Question

A kitchen floor has 15`1/2` tiles in an area of 2`3/5` square feet. How many tiles are in one square foot?

Answer 1

`155/26`

Explanation:

If a kitchen floor has `15 1/2` tiles in an area of `2 3/5` square feet, then to calculate the amount of tiles in a single square foot we simply need to divide `15 1/2` by `2 3/5`.

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"`

We know the area and the number of tiles:

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

And can rewrite that as:

`15 1/2 div 2 3/5 = "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 3/5`

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

`15 5/10 div 2 6/10`

This works, because `3/5=(3*2)/(5*2)=6/10` and `1/2=(1*5)/(2*5)=5/10`

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 = 155/10`

`2 6/10 = ((2*10) + 6)/ 10 = 26/10`

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

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.