Grade 3: Relating Multiplication and Division: Overview
Free worksheets, online interactive activities and other resources to support children learning the relationship between multiplication and division. In this chapter your students will learn how to use arrays to show the relationship between multiplication and division. Students will learn that division can be. Multiplication and division are closely related, given that division is the If we have 4 x 5 = 20, its inverse relations (in the form of a division) will.
The Connection Between Division and Multiplication
What is 50 divided by 10 going to be? How do I know that? Well, five times 10, five times 10, five times 10, is equal to Is equal to So let's keep thinking about this. If someone walked up to you in the street again, and said blank, blank, divided by, divided by two, blank divided by two is equal to, is equal to nine. How would you figure out what blank is?
Something divided by two is equal to nine. Well, one way to think about it, and if we just follow here, if you said 50 divided by five is 10, you could say 10 times five is 50, so right over here we could say well, nine times two, nine times two, must be equal to blank. Must be equal to our blank.
Well we know what nine times two is, that is 18, so this must be And that's really describing how 18, two, and nine relate to each other. Two nines is 18, or nine twos is 18, or if I were to divide 18 into two groups, each group would have nine.
Or if I were to divide into groups of two, you would have nine groups.
The Relation between Multiplication and Division - Elementary Math
Any way you look at it, 18 divided by two is nine, nine times two is When you divide to find the number of groups, the division is called measuring or repeated subtraction.
It is easy to see that you can keep subtracting 4 from 24 until you reach zero. Each 4 you subtract is a group or basket. A farmer has 24 apples.
How many baskets of 4 can she fill? Manipulatives and visual aids are important when teaching multiplication and division.
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Students have used arrays to illustrate the multiplication process. Arrays can also illustrate division. Since division is the inverse, or opposite, of multiplication, you can use arrays to help students understand how multiplication and division are related.
If in multiplication we find the product of two factors, in division we find the missing factor if the other factor and the product are known. In the multiplication model below, you multiply to find the number of counters in all. In the division model you divide to find the number of counters in each group. The same three numbers are used. So when multiplying or dividing, students can use a fact from the inverse operation.
Students can also check their work by using the inverse operation. Notice that the numbers in multiplication and division sentences have special names.