	. $1$	$2$	$3$
		$4$	$6$	$8$
	$3$	$1$	$2$
	$5$	$6$

Step 9

Multiply $1$ by $1$ . Place the result in the next column in the result line. There is one result line for each digit in $7.123$ .


		$1$	$5$	. $6$
$⨯$	$7$	. $1$	$2$	$3$
		$4$	$6$	$8$
	$3$	$1$	$2$
$1$	$5$	$6$

Step 10

Multiply $7$ by $6$ . Place the ones digit $(2)$ in the result line and carry the tens digit $(4)$ . There is one result line for each digit in $7.123$ .

			$4$
		$1$	$5$	. $6$
$⨯$	$7$	. $1$	$2$	$3$
		$4$	$6$	$8$
	$3$	$1$	$2$
$1$	$5$	$6$
	$2$

Step 11

Multiply $7$ by $5$ and add the carried $4$ . Place the ones digit $(9)$ in the result line and carry the tens digit $(3)$ . There is one result line for each digit in the $7.123$ .

		$3$	$4$
		$1$	$5$	. $6$
$⨯$	$7$	. $1$	$2$	$3$
		$4$	$6$	$8$
	$3$	$1$	$2$
$1$	$5$	$6$
$9$	$2$

Step 12

Multiply $7$ by $1$ and add the carried $3$ . Place the ones digit $(0)$ in the result line and carry the tens digit $(1)$ . There is one result line for each digit in the $7.123$ .


				$1$	$5$	. $6$
		$⨯$	$7$	. $1$	$2$	$3$
				$4$	$6$	$8$
			$3$	$1$	$2$
		$1$	$5$	$6$
$1$	$0$	$9$	$2$

Step 13

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


				$1$	$5$	. $6$
		$⨯$	$7$	. $1$	$2$	$3$
				$4$	$6$	$8$
			$3$	$1$	$2$
		$1$	$5$	$6$
$1$	$0$	$9$	$2$
						$8$

Step 14

Add the numbers in each column. In this case, add $6 + 2 + 0 + 0$ , then place the $8$ in the result line.


				$1$	$5$	. $6$
		$⨯$	$7$	. $1$	$2$	$3$
				$4$	$6$	$8$
			$3$	$1$	$2$
		$1$	$5$	$6$
$1$	$0$	$9$	$2$
					$8$	$8$

Step 15

Add the numbers in each column. In this case, add $4 + 1 + 6 + 0$ , then place the $1$ in the result line and carry the $1$ .


				$1$	$5$	. $6$
		$⨯$	$7$	. $1$	$2$	$3$
				$4$	$6$	$8$
			$3$	$1$	$2$
		$1$	$5$	$6$
$1$	$0$	$9$	$2$
				$1$	$8$	$8$

Step 16

Add the numbers in each column. In this case, add $0 + 3 + 5 + 2 + 1$ , then place the $1$ in the result line and carry the $1$ .


				$1$	$5$	. $6$
		$⨯$	$7$	. $1$	$2$	$3$
				$4$	$6$	$8$
			$3$	$1$	$2$
		$1$	$5$	$6$
$1$	$0$	$9$	$2$
			$1$	$1$	$8$	$8$

Step 17

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


				$1$	$5$	. $6$
		$⨯$	$7$	. $1$	$2$	$3$
				$4$	$6$	$8$
			$3$	$1$	$2$
		$1$	$5$	$6$
$1$	$0$	$9$	$2$
		$1$	$1$	$1$	$8$	$8$

Step 18

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


				$1$	$5$	. $6$
		$⨯$	$7$	. $1$	$2$	$3$
				$4$	$6$	$8$
			$3$	$1$	$2$
		$1$	$5$	$6$
$1$	$0$	$9$	$2$
	$1$	$1$	$1$	$1$	$8$	$8$

Step 19

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


				$1$	$5$	. $6$
		$⨯$	$7$	. $1$	$2$	$3$
				$4$	$6$	$8$
			$3$	$1$	$2$
		$1$	$5$	$6$
$1$	$0$	$9$	$2$
$1$	$1$	$1$	$1$	$1$	$8$	$8$

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 $4$ , so the answer must have $4$ decimal places as well.

$111.1188$