William wants to tile the floor of a rectangular room measuring one meter by eight meters. If the tiles are square with length 20 centimeters, how many will he need?
Let’s start by drawing a sketch of this rectangular room. We know that the shortest side will be one meter. And the longer side will be eight meters. We’re told that William wants to put down square tiles that are 20 centimeters long.
If William starts by putting tiles along the one-meter width, then how many 20-centimeter tiles will fit into this edge? Let’s recall that one meter is equal to 100 centimeters. So we need to work out how many 20-centimeter tiles will fit into 100 centimeters. We calculate 100 divided by 20, which is five.
Now we know that, along the width one meter, there will be five tiles. Now let’s consider how many tiles will fit along the length of the rectangular room that we know is eight meters long. Here we can consider how many centimeters will be in eight meters. If we consider the conversion that one meter is equal to 100 centimeters, then eight meters is eight times larger. So our 100 centimeters must also be eight times larger. So we can say that, in meters, it’s equal to 800 centimeters.
And now to calculate how many 20-centimeter tiles fit into 800 centimeters, we work out 800 divided by 20, which gives us 40. So now if we look at the diagram of our rectangular room, we can see that there are 40 tiles along the length and five tiles along the width. We could think of this as five rows of 40 tiles each. To work out the total number of tiles, this would be equal to five times 40, which is 200. So our answer for the number of tiles that William needs is 200.