Video Transcript
Evaluate 87 times two plus 87 times 98 using the distributive property.
Before we think about what the distributive property is, let’s just have a look at this number sentence. It contains three separate operations. There are two multiplication symbols and one addition symbol. We know that the rules about the order of operations tell us that we always need to multiply before we add or subtract. So we’d need to work out the answer to 87 times two. Then the answer to 87 times 98 and then finally add the two together. We’re told that we need to evaluate the number sentence or find the answer using the distributive property. Let’s remind ourself what this is.
The distributive property tells us that if we add two numbers together, let’s call them 𝑏 and 𝑐, and then multiply them by another number. We’ll call that 𝑎. This is exactly the same as if we multiplied both numbers in the addition by the number that we’re multiplying by and then added them together. So 𝑎 multiplied by 𝑏, 𝑎𝑏, plus 𝑎 multiplied by 𝑐 or 𝑎𝑐. Now, which of these two statements, written using letters, can we see over here? Well, it’s the second one, isn’t it? 𝑎 multiplied by 𝑏 is the same as 87 times two. And then 𝑎 multiplied by 𝑐 is the same as 87 times 98. 𝑎 must be worth 87.
Just to make things easier to follow as we work through the answer, we’re going to swap our two parts to our distributive property around. There we go. Now, we’ve put the format that we’ve got already on the left. So now, let’s use the distributive property to write our number sentence in another way. First, we need to write the number we’re multiplying by, which is 87. That’s the same number in both multiplications. And then inside parentheses or brackets, we need to write the two numbers that form part of the addition. Two plus 98. Can you see now how we’ve used the distributive property to turn this statement into this statement.
But why do we want to rearrange it like this? Couldn’t we just have worked the answer like we said at the start? To work out both multiplications and then add the two together. Well, by doing what we’ve done, we’ve helped ourselves in two ways. Firstly, if you look at the way we were going to find the answer, there were three different steps. Three different things we needed to do. Step one, we needed to work out 87 multiplied by two. That would have been okay to do. But the next step would have been fairly tricky, because we’d then have had to have worked out 87 multiplied by 98. That’s a little bit harder. And then our third step would’ve been to add the two products together. Three steps to find the answer. But by using the distributive property to rearrange the number sentence, we’ve now only got two steps.
These parts in parentheses or brackets, which means we need to do it first. So our first step is to add two and 98 together. And then our second step is to multiply 87 by whatever the total of those two numbers is. So the first reason why we’d want to do this is there are less steps. And the second reason why we’d want to do this is because of the numbers involved. If we add together two and 98, we can see that it makes 100. So our calculation becomes 87 multiplied by 100, a nice round number. So much easier than working out 87 times 98. When we multiply a number by 100, the digits shift two places to the left. So 87 times 100 is 8700.
We used the distributive property to help us find the answer. If we added together two and 98 first, we made a round number, 100. So what we had to do then was to multiply 87 by 100 to find the answer. We converted our problem into two steps. And those two steps were very straightforward steps.
87 times two plus 87 times 98 equals 8700.
