Paul is tiling his bathroom. He would like to make the pattern shown below. What percentage of the area will be covered by white tiles?
The percentage of the area that will be covered in white tiles can be found by dividing the area covered by white tiles by the total area covered in tiles, then multiplying this by 100. Let’s begin then by finding the total number of tiles on the bathroom floor.
The bathroom is in the shape of a rectangle. It has a width of six tiles and a height of five tiles. We can find the total number of square tiles in the pattern by multiplying the number of tiles in each row, which is six, by the number of rows, which is five. This is the same as finding the area of the rectangular floor. Six multiplied by five is 30, so Paul will need a total of 30 tiles to cover his bathroom floor.
Let’s now calculate the number of white tiles. We can see that there are square white tiles and triangular white tiles, which are the square white tiles cut in half. We’ll begin then by counting the number of whole square white tiles that there are. That’s 14. There are also one, two, three, four, five, six, seven, eight half tiles. So there’s a total of 14 full white tiles and eight half tiles. We can make four full tiles with these eight half tiles. This means there are a total of 14 plus four, which is 18, white tiles.
Remember, we said that, to work out the percentage of the area covered by white tiles, we divide the number of white tiles by the total area of the floor and then we multiply by 100. In this case, that’s 18 over 30 multiplied by 100. We can put this into our calculator, and it gives us an answer of 60 percent.
If, however, a question like this had appeared on a non-calculator paper, we could actually convert the original fraction of eighteen thirtieths into a percentage fairly easily. Remember, percent means out of 100. So to change a fraction into a percentage, we begin by making the denominator 100. We can’t multiply 30 easily to get 100. But we can simplify this fraction to make the denominator 10, which is a factor of 100.
30 divided by three is 10. So we also divide the numerator by three, and we get six-tenths. Eighteen thirtieths is equivalent to six-tenths. To make the denominator of this fraction 100, we multiply it by 10. 10 multiplied by 10 is 100 as required. We have to do the same to the numerator. And doing so, we can see that six-tenths is equivalent to sixty one hundredths, which is equal to 60 percent. The percentage of the area that will be covered by white tiles then is 60 percent.