Does the associative property apply to subtraction?
To answer this question, we need to understand what the phrase associative property means. If we don’t know what those words means, we’re going to find it difficult to actually answer the question. So, let’s remind ourselves what the associative property is.
The associative property applies when we have a calculation when we have to do more than one thing. Here’s an example with multiplication. We’ve got a calculation 10 multiplied by three multiplied by five. And we could start by multiplying different parts of that number sentence. In the first example, we could multiply 10 by three first and then multiply by five. Another way of doing it would be to multiply three by five first and then multiply 10 by whatever the answer to that was.
Let’s see what happens when we do this. 10 times three is 30, and if we multiply 30 by five, we get the answer 150. Remember, the next number sentence, we need to work out three multiplied by five first. Three times five is 15. So, we need to multiply 10 by the answer. And 10 times 15 equals 150 again. So, it doesn’t matter which part of the number sentence we do first. It gives the same answer. And that’s the associative property.
We’ve reminded ourselves how it works with multiplication. But the question asked us, does the associative property apply to subtraction? Let’s invent a subtraction for us to test this with. What about 16 take away 10 take away five? What are the two ways that we could find the answer out? Well, firstly we could subtract 10 from 16 first of all and then take away five. Or we could calculate 10 take away five first and then subtract this from 16.
If the associative property is true and does apply to subtraction, then we’ll be able to write an equal sign in between our two answers. They’ll be exactly the same. Let’s see if they are exactly the same. 16 take away 10 leaves us with six. Now we need to subtract the five, six take away five equals one. What if we work out 10 take away five first? Well, 10 take away five leaves us with five. Now we need to take away this from 16. We can see already this is not going to equal the same as one. 16 take away five equals 11.
We can’t write an equal sign in between them. In fact, the symbol for is not equal to looks like this. So, we could write this in between them. We can’t just subtract in any order. And so, although it works for multiplication, and also it works for addition too, the associative property does not apply to subtraction. So, really this is quite a straightforward question. It is a yes–no answer. Does the associative property apply to subtraction? No.