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Using Mental Math to Solve One-Step 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.

After reading this lesson, you'll know how you can solve one-step math problems without having to write anything down. Learn the technique you can use to help you solve the problem in your head.

A One-Step Problem

One-step problems are everywhere. You come across them in your math classes, in your math textbooks, and in the real world such as in games or when you are shopping. We define one-step problems as those math problems that require just one operation to solve. Here is an example of such a math problem:

A number plus 3 is equal to 10. What is the number?

To solve this problem, all you need to do is to perform one step.

Mental Math

You can solve this type of problem with mental math. When you use mental math you are using just your brain to help you solve a problem. With mental math, you don't need to write anything but the answer down. You read or listen to the problem and then you think about what you need to do to solve it and then you go ahead and solve it.

There is a technique you can use that will help you solve this type of problem easier. For the problem you just read, the technique involves using an opposite operation to help you find the answer. The problem you read is asking you to find a number that when 3 is added to it, you get 10. Well, thinking about it, you'll see that if you perform the opposite operation, subtraction, you'll find your answer. If you subtract 3 from the 10, you'll find the number that will equal 10 when you add 3 to it. 10 - 3 is equal to 7, so your answer is 7.

Checking Your Problem

After you've gotten your answer, it is always a good idea to check your answer when doing mental math. To do this, put your answer into the problem and see if your answer solves the problem. For the problem we were working on, does 7 plus 3 equal 10? Yes it does, so 7 is the correct answer.

Example

Let's look at another example.

Sally, Jeffrey, and Sue are playing a numbers game. Whoever guesses the correct number first gets to pick the kind of cookie they will bake. Sally goes first and gives a problem for the others to solve. Sally says, 'I am thinking of a number that equals 14 when you subtract 21 from it. What number am I thinking of?'

Jeffrey and Sue think about it for a while but Jeffrey is the one who first blurts out 35! Is Jeffrey correct?

Let's see.

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