Chemistry Examples

$789 \cdot 456$

Step 1

Multiply using long multiplication.

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Step 1.1

Multiply $6$ by $9$ . Place the ones digit $(4)$ in the result line and carry the tens digit $(5)$ . There is one result line for each digit in $456$ .

		$5$
	$7$	$8$	$9$
$⨯$	$4$	$5$	$6$
			$4$

Step 1.2

Multiply $6$ by $8$ and add the carried $5$ . Place the ones digit $(3)$ in the result line and carry the tens digit $(5)$ . There is one result line for each digit in the $456$ .

	$5$	$5$
	$7$	$8$	$9$
$⨯$	$4$	$5$	$6$
		$3$	$4$

Step 1.3

Multiply $6$ by $7$ and add the carried $5$ . Place the ones digit $(7)$ in the result line and carry the tens digit $(4)$ . There is one result line for each digit in the $456$ .


	$7$	$8$	$9$
$⨯$	$4$	$5$	$6$
$4$	$7$	$3$	$4$

Step 1.4

Multiply $5$ by $9$ . Place the ones digit $(5)$ in the result line and carry the tens digit $(4)$ . There is one result line for each digit in $456$ .

		$4$
	$7$	$8$	$9$
$⨯$	$4$	$5$	$6$
$4$	$7$	$3$	$4$
		$5$

Step 1.5

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 $456$ .

	$4$	$4$
	$7$	$8$	$9$
$⨯$	$4$	$5$	$6$
$4$	$7$	$3$	$4$
	$4$	$5$

Step 1.6

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 $456$ .


		$7$	$8$	$9$
	$⨯$	$4$	$5$	$6$
	$4$	$7$	$3$	$4$
$3$	$9$	$4$	$5$

Step 1.7

Multiply $4$ by $9$ . Place the ones digit $(6)$ in the result line and carry the tens digit $(3)$ . There is one result line for each digit in $456$ .

			$3$
		$7$	$8$	$9$
	$⨯$	$4$	$5$	$6$
	$4$	$7$	$3$	$4$
$3$	$9$	$4$	$5$
		$6$

Step 1.8

Multiply $4$ by $8$ and add the carried $3$ . Place the ones digit $(5)$ in the result line and carry the tens digit $(3)$ . There is one result line for each digit in the $456$ .

		$3$	$3$
		$7$	$8$	$9$
	$⨯$	$4$	$5$	$6$
	$4$	$7$	$3$	$4$
$3$	$9$	$4$	$5$
	$5$	$6$

Step 1.9

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 $456$ .


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

Step 1.10

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


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

Step 1.11

Add the numbers in each column. In this case, add $3 + 5 + 0$ , then place the $8$ in the result line.


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

Step 1.12

Add the numbers in each column. In this case, add $7 + 4 + 6$ , then place the $7$ in the result line and carry the $1$ .


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

Step 1.13

Add the numbers in each column. In this case, add $4 + 9 + 5 + 1$ , then place the $9$ in the result line and carry the $1$ .


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

Step 1.14

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


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

Step 1.15

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


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


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

Step 2

The result of $789 \cdot 456$ is $359784$ .

$359784$