Basic Math Examples

5.7 \cdot 12.6

$5.7 \cdot 12.6$

Step 1

Multiply using long multiplication.

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Step 1.1

Multiply

6

$6$ by

7

$7$ . Place the ones digit

(2)

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

(4)

$(4)$ . There is one result line for each digit in

12.6

$12.6$ .

		$4$ $4$
		$5$ $5$	. $7$ $7$
$\times$ $⨯$	$1$ $1$	$2$ $2$	. $6$ $6$
			$2$ $2$

Step 1.2

Multiply

6

$6$ by

5

$5$ and add the carried

4

$4$ . Place the ones digit

(4)

$(4)$ in the result line and carry the tens digit

(3)

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

12.6

$12.6$ .


		$5$ $5$	. $7$ $7$
$\times$ $⨯$	$1$ $1$	$2$ $2$	. $6$ $6$
	$3$ $3$	$4$ $4$	$2$ $2$

Step 1.3

Multiply

2

$2$ by

7

$7$ . Place the ones digit

(4)

$(4)$ in the result line and carry the tens digit

(1)

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

12.6

$12.6$ .

		$1$ $1$
		$5$ $5$	. $7$ $7$
$\times$ $⨯$	$1$ $1$	$2$ $2$	. $6$ $6$
	$3$ $3$	$4$ $4$	$2$ $2$
		$4$ $4$

Step 1.4

Multiply

2

$2$ by

5

$5$ and add the carried

1

$1$ . Place the ones digit

(1)

$(1)$ in the result line and carry the tens digit

(1)

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

12.6

$12.6$ .


		$5$ $5$	. $7$ $7$
$\times$ $⨯$	$1$ $1$	$2$ $2$	. $6$ $6$
	$3$ $3$	$4$ $4$	$2$ $2$
$1$ $1$	$1$ $1$	$4$ $4$

Step 1.5

Multiply

1

$1$ by

7

$7$ . Place the result in the next column in the result line. There is one result line for each digit in

12.6

$12.6$ .


		$5$ $5$	. $7$ $7$
$\times$ $⨯$	$1$ $1$	$2$ $2$	. $6$ $6$
	$3$ $3$	$4$ $4$	$2$ $2$
$1$ $1$	$1$ $1$	$4$ $4$
	$7$ $7$

Step 1.6

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

12.6

$12.6$ .


		$5$ $5$	. $7$ $7$
$\times$ $⨯$	$1$ $1$	$2$ $2$	. $6$ $6$
	$3$ $3$	$4$ $4$	$2$ $2$
$1$ $1$	$1$ $1$	$4$ $4$
$5$ $5$	$7$ $7$

Step 1.7

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

2 + 0 + 0

$2 + 0 + 0$ , then place the

2

$2$ in the result line.


		$5$ $5$	. $7$ $7$
$\times$ $⨯$	$1$ $1$	$2$ $2$	. $6$ $6$
	$3$ $3$	$4$ $4$	$2$ $2$
$1$ $1$	$1$ $1$	$4$ $4$
$5$ $5$	$7$ $7$
			$2$ $2$

Step 1.8

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

4 + 4 + 0

$4 + 4 + 0$ , then place the

8

$8$ in the result line.


		$5$ $5$	. $7$ $7$
$\times$ $⨯$	$1$ $1$	$2$ $2$	. $6$ $6$
	$3$ $3$	$4$ $4$	$2$ $2$
$1$ $1$	$1$ $1$	$4$ $4$
$5$ $5$	$7$ $7$
		$8$ $8$	$2$ $2$

Step 1.9

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

3 + 1 + 7

$3 + 1 + 7$ , then place the

1

$1$ in the result line and carry the

1

$1$ .


		$5$ $5$	. $7$ $7$
$\times$ $⨯$	$1$ $1$	$2$ $2$	. $6$ $6$
	$3$ $3$	$4$ $4$	$2$ $2$
$1$ $1$	$1$	$4$
$5$	$7$
	$1$	$8$	$2$

Step 1.10

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

$0 + 1 + 5 + 1$ , then place the

$7$ in the result line.


		$5$	. $7$
$⨯$	$1$	$2$	. $6$
	$3$	$4$	$2$
$1$	$1$	$4$
$5$	$7$
$7$	$1$	$8$	$2$


		$5$	. $7$
$⨯$	$1$	$2$	. $6$
	$3$	$4$	$2$
$1$	$1$	$4$
$5$	$7$
$7$	$1$	$8$	$2$

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

$2$ , so the answer must have

$2$ decimal places as well.

$71.82$