Question Video: Identifying the Associative Property of Multiplication Mathematics

Video Transcript

Which of the following illustrates the associative property of multiplication? (A) 𝑎 times 48 times 10 is equal to 𝑎 times 48 plus 10. (B) 𝑎 times 48 plus 10 is equal to 𝑎 plus 48 times 10. (C) 𝑎 plus 48 times 10 is equal to 𝑎 plus 48 plus 10. (D) 𝑎 plus 48 times 10 is equal to 𝑎 times 48 plus 10. Or (E) 𝑎 times 48 times 10 is equal to 𝑎 times 48 times 10.

The associative property is the property that deals with the grouping of a certain operation. For example, if we have 𝑎 times 𝑏 times 𝑐, the 𝑏 times 𝑐 has been grouped together. And by order of operations, we would calculate 𝑏 times 𝑐 and then we would multiply it by 𝑎. However, this associative property of multiplication tells us that when we’re dealing with multiplication, we could group 𝑎 times 𝑏 and then multiply it by 𝑐 and the outcomes would be the same. We’re saying 𝑎 times 𝑏 times 𝑐 is equal to 𝑎 times 𝑏 times 𝑐.

But the observation we need to see here is that this law works when we are only dealing with multiplication. When we refer to the associative property, we usually are wanting to regroup items. Now we can look at these four options. In option (A), there was a regrouping. However, all the sudden something is being added on one side, which means this would not work. In fact, options (B) through (D) are all mixing addition and multiplication, which means the associative property of multiplication does not apply to them.

Option (E) has regrouped and is only working with multiplication as the operation. So we can say 𝑎 times 48 times 10 will be equal to 𝑎 times 48 times 10. If you wanted to further show that this is true, we know that 𝑎 times 48 would be 48𝑎. And we can multiply 48𝑎 by 10, which would give us 480 times 𝑎. On the right-hand side, we would then multiply 48 by 10, which is 480, and then multiply that value by 𝑎, which is 480𝑎. And we get a true statement.