Topic F: Distributive property and problem solving using units of 2–5 and 10
Current time:0:00Total duration:3:01
A theater has a total of 63 seats in a rectangular grid. Here they are, right over here. It currently has 9 rows, each with an equal number of seats. We see that-- 1, 2, 3, 4, 5, 6, 7, 8, 9 rows. How many total seats will it have if it adds 2 seats per row? So what we want to figure out is the total number of seats. So let's say that the total is going to be equal to the number of seats that the theater already has. And they tell us that they have 63 seats in a rectangular grid. So it's going to be 63 seats plus the new seats, plus however many it adds. So plus the new seats. Well, what are the new seats going to be? Well, the new seats are going to be-- I have 9 rows, and I'm adding 2 seats per row. So the new seats are going to be 9 rows times 2 seats per row. So we could say that the total is going to be equal to 63 plus 9 times 2. And we 'll talk more about order of operations. But clearly, in this situation, we want to multiply 9 times 2 to figure out the total new number of seats. And then we want to add that to 63. And if we just write it like this, multiplication takes-- you will always do multiplication. And when you just see it in a row like this, you'll do the multiplication before you do the addition. So this is literally saying, hey, multiply 9 times 2 first, then add to 63, which is exactly what we care about. And what is 9 times 2? Well, let's add those 2 seats per row. So that's 2, 4, 6, 8, 10, 12, 14, 16, and 18. So 2 times 9. 2, 4, 6, 8, 10, 12, 14, 16, 18 is 18. So we're adding 18 new seats. So let me write this down. I covered up my old total. So total is equal to 63 plus 18. I had 63 seats. I'm now adding 18 seats. So total-- my total number of seats-- is now going to be 63 plus 18. Let's see, 8 plus 3 is 11. 60 plus 10 is 70. 70 plus 11 is going to be-- I have 80-- I have 81 seats. I now have 9 rows with 9 seats each, which gets me 81 total.