Finite Math Examples

$157 \cdot 51.69$

Step 1

Multiply using long multiplication.

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Step 1.1

Multiply $9$ by $7$ . Place the ones digit $(3)$ in the result line and carry the tens digit $(6)$ . There is one result line for each digit in $51.69$ .

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

Step 1.2

Multiply $9$ by $5$ and add the carried $6$ . Place the ones digit $(1)$ in the result line and carry the tens digit $(5)$ . There is one result line for each digit in the $51.69$ .

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

Step 1.3

Multiply $9$ by $1$ and add the carried $5$ . Place the ones digit $(4)$ in the result line and carry the tens digit $(1)$ . There is one result line for each digit in the $51.69$ .


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

Step 1.4

Multiply $6$ by $7$ . Place the ones digit $(2)$ in the result line and carry the tens digit $(4)$ . There is one result line for each digit in $51.69$ .

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

Step 1.5

Multiply $6$ by $5$ and add the carried $4$ . Place the ones digit $(4)$ in the result line and carry the tens digit $(3)$ . There is one result line for each digit in the $51.69$ .

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

Step 1.6

Multiply $6$ by $1$ and add the carried $3$ . Place the result in the next column in the result line. There is one result line for each digit in $51.69$ .


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

Step 1.7

Multiply $1$ by $7$ . Place the result in the next column in the result line. There is one result line for each digit in $51.69$ .


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

Step 1.8

Multiply $1$ by $5$ . Place the result in the next column in the result line. There is one result line for each digit in $51.69$ .


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

Step 1.9

Multiply $1$ by $1$ . Place the result in the next column in the result line. There is one result line for each digit in $51.69$ .


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

Step 1.10

Multiply $5$ by $7$ . Place the ones digit $(5)$ in the result line and carry the tens digit $(3)$ . There is one result line for each digit in $51.69$ .

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

Step 1.11

Multiply $5$ by $5$ and add the carried $3$ . Place the ones digit $(8)$ in the result line and carry the tens digit $(2)$ . There is one result line for each digit in the $51.69$ .

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

Step 1.12

Multiply $5$ 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 $51.69$ .


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

Step 1.13

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


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

Step 1.14

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


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

Step 1.15

Add the numbers in each column. In this case, add $4 + 4 + 7 + 0$ , then place the $5$ in the result line and carry the $1$ .


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

Step 1.16

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


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

Step 1.17

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


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

Step 1.18

Add the numbers in each column. In this case, add $0 + 0 + 0 + 7 + 1$ , then place the $8$ in the result line.


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


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

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.

$8115.33$