A Common Math Error I’ve Been Seeing Lately

Have you accidentally done this with your child’s homework?

With so many math strategies to choose from, it’s easy to get confused. Today I’ll talk about a common mistake I’ve been seeing and how to correct it.

The Problem

Suppose we are tasked with the following subtraction:

We add and subtract 2 to make the subtraction easier.

Then complete the problem, perhaps by subtracting by place-value.

You realize this isn’t the right answer at all. You should have 649 NOT 653. What happened? Why is it wrong?

The Error

The error is here:

It may seem like we are adding and subtracting 2, but we are actually adding 4 because we are subtracting -2. You can see this in the following steps:

Recall subtracting a negative number is the same as adding a positive number.

That’s why our answer is 4 more than it should be!

The Fix

Instead of adding and subtracting 2, add 2 to both numbers, like this:

This is now equivalent to adding and subtracting 2.

It may be helpful to think about this as shifting 1598 and 949 two units right. By doing this the distance between the two numbers doesn’t change, and therefore is a valid move.

Now we can subtract by place value and obtain the correct answer.

Why is this a common mistake?

This is an easy mistake to make because we use a very similar tactic with addition problems. For example, suppose we were adding 1598 + 949. We may decide to add and subtract 2 to make the computation easier.

In this case, positive 2 plus negative 2 equals zero so our sum is unchanged and the technique is valid.

Remember This…

With subtraction problems imagine the numbers are on a number line and you are trying to find the distance in between them. You can shift them left or right to obtain easier numbers to work with because it doesn’t change the distance.

That means you can add the same number to both or subtract the same number from both values, but remember don’t add and subtract because that changes the distance!

Next Lesson: Intro to Distance, Rate & Time


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