Fourth Grade - Lesson 2.5 Multiplying Using the Distributive Property

Hey everyone, this is mister Seattle. He has one on one. And today we are going to learn how to multiply using the distributive property. You can use the distributive property to break apart numbers to make them easier to multiply. The description of property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products together. So what this definition is stating is that rather than just multiplying 6 times 13 and getting our product, I could break 13 apart into two smaller digits that have basic facts that I might be able to multiply easier in my head and then add those two products together. So let's try that out. Sorry. 6 times 13. So we know that 13 can be broken up by multiplying by adding 8 plus 5. So I'm going to break 13 apart up into 8 and 5 and multiply each factor by 6. 6 times 8, 6 times 5. Now these are basic facts that are easier for me to do in my head. 6 times 8 equals 48. 6 times 5 equals 30. Now remember, our last sentence in our list step in our definition is adding the products. So now we add 48 plus 30 8 plus zero equals 8, four plus three equals 7. So we know that 6 times 13 equals 78. And this is using the distributive property. Now there's not only one right way to breaking apart. 13 can be broken apart in different ways. I also know that 13 can be broken apart into ten and three. So let's try that out. So we write our problem 6 times 13, and now I want to try breaking 6 times ten and 6 times three. 6 times ten equals 60. 6 times three equals 18. Now it's time to add our two products together, 60 plus 18, zero and 8 gives us 8, 6 plus one is 7. We still come up with the same product of 78. It's whichever way you feel more comfortable breaking apart your factor of 13. Let's try one more problem together. Let's take 5 times 14. Now to break it apart in two different ways. So let me write it out on each side so that you can see. Different ways to break apart your factor. I know that 14 can also be 7 plus 7. So I'm going to multiply 5 times 7 and 5 times 7. To get two separate products, I know that my basic fact of 5 times 7 equals 35. Third half. So now it's time to add 35 plus 35 plus 5 is ten, carry the one. Three plus three is 6 plus one is 7 and our product is 70. Now let's break it apart differently on our second problem. Let's see if we get the same answer. 14 can also be broken up into ten and four, so 5 times ten and 5 times four. 5 times ten equals 50. 5 times four equals 20, take out two products, 50 plus 20, and add them together zero plus zero zero 5 plus two is 7. And we have the same product of 70. And this is how we can multiply by using the distributive property. I hope this helps. Thanks for watching.