Word Problems and Subtraction

When you read a word problem, and you see words like difference, less than, decreased by, or fewer, then you know you’re going to need to subtract.

Let’s look at an example. 6 less than a number is 8. What is the number? Since they’re asking us what the number is, that means we don’t know it, and if we don’t know a number, then we use a variable for it.


The transcript is provided for your convenience
So, right here where we see “a number”, I’m going to put a variable, I’m going to use x. This phrase “less than” tells us that we need to subtract. So, we have 6. We’re subtracting, we’ve got a number. Is, is an equal sign, 8.

But, less than is a tricky phrase. It does mean to subtract, but again, you have to reverse the order of the things you’re subtracting. For example, if we said that we have $5 less than Jimmy has, that means that Jimmy has more money than we do. We have to do Jimmy’s money minus $5 in order to find out how much money we have. So, 6 less than x is going to be x minus 6 is equal to 8.

So, what number would we subtract 6 from to get 8? That number is 14. So, that means x is 14. Now, if you didn’t know that the number was 14, then you could solve this algebraically by adding 6 to both sides. So, you’d have, again, x equals 14, because 8 plus 6 is 14.