Basic Math Examples

3.5 \cdot 15

$3.5 \cdot 15$

Step 1

Multiply using long multiplication.

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Step 1.1

Multiply

5

$5$ by

0

$0$ . Place the result in the next column in the result line. There is one result line for each digit in

15

$15$ .


	$3$ $3$	. $5$ $5$	$0$ $0$
$\times$ $⨯$		$1$ $1$	$5$ $5$
			$0$ $0$

Step 1.2

Multiply

5

$5$ by

5

$5$ . Place the ones digit

(5)

$(5)$ in the result line and carry the tens digit

(2)

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

15

$15$ .

	$2$ $2$
	$3$ $3$	. $5$ $5$	$0$ $0$
$\times$ $⨯$		$1$ $1$	$5$ $5$
		$5$ $5$	$0$ $0$

Step 1.3

Multiply

5

$5$ by

3

$3$ and add the carried

2

$2$ . Place the ones digit

(7)

$(7)$ in the result line and carry the tens digit

(1)

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

15

$15$ .


	$3$ $3$	. $5$ $5$	$0$ $0$
$\times$ $⨯$		$1$ $1$	$5$ $5$
$1$ $1$	$7$ $7$	$5$ $5$	$0$ $0$

Step 1.4

Multiply

1

$1$ by

0

$0$ . Place the result in the next column in the result line. There is one result line for each digit in

15

$15$ .


	$3$ $3$	. $5$ $5$	$0$ $0$
$\times$ $⨯$		$1$ $1$	$5$ $5$
$1$ $1$	$7$ $7$	$5$ $5$	$0$ $0$
		$0$ $0$

Step 1.5

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

15

$15$ .


	$3$ $3$	. $5$ $5$	$0$ $0$
$\times$ $⨯$		$1$ $1$	$5$ $5$
$1$ $1$	$7$ $7$	$5$ $5$	$0$ $0$
	$5$ $5$	$0$ $0$

Step 1.6

Multiply

1

$1$ by

3

$3$ . Place the result in the next column in the result line. There is one result line for each digit in

15

$15$ .


	$3$ $3$	. $5$ $5$	$0$ $0$
$\times$ $⨯$		$1$ $1$	$5$ $5$
$1$ $1$	$7$ $7$	$5$ $5$	$0$ $0$
$3$ $3$	$5$ $5$	$0$ $0$

Step 1.7

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

0 + 0

$0 + 0$ , then place the

0

$0$ in the result line.


	$3$ $3$	. $5$ $5$	$0$ $0$
$\times$ $⨯$		$1$ $1$	$5$ $5$
$1$ $1$	$7$ $7$	$5$ $5$	$0$ $0$
$3$ $3$	$5$ $5$	$0$ $0$
			$0$ $0$

Step 1.8

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

5 + 0

$5 + 0$ , then place the

5

$5$ in the result line.


	$3$ $3$	. $5$ $5$	$0$ $0$
$\times$ $⨯$		$1$ $1$	$5$ $5$
$1$ $1$	$7$ $7$	$5$ $5$	$0$ $0$
$3$ $3$	$5$ $5$	$0$ $0$
		$5$ $5$	$0$ $0$

Step 1.9

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

7 + 5

$7 + 5$ , then place the

2

$2$ in the result line and carry the

1

$1$ .


	$3$ $3$	. $5$ $5$	$0$ $0$
$\times$ $⨯$		$1$ $1$	$5$ $5$
$1$ $1$	$7$ $7$	$5$ $5$	$0$ $0$
$3$ $3$	$5$ $5$	$0$ $0$
	$2$ $2$	$5$ $5$	$0$ $0$

Step 1.10

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

1 + 3 + 1

$1 + 3 + 1$ , then place the

5

$5$ in the result line.


	$3$ $3$	. $5$ $5$	$0$ $0$
$\times$ $⨯$		$1$ $1$	$5$ $5$
$1$ $1$	$7$ $7$	$5$ $5$	$0$ $0$
$3$ $3$	$5$ $5$	$0$ $0$
$5$ $5$	$2$ $2$	$5$ $5$	$0$ $0$


	$3$ $3$	. $5$ $5$	$0$ $0$
$\times$ $⨯$		$1$ $1$	$5$ $5$
$1$ $1$	$7$ $7$	$5$ $5$	$0$ $0$
$3$ $3$	$5$ $5$	$0$ $0$
$5$ $5$	$2$ $2$	$5$ $5$	$0$ $0$

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

$2$ , so the answer must have

2

$2$ decimal places as well.

52.5

$52.5$