Learn about Associative and Distributive Property In this track we will learn how to use associative and distributive properties at the same time okay. There are two questions, first question ask us to evaluate the following expression using the distributive and associative properties. Let’s do the first one first, which is 12 + 4 + 18 + 46. Now I could just simply add all four but there is a faster way of doing it okay, and we will use the associative property to arrange for this. So first thing that we’re going to do is look at the laws that we know, we know the associative law and we know the commutative law. So let’s see what we know. The easiest way to so this is look for numbers that when added which would gives us multiples of 10, 12 + 4 would not give us a multiple of 10 12 and 18 when added will give us a multiple of 10, 4 and 46 when added will give us a multiple of 10. The reason we know that is if I add the last two digits 8 and 2 the answer is 0, 4 + 6 the answer of the last digit is 0. So the first thing were going to do is arrange them differently, so instead of saying 12 + 4 + 18 + 46 will use the commutative law to arrange it differently. Which means I can do 12 + 18 + 4 + 46. All I did was to swap the places of these two which I can do because of commutative law. Now let’s create a little bit of extra space and now that we’ve written 12 + 18 + 4 + 46, I can now use the associative property to make groups of the compatible numbers. So let’s say 12 + 18 + 4 + 46. I can group them together because that is the associative property okay. Now that I have these 12 + 18 is easy to add manually which is 30 + 4 + 46 is 50 which means the final answer for this is 80. I simply use the commutative and associative laws to make it easy for me to add these four numbers okay. Let’s try the second one. The second problem is 5 × 2 × 12. Let’s create a little bit of extra space. And the first thing we’re going to do is again use the commutative property because we know that 5 × 2 and 12. Let’s look for numbers which when multiplied will give us a multiple of 10. Again 5 × 2 × 12 can also be written as 5 × 2 × 12. So 5 × 2 is 10 multiplied by 12 is 120. It’s relatively easy as long as I can group them together okay. Let’s look at the third problem which is a word problem with says Paul makes four different types of cartoons, he sketches 18 cartoons of Tom and Jerry, 36 of Scooby-Doo, 42 of Spider Man and 14 of Batman. How many cartoons does he make in all, use associative of property. So I'm going to change the color of my pen and let’s write down what we know. For the second problem what we know is Paul makes 18 cartoons of Tom and Jerry. He makes 36 of Scooby-Doo, he makes 42 of Spider man and he makes 14 of Batman. We need to compute how may cartoons does he make at all, so what I'm going to do is the total number of cartoons made equals 18 + 36 + 42 + 14. Again first I'm going to rearrange these so I coupled the ones that I add up to a multiple of 10, which would be these two, right. So let’s write this down as 18 + 42 + 36 + 14 creating a little bit of extra space and again what I use here is simple commutative law of addition. Now I can use associative law to say this is the same as 18 + 42 + 36 + 14, 18 + 42 is 60 + 36 + 14 is 50. When I add these two together the final answers is 110 and that is the correct answer.