Basic Math Examples

$12.25 \cdot 3.14$

Step 1

Multiply using long multiplication.

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Step 1.1

Multiply $4$ by $5$ . Place the ones digit $(0)$ in the result line and carry the tens digit $(2)$ . There is one result line for each digit in $3.14$ .

			$2$
	$1$	$2$	. $2$	$5$
$⨯$		$3$	. $1$	$4$
				$0$

Step 1.2

Multiply $4$ by $2$ and add the carried $2$ . 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 $3.14$ .

		$1$	$2$
	$1$	$2$	. $2$	$5$
$⨯$		$3$	. $1$	$4$
			$0$	$0$

Step 1.3

Multiply $4$ by $2$ 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 $3.14$ .

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

Step 1.4

Multiply $4$ by $1$ . Place the result in the next column in the result line. There is one result line for each digit in $3.14$ .


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

Step 1.5

Multiply $1$ by $5$ . Place the result in the next column in the result line. There is one result line for each digit in $3.14$ .


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

Step 1.6

Multiply $1$ by $2$ . Place the result in the next column in the result line. There is one result line for each digit in $3.14$ .


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

Step 1.7

Multiply $1$ by $2$ . Place the result in the next column in the result line. There is one result line for each digit in $3.14$ .


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

Step 1.8

Multiply $1$ by $1$ . Place the result in the next column in the result line. There is one result line for each digit in $3.14$ .


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

Step 1.9

Multiply $3$ by $5$ . Place the ones digit $(5)$ in the result line and carry the tens digit $(1)$ . There is one result line for each digit in $3.14$ .

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

Step 1.10

Multiply $3$ by $2$ 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 $3.14$ .

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

Step 1.11

Multiply $3$ by $2$ . Place the result in the next column in the result line. There is one result line for each digit in $3.14$ .

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

Step 1.12

Multiply $3$ by $1$ . Place the result in the next column in the result line. There is one result line for each digit in $3.14$ .


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

Step 1.13

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


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

Step 1.14

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


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

Step 1.15

Add the numbers in each column. In this case, add $9 + 2 + 5$ , then place the $6$ in the result line and carry the $1$ .


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

Step 1.16

Add the numbers in each column. In this case, add $4 + 2 + 7 + 1$ , then place the $4$ in the result line and carry the $1$ .


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

Step 1.17

Add the numbers in each column. In this case, add $0 + 1 + 6 + 1$ , then place the $8$ in the result line.


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

Step 1.18

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


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


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

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

$38.465$