Algebra Examples

15 \cdot 12

$15 \cdot 12$

Step 1

Multiply using long multiplication.

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Step 1.1

Multiply

2

$2$ by

5

$5$ . Place the ones digit

(0)

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

(1)

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

12

$12$ .

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

Step 1.2

Multiply

2

$2$ by

1

$1$ and add the carried

1

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

12

$12$ .


	$1$ $1$	$5$ $5$
$⨯$ $⨯$	$1$ $1$	$2$ $2$
	$3$ $3$	$0$ $0$

Step 1.3

Multiply

1

$1$ by

5

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

12

$12$ .


	$1$ $1$	$5$ $5$
$⨯$ $⨯$	$1$ $1$	$2$ $2$
	$3$ $3$	$0$ $0$
	$5$ $5$

Step 1.4

Multiply

1

$1$ by

1

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

12

$12$ .


	$1$ $1$	$5$ $5$
$⨯$ $⨯$	$1$ $1$	$2$ $2$
	$3$ $3$	$0$ $0$
$1$ $1$	$5$ $5$

Step 1.5

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

0 + 0

$0 + 0$ , then place the

0

$0$ in the result line.


	$1$ $1$	$5$ $5$
$⨯$ $⨯$	$1$ $1$	$2$ $2$
	$3$ $3$	$0$ $0$
$1$ $1$	$5$ $5$
		$0$ $0$

Step 1.6

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

3 + 5

$3 + 5$ , then place the

8

$8$ in the result line.


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

Step 1.7

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

0 + 1

$0 + 1$ , then place the

1

$1$ in the result line.


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


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

Step 2

The result of

15 \cdot 12

$15 \cdot 12$ is

180

$180$ .

180

$180$