Pre-Algebra Examples

$521 \cdot 45$

Step 1

Multiply

$5$ by

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

$45$ .


	$5$	$2$	$1$
$⨯$		$4$	$5$
			$5$

Step 2

Multiply

$5$ by

$2$ . Place the ones digit

$(0)$ in the result line and carry the tens digit

$(1)$ . There is one result line for each digit in

$45$ .

	$1$
	$5$	$2$	$1$
$⨯$		$4$	$5$
		$0$	$5$

Step 3

Multiply

$5$ by

$5$ and add the carried

$1$ . Place the ones digit

$(6)$ in the result line and carry the tens digit

$(2)$ . There is one result line for each digit in the

$45$ .


	$5$	$2$	$1$
$⨯$		$4$	$5$
$2$	$6$	$0$	$5$

Step 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

$45$ .


	$5$	$2$	$1$
$⨯$		$4$	$5$
$2$	$6$	$0$	$5$
		$4$

Step 5

Multiply

$4$ by

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

$45$ .


	$5$	$2$	$1$
$⨯$		$4$	$5$
$2$	$6$	$0$	$5$
	$8$	$4$

Step 6

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

$45$ .


		$5$	$2$	$1$
	$⨯$		$4$	$5$
	$2$	$6$	$0$	$5$
$2$	$0$	$8$	$4$

Step 7

Add the numbers in each column. In this case, add

$5 + 0$ , then place the

$5$ in the result line.


		$5$	$2$	$1$
	$⨯$		$4$	$5$
	$2$	$6$	$0$	$5$
$2$	$0$	$8$	$4$
				$5$

Step 8

Add the numbers in each column. In this case, add

$0 + 4$ , then place the

$4$ in the result line.


		$5$	$2$	$1$
	$⨯$		$4$	$5$
	$2$	$6$	$0$	$5$
$2$	$0$	$8$	$4$
			$4$	$5$

Step 9

Add the numbers in each column. In this case, add

$6 + 8$ , then place the

$4$ in the result line and carry the

$1$ .


		$5$	$2$	$1$
	$⨯$		$4$	$5$
	$2$	$6$	$0$	$5$
$2$	$0$	$8$	$4$
		$4$	$4$	$5$

Step 10

Add the numbers in each column. In this case, add

$2 + 0 + 1$ , then place the

$3$ in the result line.


		$5$	$2$	$1$
	$⨯$		$4$	$5$
	$2$	$6$	$0$	$5$
$2$	$0$	$8$	$4$
	$3$	$4$	$4$	$5$

Step 11

Add the numbers in each column. In this case, add

$0 + 2$ , then place the

$2$ in the result line.


		$5$	$2$	$1$
	$⨯$		$4$	$5$
	$2$	$6$	$0$	$5$
$2$	$0$	$8$	$4$
$2$	$3$	$4$	$4$	$5$

Step 12

The result of

$521 \cdot 45$ is

$23445$ .

$23445$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$