How to Complete the Division Sentence

Instructor: Dina Albert
If you have every bought food for a party, or shared food with family or friends, you might not have realized you were using multiplication and division. In this lesson, you will learn how to complete a division sentence by using multiplication.

Number Sentences

In everyday life and math, you will read, write and solve many number sentences. When numbers are grouped together and include mathematical operations, this is known as a number sentence. When we have a division sentence, the numbers are grouped together with the operation of division.

Multiplication and division are opposite operations. This means that what one operation does, the other operation can undo. Let's look at an example:


Notice in this image how the arrow points in both directions. This is because multiplication and division can use the same picture, but we read it in opposite directions. For example, we can start with the total of a six triangles and divide them into two groups of three, or we can 'reverse' our direction starting with two groups of three, and multiply 2 x 3 to get a total of 6 triangles.

Completing Division Sentences

We can use the idea of an opposite operation to help us complete division sentences. Let's say there are 10 cookies, and we want to know how many people can share them if each person gets 5 cookies.

Here is our division sentence: 10 / _____ = 5.

Let's rewrite this sentence using the opposite operation of multiplication. When we 'reverse' our direction, we'll start with the 5.

Here is our multiplication sentence: 5 x _____ = 10.

The goal is to end up with 10. Now we can use our multiplication facts, or a multiplication chart, to complete the sentence. We know that 5 x 2 = 10, so 2 is our missing number.

Another way to solve this problem is to remember that multiplication is the same as adding equal groups. So we can ask: How many times can we add by 5 until we get to 10?

Let's try it: 5 + 5 = 10. Here we added two 5's. Our missing number is 2.

More Practice with Division Sentences

You can choose to use either method depending on the type of sentence, or what is easier for you. For now, we will practice using both methods.

Practice Problem One

What if we have 4 guests coming to our party and we want each one to get 2 goody bags. How many goody bags should we make?

Let's start by writing a division sentence: _____ bags / 4 guests = 2 bags per guest.

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