A kitchen floor has 151/212 tiles in an area of 23/535 square feet. How many tiles are in one square foot?

1 Answer
Nov 15, 2015

155/2615526

Explanation:

If a kitchen floor has 15 1/21512 tiles in an area of 2 3/5235 square feet, then to calculate the amount of tiles in a single square foot we simply need to divide 15 1/21512 by 2 3/5235.

An easy way to think about that is that the total number of tiles equals the area multiplied by the number of tiles per square foot.

"number of tiles" = area * "tiles per square foot"number of tiles=areatiles per square foot

We know the area and the number of tiles:

15 1/2 = 2 3/5 * "tiles per square foot"1512=235tiles per square foot

And can rewrite that as:

15 1/2 div 2 3/5 = "tiles per square foot"1512÷235=tiles per square foot

Our problem is now to divide two mixed numbers. We're going to need to take two steps to simplify this for ourselves. First, let's make the denominators of those two fractions equal.

15 1/2 div 2 3/51512÷235

10 is divisible by both 2 and 5, so let's make the denominator 10.

15 5/10 div 2 6/1015510÷2610

This works, because 3/5=(3*2)/(5*2)=6/1035=3252=610 and 1/2=(1*5)/(2*5)=5/1012=1525=510

We can always multiply the numerator and denominator by the same number and we'll get a fraction of equal value.

We now want to express both numbers as improper fractions.

15 5/10 = ((15*10) + 5)/ 10 = 155/1015510=(1510)+510=15510

2 6/10 = ((2*10) + 6)/ 10 = 26/102610=(210)+610=2610

So now we're diving two improper fractions, like so:
155/10 div 26/1015510÷2610

Because we have two fractions we can simply flip one of the fractions, and multiply:

155/10 * 10/26 = (155 * 10)/(10*26) = (155 * \cancel{10})/(\cancel{10}*26) = 155/26

And, that's our answer.