## Grades K-8 Worksheets

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This lesson is on multiples. A *multiple* is a number you say when you "count by" a number, or use skip-counting. When counting by fives, it is like saying only the answers on the 5 times table:

5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60.and so on.

All of these numbers are called *multiples* of five.

Work through the examples and explanations in this lesson with your children and then try the worksheet that you will find at the bottom of this page.

Multiples are most often thought about as skip counting, or "count by" numbers.

You will find more on skip-counting here.

**Multiples of 5**

Let's use a real-world example. If you were going to count up the value of a stack of nickels, you would "count by" fives, since each nickel is worth five cents.

All the numbers you say as you count by fives are the *multiples* of five. You might also recognize that they are the products, or answers, to the times table for fives.

5 x 1 = 5

5 x 2 = 10

5 x 3 = 15

5 x 4 = 20

5 x 5 = 25

5 x 6 = 30

5 x 7 = 35

5 x 8 = 40

5 x 9 = 45

5 x 10 = 50

5 x 11 = 55

5 x 12 = 60

The pattern continues on past the times tables you've seen most often. Just keep on adding another set of five for each multiple of five.

**Multiples of 10**

Let’s try another example. This time, we’ll count dimes. Since dimes are worth ten cents, we’ll “count by” tens. This will give us the *multiples* of 10.

So the *multiples* of 10 are: 10,20,30,40,50,60,70,80,90,100,110,120,130,140,150, and so on. Just keep on adding another set of 10 for each *multiple* of 10.

**Multiples of 12**

Of course, there are many examples besides money. How about eggs? Eggs come by the dozen, and a dozen is 12. To find the multiples of 12, I count each set of 12.

So the *multiples* of 12 are: 12, 24, 36, 48, 60, 72, and so on.

**More Multiples**

You can also figure out multiples by making your own sets with anything you can count. For example, you can make sets of three candies to figure out the multiples of three.

So the multiples of three are: 3, 6, 9, 12, and so on.

**Finding Multiples By Dividing**

Since multiplication and division are inverse operations, meaning that they are related to one another and “un-do” each other, division can also be used to determine whether or not a given number is a multiple of another. See the examples below:

Since 12 can be divided evenly by 3 (12 ÷ 3 = 4), 12 is a multiple of 3.4 sets of 3 would equal 12. |

Since 77 can be divided evenly by 11 (77 ÷ 11 = 7), 77 is a multiple of 11.7 sets of 11 would equal 77. |

Since 56 can be divided evenly by 8 (56 ÷ 8 = 7), 56 is a multiple of 8.7 sets of 8 would equal 56. |

**Multiples Worksheets**

Click the links below and get your children to try the worksheets that provide practice questions on multiples.

- Multiples (2-page worksheet. Includes Guided Practice)
- Division and Multiples (2-page worksheet. Includes Guided Practice)