Fractions and Multiples

In our text (pg 216) it has a very interesting note on the relationship between a factor and a multiple. It states that if one number is a factor of a second number of divides the second then the second number is a multiple of the first.

For example,

4 is a factor of 20, as 20 is a multiple of 4.

Here is the rule for Factor and Multiple: If a and b are whole numbers and a does not equal 0, then a is a factor of b and only if there is a whole number c such that ac = b. We can say that a divides b or that b is a multiple of a.

This is a lot of words and there is always an easy, hands on way to to see how this works!

I will focus on two models to demonstrate factors and multiples much easier.

Linear Model:

This shows all the factors of 12 and the multiples of it as well. We can use this model to figure out the factors and multiples of any number.

Next, we have the retangular model. In this model, one number is shown by squares or tiles, and the two demensions of the rectangle will show the factors of the number. This is an easy effective way to teach ourselves and students how to know which numbers will evenly divided into eachother. Building longs of numbers and placing them together will determine the outcome. If there are left over tiles, then the number is NOT a factor.

Example: Try to make a rectangle out of the number 12. We can show this by having a 3 X 4 rectangle, 6 X 2 or 1 X 12. but, we cannot make a rectangle with any side using any other number. there would be left over units.