LESSON: Operations with Whole Numbers

READ: Multiplying Whole Numbers

Multiplying Whole Numbers

Addition and multiplication are related. When you are multiplying larger numbers, it will be help you to think that multiplication is just a short cut for addition.

Example

$5 \times 6 = \underline{\;\;\;\;\;\;\;\;\;\;}$

What does it MEAN when we multiply five times 6? $5 \times 6$ means that we are going to need five groups of six.

We could add 5 six times.

$5 + 5 + 5 + 5 + 5 + 5 = \underline{\;\;\;\;\;\;\;\;\;\;}$

However, it is easier to use our times tables.

$5 \times 6 = 30$

What is a factor?

A factor is the name of the two values being multiplied.

30 is the product of the factors 5 and 6.

What does the word product mean?

The product is the answer in a multiplication problem.

Example

$567 \times 3 = \underline{\;\;\;\;\;\;\;\;\;\;\;}$

If you think about this like addition, we have 567 added three times. That is a lot of work, so let’s use our multiplication short cut.

First, let’s line up our numbers according to place value.

To complete this problem, we take the digit 3 and multiply it times each digit of the top number. The three is called the multiplier in this problem because it is the number being multiplied.

$7 \times 3 = 21$

We can put the 1 in the ones place and carry the 2 (a ten) to the next column.

$& \quad 5^267\ & \underline {\times \quad \ \ 3}\ & \qquad \ \ 1$

Next, we multiply the 3 times 6 and add the two we carried.

$6 \times 3 = 18 + 2 = 20$

$& \quad ^25^267\ & \underline {\times \quad \quad 3}\ & \quad \quad \ 0 1$

Next, we multiply the 3 times 5 and add the two we carried.

$& \quad 5^26^27\ & \underline {\times \qquad 3}\ & \quad 1,701$

Our product is 1, 701.

What about three digits by two digits?

Example

$234 \times 12 =\underline{\;\;\;\;\;\;\;\;\;\;}$

First, we need to line up the digits according to place value.

Example

$& \qquad 234\ & \underline {\times \quad \ \ 12}$

Our multiplier here is 12. 12 had two digits. We need to multiply each digit of the top number with each digit of the number 12. We can start with the 2 of the multiplier.

$& \qquad 234\ & \ \underline {\times \quad \ 12}\ & \qquad 468 \quad Here \ is \ the \ result \ of \ multiplying \ the \ first \ digit \ of \ the \ multiplier.$

Next, we multiply the 1 by each digit. Because we already multiplied one digit, we start of the second row of numbers with a zero to hold the place of the one number we already multiplied. Here is what this looks like.

Our product is 2,808.

You could multiply even more digits by more digits.

You just need to remember two things.

Multiply each digit of the multiplier one at a time.
Add in a zero for each digit that you have already multiplied.