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Using Equal Groups to Solve Math Problems

Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

A math word problem is much easier to solve if it contains one bit of special information. If the problem mentions equal groups, then you'll learn how you can easily solve the problem using either multiplication or division.

A Math Problem

In this lesson, you'll learn how to solve equal-groups math problems. These are word problems where you have a number of equal groups. It is then your job to find the missing number in the problem.

For example, you might get a problem like this one.

Jason has 12 candies that he wants to give to 3 friends. If each friend gets an equal amount, how many candies does each friend get?

Your job is to find out how many candies each person gets.

Equal Groups

This word problem is an equal-groups problem because the problem mentions that each friend gets an equal amount. If the problem said that each friend gets the same number of candies, it would still be an equal-groups problem because same and equal mean the same thing. The problem doesn't have to specifically use the words equal or same; the problem just has to tell you that whatever is happening is the same for each individual object.

When you have an equal-groups math problem, it actually makes your job of solving it easier. Because you have a number of equal groups, there are only two arithmetic operations that can help you.

To solve these equal-groups problems, use multiplication or division to find your answer. The multiplication and division operations work for these types of problems because multiplication and division themselves deal with equal groups. For example, 3 * 4 tells you that you have three equal groups of 4. You can then use this information to find your missing number. You can either divide your total by the number of groups or the number of objects in each group. Or, you can figure out what number times your number of objects in each group or number of groups will equal your total. If you are asked to find the total, then you can multiply your number of objects in each group by the number of groups.

Solving It

So, looking at your problem, you see that you have a total of 12 candies. You want to divide these 12 candies equally among 3 friends. So, this tells you that you can either solve this problem by dividing 12 / 3, or you can solve it by finding out what multiplied by 3 will give you 12. Your answer will be the same.

If you divide 12 by 3, you get this:

12 / 3 = 4

If you try to figure out what multiplied by 3 will give you 12, you get this:

3 * x = 12

3 * 4 = 12

x = 4

Either way, you get the same answer of 4. So, each friend gets 4 candies.

Example

Let's look at another example.

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