Pre-Algebra Examples

$47.93 \cdot 2.54$

Step 1

Multiply using long multiplication.

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Step 1.1

Multiply $4$ by $3$ . Place the ones digit $(2)$ in the result line and carry the tens digit $(1)$ . There is one result line for each digit in $2.54$ .

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

Step 1.2

Multiply $4$ by $9$ and add the carried $1$ . Place the ones digit $(7)$ in the result line and carry the tens digit $(3)$ . There is one result line for each digit in the $2.54$ .

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

Step 1.3

Multiply $4$ by $7$ and add the carried $3$ . 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 $2.54$ .

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

Step 1.4

Multiply $4$ by $4$ and add the carried $3$ . Place the ones digit $(9)$ in the result line and carry the tens digit $(1)$ . There is one result line for each digit in the $2.54$ .


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

Step 1.5

Multiply $5$ by $3$ . Place the ones digit $(5)$ in the result line and carry the tens digit $(1)$ . There is one result line for each digit in $2.54$ .

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

Step 1.6

Multiply $5$ by $9$ and add the carried $1$ . Place the ones digit $(6)$ in the result line and carry the tens digit $(4)$ . There is one result line for each digit in the $2.54$ .

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

Step 1.7

Multiply $5$ by $7$ 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 $2.54$ .

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

Step 1.8

Multiply $5$ by $4$ and add the carried $3$ . Place the ones digit $(3)$ in the result line and carry the tens digit $(2)$ . There is one result line for each digit in the $2.54$ .


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

Step 1.9

Multiply $2$ by $3$ . Place the result in the next column in the result line. There is one result line for each digit in $2.54$ .


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

Step 1.10

Multiply $2$ by $9$ . Place the ones digit $(8)$ in the result line and carry the tens digit $(1)$ . There is one result line for each digit in $2.54$ .

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

Step 1.11

Multiply $2$ by $7$ and add the carried $1$ . Place the ones digit $(5)$ in the result line and carry the tens digit $(1)$ . There is one result line for each digit in the $2.54$ .

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

Step 1.12

Multiply $2$ by $4$ 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 $2.54$ .


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

Step 1.13

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


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

Step 1.14

Add the numbers in each column. In this case, add $7 + 5 + 0$ , then place the $2$ in the result line and carry the $1$ .


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

Step 1.15

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


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

Step 1.16

Add the numbers in each column. In this case, add $9 + 9 + 8 + 1$ , then place the $7$ in the result line and carry the $2$ .


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

Step 1.17

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


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

Step 1.18

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


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


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

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.

$121.7422$