Lesson 11: Scales without units
Maya and Mabel are inspecting a 80 to 1 scale floor plan of their new house. The dimensions of the living room in the scaled plan are 4 centimeters by 5 centimeters right over here. What is the area of the living room in the real world? So they gave us these dimensions right over here. This is the scale plan, and then we could figure out these dimensions in the real world by looking at the scale factor right over here. It's an 80 to 1 scale floor plan. And we can assume that the house is much bigger than the floor plan. So the 80, for every 80 units in the house, that represents 1 unit on the floor plan. So if we had 80 meters in the house, that would be represented as 1 meter on the floor plan. If we had 80 centimeters in the house, that would be represented by 1 centimeter in the floor plan. And it goes the other way around. 1 centimeter on the floor plan would represent 80 centimeters in the house. And it's always important to do-- if this confuses you, just always do a reality check that the house should be bigger than the floor plan. So if the floor plan for this dimension of our living room is 4 centimeters, the actual house will be 80 times that. And 80 times 4 is 320-- let me do that in a blue color-- is equal to 320 centimeters. And we can do the same thing for the length of the living room. So 80 times 5 centimeters is going to get us to-- is going to be-- 80 times 5 is 400 centimeters. So we could figure out the area of this room in centimeters, if we like, and I guess, why not? It might be easier to convert it to meters later. So let's see, 400 centimeters times 320 centimeters. Let me write this down. 400 times 320. Let's think about it. 4 times 32 is going to be 120, plus 8, 128. And I have 1, 2, 3 zeroes. 1, 2, 3. So it's going to be 128,000 centimeters squared. Now that's a lot of square centimeters. What would we do if we wanted to convert it into meters? Well, we just have to figure out how many square centimeters are there in a square meter. So let's think about it this way. A meter is equal to-- 1 meter is equal to 100 centimeters. So a square meter, so that's right over there. 1 meter squared would be 1 meter by 1 meter, which is the same thing as 100 centimeters by 100 centimeters. And so if you were to calculate this area in centimeters, 100 times 100 is 10,000, is equal to 10,000 centimeters squared. So you have 10,000 square centimeters for every square meter. And so, if you want to convert 128,000 centimeters squared to meters squared, you would divide by 10,000. So dividing that by 10,000 would give us 12.8 square meters. Now, another way you could've done it, and maybe this would have been easier, is to convert it up here. Instead of saying 400 centimeters times 320 centimeters, you would say, well, 400 centimeters, that's going to be 4 meters. And 320 centimeters, well, that's 3.2 meters. And you would say, OK, 4 times 3.2, that is 12.8 square meters. But either way, the area of the living room in the real world in meters squared, or square meters, is 12.8.