Topic F: Distributive property and problem solving using units of 2–5 and 10
Current time:0:00Total duration:3:32
Abe went running 4 days this past week. He ran 9 kilometers on each day. In that same week, Beth ran 15 fewer kilometers than Abe. How many kilometers did Beth run that week? So I encourage you to pause this video and to try this on your own, try to figure out, how many kilometers did Beth run that week? So there's a couple of ways to think about it or a couple of ways to visualize it. The first thing we might want to do-- in fact, the first thing we definitely want to do-- is to figure out, well, how far did Abe run in that week? Well, he went 4 days, and each day, he went 9 kilometers. So we could say that he went-- let me do that blue color-- 4 days times 9 kilometers per day. And we could visualize that. So this is how much he went in one day. This is how much he went in two days. This is how much he'd go in three days. This is how much he would go in four days. So what is this? What is 4 times 9 kilometers? Well, this is essentially 9 plus 9 plus 9 plus 9. So we could just add up the 9's. 9 plus 9 is 18, plus 9 is 27, plus 9 is 36. So he ran a total of 36 kilometers. Now, that's not what they're asking us for. They're asking us for the number of kilometers Beth ran that week. And they tell us that she ran 15 fewer kilometers than Abe. So this right over here, Abe's total distance-- if we start from here, and we were to go all the way over the week, all the way to here, he ran 36 total kilometers. Beth ran 15 fewer kilometers than Abe. So let's go back 15 kilometers. So Beth ran 15 fewer kilometers than Abe. So that's 15 fewer kilometers. And so the number of kilometers that Beth ran would be this distance. It would be this distance right over here. So this is kilometers Beth ran. Let me write it like this-- Beth's distance in the week. Beth's distance would be this distance right over here. So how do we figure that out? Well, if we say Beth's distance-- let's just use the letter B for shorthand. So Beth's distance plus 15 kilometers is going to be equal to Abe's distance, is going to be equal to 36 kilometers. Or another way of thinking about it-- Beth's distance is going to be equal to Abe's distance, so 36 kilometers, minus 15. So what is Beth's distance going to be equal to? Well, 36 minus 15-- 6 minus 5 is 1. 30 minus 10 is 20. So it's going to be 21. So Beth's distance is 21 kilometers.