Division as Inverse Multiplication

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Division is the opposite of multiplication. You can use it when you want to split a group into several smaller but equally large groups.

A division consists of a dividend, a colon and a divisor. When you divide, you actually answer the question “What number do I multiply by the divisor to get the dividend?”

Rule

Important Words and Expressions

DIVIDEND \div DIVISOR

Let’s have a look at how division can simplify our lives. Imagine that you have $12$ bananas, and you want to split them between yourself and $3$ neighbors. How do you divide $12$ bananas by $4$ ? How many will each one of you get? If you don’t know how to divide, you can solve the problem by making four separate piles and put a banana in each pile, one by one, until there are no bananas left.

Four stacks of three bananas each

This can take a lot of time, and you have to write a lot. Luckily, there is another way to do it: Because you know how to multiply, you can use multiplication to distribute the bananas with the help of division! Multiplication and division are opposites in the same way plus and minus are; what one of them does, the other one can reverse.

Think About This

Is it true that twelve bananas divided by four people will give you three bananas each when we know that

3 \cdot 4 = 12 ?

The answer is yes! You need $4$ threes to get to $12$ . Because of this, dividing $12$ bananas between you and your $3$ neighbors will give you $3$ bananas each.

Let’s take a look at some examples using the times tables:

Example 1

From the times tables you know that $5 \cdot 3 = 15$ . What is $15 \div 3$ ?

You can see that $15$ is the dividend and $3$ is the divisor. Therefore, the question is: What number do you have to multiply by $3$ to get $15$ ? The answer is $5$ , and you write it like this:

15 \div 3 = 5

Example 2

From the times tables you know that $9 \cdot 8 = 72$ . What is $72 \div 9$ ?

You can see that $72$ is the dividend and $9$ is the divisor. Therefore, the question is: What number do you have to multiply by $9$ to get $72$ ? The answer is $8$ , and you write it like this:

72 \div 9 = 8

Example 3

From the times tables you know that $6 \cdot 7 = 42$ . What is $42 \div 6$ ?

You can see that $42$ is the dividend and $6$ is the divisor. Therefore, the question is: What number do you have to multiply by $6$ to get $42$ ? The answer is $7$ , and you write it like this:

42 \div 6 = 7

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