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

In this video, we will learn how to identify and apply the commutative property of multiplication to multiply numbers up to 10 × 10 in any order.

09:50

Video Transcript

Commutative Property of Multiplication

In this video, we will learn how to identify and apply the commutative property of multiplication to multiply numbers up to 10 times 10 in any order.

What is the commutative property of multiplication? It tells us that we can multiply factors in any order and the product will stay the same. Here are six chicks arranged into two groups of three. We know that two times three equals six. Two and three are factors of six. These are the numbers we multiply together to make six. So we can say that six is the product of two and three. We’ve learned that the commutative property of multiplication tells us that we can multiply factors in any order and the product will stay the same.

So if two times three equals six, we know that three times two equals six. It doesn’t matter if we have two groups of three or three groups of two; the product is still six.

In the same way, if we arrange 15 squares into five groups of three to show that five times three equals 15, we can also arrange our 15 squares into three groups of five. Three and five are factors of 15. And we know the commutative property of multiplication tells us, “It doesn’t matter which order we multiply the factors; the product stays the same.” Five times three equals 15, and three times five equals 15.

We can use arrays to show how the commutative property of multiplication works. This array shows eight rows of four. We can find the product of eight and four by counting in fours eight times. Here we go. Four, eight, 12, 16, 20, 24, 28, 32. Eight times four is 32. If we change the order of the factors, the product stays the same.

Let’s put into practice what we’ve learned about the commutative property of multiplication by answering some questions now.

Use less than, equal to, or greater than to fill in the blank: Four times six what six times four.

In this question, we have to fill in the blank to make the statement correct. Is four times six less than six times four or is four times six equal to six times four or is four times six greater than six times four? Let’s use an array to help us calculate four times six. This array has four rows of six. We know that one row of six or one times six is six, two times six is 12, three times six is 18, four times six is 24. So what is six times four? This array shows six rows of four.

Let’s count in fours to find six times four. Four, eight, 12, 16, 20, 24. Four and six are factors of 24. It doesn’t matter which order we multiply the factors; the product stays the same. This question is all about the commutative property of multiplication. It doesn’t matter which order we multiply the factors; the product stays the same. Four times six is equal to six times four. The missing symbol is equal to.

Complete: eight times five equals five times what.

We have to find the missing number in this equation. Because there’s an equal sign in the middle, we know that eight times five is equal to five multiplied by our missing number. This array shows eight rows of five counters. Let’s count in fives to find the total number of counters. Five, 10, 15, 20, 25, 30, 35, 40. So we know that eight times five is 40. And if we turn our array the other way round to show five rows of eight, then the product will be the same. Eight rows of five are 40, and five rows of eight are 40. The missing number is eight. We know that we can multiply eight and five in any order; the product will still be 40. Eight times five is equal to five times eight.

Madison is skip counting to find five times four. Four, eight, 12, 16, 20. How else could she skip count to find five times four? Two, four, six, eight, 10, 12, 14, 20. Two, four, eight, 12, 16, 20. Five, 10, 15, 20. Five, seven, 10, 14, 20. Which other equation would this solve? Four times four, four plus five, five times five, or four times five.

In this question, Madison is skip counting to find five times four. She counted in fours five times. Four, eight, 12, 16, 20. We have to find another way to skip count to find five times four. Madison skip counted in fours five times to find five times four. What would happen if we changed the order of the two numbers we’re multiplying? Instead of finding five times four, we could find four times five. We’d need to count in fives four times. Five, 10, 15, 20.

The product is the same. So although our first possible answer takes us to the number 20, it doesn’t show five times four or four times five. Two, four, six, eight, 10, 12, 14, 20. It looks like someone was skip counting in twos, but they did leave out the numbers 16 and 18. So this isn’t a way of skip counting to show five times four. Two, four, eight, 12, 16, 20. This doesn’t show five times four. We start off by skip counting in twos and then in fours. So we can eliminate this answer. Five, 10, 15, 20. This is four times five, skip counting in fives four times. This is another way Madison could skip count to find five times four.

Which other equation would this solve? Four times four, four plus five, five times five, or four times five. If five times four equals 20, then four times five equals 20. This question is all about the commutative property of multiplication. It doesn’t matter which order we multiply two factors; the product stays the same. If five times four is 20, then four times five is 20.

What have we learned in this video? We have learned how to identify and apply the commutative property of multiplication to multiply numbers up to 10 times 10 in any order.

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