Commutative Property of Multiplication

"I have never been on the red carpet for a film before, Imani. How did you manage this?" "Oh, I just happened to get VIP tickets." "The auditorium has two sections. I wonder how many people can sit in each one?" "A quick scan tells me there are four rows of eight at the front, and eight rows of four at the back." "Hmm, I wonder how we can solve this?" To help Mr. Squeaks calculate how many people can fit in each section, we can use the commutative property of multiplication. The commutative property of multiplication is when the order of multiplication does not change the product. To use the commutative property of multiplication, we can use arrays along with following these four steps. First, write the number sentence. Next, write the number sentence in a different order. Then, set up arrays for both problems. Finally, solve and find the products of both number sentences. The commutative property of multiplication is useful because it can save time. For example, it can be quicker to multiply four by two than it is to multiply two by four. Now that we know the steps we can take to use the commutative property of multiplication, let's practise. First, write the expression six times three. Next, rewrite this as three times six. Then, set up the arrays needed. For six times three, we need six rows of three. For three times six, we need three rows of six. Now we can solve and find the products! Using the array to help, six times three gives a product of eighteen. We can also see that three times six gives a product of eighteen. The order of multiplication did not change the product! Let's look at one more example. First, write the expression two times five. Next, rewrite this as five times two. Then, set up arrays for both problems. For two times five, we need two rows of five. For five times two, we need five rows of two. Finally, calculate the product of both problems. Using the array to help, two times five gives a product of ten. We can also see that five times two gives a product of ten. The product for both problems is ten, even though we changed the order of multiplication! Now you know how the commutative property of multiplication works, let's help Mr. Squeaks. Remember, the front section had four rows of eight, so you would write this as four times eight. What is the next step? You can rewrite it as eight times four, to represent the back section. Can you remember the next step? Set up an array for both problems. How do you set up an array for four times eight? You need an array with four rows of eight. What array do you need for eight times four? You need an array with eight rows of four. Now you can find the product of both. What is the product of four times eight? Four times eight is thirty-two. What about eight times four? Eight times four also gives a product of thirty-two. That means a total of thirty-two people can fit in each section! To solve problems using the commutative property of multiplication, remember: first, write the number sentence. Then, write the number sentence in a different order. Next, set up arrays for both problems. Finally, solve and find the products of both number sentences. "I forgot to ask, what is the film?" "Wait and see, Mr. Squeaks. Wait and see!" "WAIT! Imani, is that? It is...It's you!"