Calculus Examples

48 \cdot 4

$48 \cdot 4$

Step 1

Multiply using long multiplication.

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Step 1.1

Multiply

4

$4$ by

8

$8$ . Place the ones digit

(2)

$(2)$ in the result line and carry the tens digit

(3)

$(3)$ . There is one result line for each digit in

4

$4$ .

	$3$ $3$
	$4$ $4$	$8$ $8$
$⨯$ $⨯$		$4$ $4$
		$2$ $2$

Step 1.2

Multiply

4

$4$ by

4

$4$ and add the carried

3

$3$ . Place the ones digit

(9)

$(9)$ in the result line and carry the tens digit

(1)

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

4

$4$ .


	$4$ $4$	$8$ $8$
$⨯$ $⨯$		$4$ $4$
$1$ $1$	$9$ $9$	$2$ $2$

Step 1.3

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

2

$2$ , then place the

2

$2$ in the result line.


	$4$ $4$	$8$ $8$
$⨯$ $⨯$		$4$ $4$
$1$ $1$	$9$ $9$	$2$ $2$
		$2$ $2$

Step 1.4

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

9

$9$ , then place the

9

$9$ in the result line.


	$4$ $4$	$8$ $8$
$⨯$ $⨯$		$4$ $4$
$1$ $1$	$9$ $9$	$2$ $2$
	$9$ $9$	$2$ $2$

Step 1.5

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

1

$1$ , then place the

1

$1$ in the result line.


	$4$ $4$	$8$ $8$
$⨯$ $⨯$		$4$ $4$
$1$ $1$	$9$ $9$	$2$ $2$
$1$ $1$	$9$ $9$	$2$ $2$


	$4$ $4$	$8$ $8$
$⨯$ $⨯$		$4$ $4$
$1$ $1$	$9$ $9$	$2$ $2$
$1$ $1$	$9$ $9$	$2$ $2$

Step 2

The result of

48 \cdot 4

$48 \cdot 4$ is

192

$192$ .

192

$192$

48 \cdot 4

$48 \cdot 4$

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