An setup of objects, pictures, or number in columns and also rows is called an array. In this article, you will certainly learn exactly how to use arrays to display the relationship in between multiplication and division.

You are watching: Compare and contrast multiplication and division

Key standard: usage multiplication and department within 100 to fix word problems in instances involving arrays. (3.OA.A.3)

Students in grades 3 and up will learn that division can be believed of in two ways, partitioning and also measurement. Although in ~ this level students might not usage these names, you deserve to convey the definition of both type of division so the they can have a far better understanding the the division process. As soon as you division to uncover the number of objects in every group, the division is dubbed fair share or partitioning. Because that example:

A farmer is pour it until it is full baskets that apples. The farmer has 24 apples and 4 baskets. If she divides lock equally, how numerous apples will certainly she placed in every basket?


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There are other models her students can use to discover the relationship in between multiplication and division. Disclose your students to the different models and also let students select which version they discover most helpful. Here is an example using counters come multiply and also divide.


Teaching Multiplication division With Arrays graphic 05
Another strategy her students might find useful is utilizing a associated multiplication reality to divide. Below is one example.

18 ÷ 6 = ?

Think: 6 × ? = 18Six time what number is 18?

6 × 3 = 18,so 18 ÷ 6 = 3.

Dividing v 0 and 1

When students recognize the principle of division, they can proceed to discover the rules for separating with 0 and also 1. Lead students to find the rules themselves by having actually them use counters to design the division. A few examples follow.

When any kind of number (except 0) is divided by itself, the quotient is 1.


Students may be curious what happens if they division by 0. Define that it is not simple concept, and even experienced mathematicians struggle to define it! One strategy to show why the is not possible is to have actually students shot to division any number into teams of zero. No issue how plenty of groups friend make, it doesn"t work.


Division in the genuine World

Encourage students to think around the relationship in between multiplication and division when they deal with real-world problems. For example, they have the right to use a associated multiplication fact to uncover the unit price of one item—for example, the cost of one baseball lid priced in ~ 3 for $18.

$18 ÷ 3 = ?Think: 3 × ? = $18

3 × $6 = $18,so $18 ÷ 3 = $6.

The price is $6 for one baseball cap.

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