Lesson Video: Associative Property of Multiplication Mathematics • 3rd Grade

In this video, we will learn how to identify and apply the associative property of multiplication to multiply three one-digit numbers with products up to 10 × 10.

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Video Transcript

Associative Property of Multiplication

In this video, we’re going to learn how to identify and apply the associative property of multiplication to multiply three one-digit numbers. The associative property of multiplication is a maths rule that tells us the way in which factors are grouped in a multiplication doesn’t affect the product. For example, we could group these two factors together and find two times four. We know that two times four is eight. So we need to multiply eight by our remaining factor, which is five. And we know that eight times five is 40, so the product of two times four times five is 40.

But what if we were to group these two factors together and multiplied them first? We know that four times five is 20. So now we just need to multiply 20 by our remaining factor, which is two. And we know that two times 20 equals 40. It doesn’t matter how we group the factors; the product doesn’t change. Two times four is eight, and eight times five is 40. And if we multiply four times five first, we get 20. And if we multiply 20 by two, we also get 40. Let’s practice now multiplying three one-digit numbers using the associative property of multiplication.

When we multiply three numbers, we can choose which calculation to do first. Do the highlighted calculations to find the missing numbers. Six times five times two equals six times what. Six times five times two equals what times two. What is six times five times two?

In this question, we’re being asked to multiply three one-digit numbers together: six, five, and two. The question tells us that we can choose which calculation to do first. We have to do the highlighted calculations to find the missing number. In the first calculation, we have to multiply five times two first. We know that five times two is 10, so six times five times two is equal to six times 10. So the missing number in the first calculation is 10.

The second calculation is the same as the first. We’re still finding six times five times two, but this time we have to multiply six by five first. Six times five is 30. Now all we have to do is multiply 30 by two. The missing number in the first calculation is 10, and the missing number in the second calculation is 30. So to find six times five times two, if we multiply five by two first, we get 10. And then we multiply six by 10. So the product of six times five times two is 60.

Let’s check if we get the same answer in our second calculation. Six times five is 30, and 30 times two is also 60. It doesn’t matter how we group the factors; the product doesn’t change. This question is all about the associative property of multiplication. It doesn’t matter how we group the factors; the product stays the same. Six times five times two equals 60.

Let’s recap what we’ve learned about the associative property or the associative rule of multiplication. When we’re multiplying three one-digit numbers like three times two times four, it doesn’t matter how we group the factors; the product stays the same. We could find three times two first. And we can see from the array that three times two equals six. Then all we have to do is multiply our six by four. Six times four is 24. Three times two times four equals 24.

We could also find three times two times four by changing the order of the factors. Three times two times four is equal to two times four times three. And we know we can group the factors in any order. So let’s start by finding two times four. This array shows two rows of four. Two times four is eight. Now we just need to multiply eight by three. And eight times three is 24. So we’ve learned that when we’re multiplying three one-digit numbers, we can use the associative property and the commutative property. It doesn’t matter which order we multiply the numbers or how we group the factors; the product stays the same. Let’s practice what we’ve learned by answering another question now.

Compare the expressions. Pick the symbol that is missing. Two times three times six is greater than six times three times two or two times three times six is equal to six times three times two or two times three times six is less than six times three times two.

In this question, we’re given two expressions. And we have to choose the correct symbol to compare them: greater than, equal to, or less than. Our two expressions have been modeled using arrays. Our first array shows two groups of three times six. Three times six is 18. And double 18 is 36. Two times three times six equals 36. Our next model shows six lots of three times two. We know that three times two is six and six times six is 36. So six times three times two is also 36. Both of our expressions contain the same three factors of 36: two, three, and six. It doesn’t matter which order we multiply the numbers or how we group them; the product stays the same.

So the missing symbol is equal to. Two times three times six is equal to six times three times two. The missing symbol is equal to.

Fill in the blank with the missing factor: Two times what times three equals 18.

In this question, we have to find the missing factor. This part of our expression is inside a pair of brackets. This tells us that we need to multiply these two factors together first. So something multiplied by three and then multiplied by two equals 18. Two multiplied by what equals 18. We know that two times nine is 18. So what do we need to multiply by three to give us nine? Three times three is nine. So two times three times three equals 18. Three times three is nine; two times nine is 18. The missing factor is three.

Another way we could’ve found the missing factor is to start with the numbers we already had. Two times three times what equals 18. First, we can multiply two by three, which is six. Then all we need to think about is what do we time six by to give us a product of 18. And we know that six times three is 18. It doesn’t matter how we group the factors or the order in which we multiply them; the product doesn’t change. Two times three times three equals 18. Two times three times three equals 18. And three times three times two equals 18. The missing factor is three.

What have we learned in this video? We’ve learned that when we multiply three one-digit numbers, we can multiply the numbers in any order and group the factors in any order and the product stays the same.

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