Find the number of tiles needed to cover the bathroom.

eddy2017

eddy2017

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Hi, I have not been posting for a while because I have been very busy and Algebra is consuming most of my free time.
I am posting this problem to see what you think of my approach or if there is a better one or quick calculation.

A bathroom floor measures 8ft by 6ft and is to be covered by ceramic tiles, each tile measures 8 inches by 8 inches. Find the number of tiles needed to cover the bathroom.
I am gonna convert to a single unit. i have chosen inches
so 1ft=12 in
so the dimension of the bathroom floor are now
96 in by 72 in
i have been told that each tile measures 8 in by 8 in so
96 in /8in=12 in^2
72 in/ 8 in= 9^2

12in^2 * 9^2=180 tiles needed to tile the bathroom floor.
 
eddy2017 said:
A bathroom floor measures 8ft by 6ft and is to be covered by ceramic tiles, each tile measures 8 inches by 8 inches. Find the number of tiles needed to cover the bathroom.
I am gonna convert to a single unit. i have chosen inches
so 1ft=12 in
so the dimension of the bathroom floor are now
96 in by 72 in
i have been told that each tile measures 8 in by 8 in so
96 in /8in=12 in^2
72 in/ 8 in= 9^2

12in^2 * 9^2=180 tiles needed to tile the bathroom floor.
Click to expand...
The one thing I'd do differently is the final line:

12in^2 * 9^2=180 tiles needed to tile the bathroom floor.​

You're multiplying tiles by tiles, not square inches by square inches. The area, in square tiles, is 12 tiles * 9 tiles = 108 square tiles.

(Note that it's 108, not 180! Don't get careless at the end, as many of us do.)

Since I always like to check: the area of the floor is 96 in * 72 in = 6912 in^2 (which could also be calculated as 8 ft * 6 ft = 48 ft^2 = 48 * 12^2 in^2 = 6912 in^2). The area of one tile is 8 in * 8 in = 64 in^2; the area of 108 of these is 108 * 64 in^2 = 6912 in^2. So we're good.
 
Dr.Peterson said:
The one thing I'd do differently is the final line:

12in^2 * 9^2=180 tiles needed to tile the bathroom floor.​

You're multiplying tiles by tiles, not square inches by square inches. The area, in square tiles, is 12 tiles * 9 tiles = 108 square tiles.

(Note that it's 108, not 180! Don't get careless at the end, as many of us do.)

Since I always like to check: the area of the floor is 96 in * 72 in = 6912 in^2 (which could also be calculated as 8 ft * 6 ft = 48 ft^2 = 48 * 12^2 in^2 = 6912 in^2). The area of one tile is 8 in * 8 in = 64 in^2; the area of 108 of these is 108 * 64 in^2 = 6912 in^2. So we're good.
Click to expand...
Yes, thanks a lot. I was in doubt about that. I was not satisfied with mutliplying 12 in by 12 in. did not look copacetic somehow. thanks
 
eddy2017 said:
Hi, I have not been posting for a while because I have been very busy and Algebra is consuming most of my free time.
I am posting this problem to see what you think of my approach or if there is a better one or quick calculation.

A bathroom floor measures 8ft by 6ft and is to be covered by ceramic tiles, each tile measures 8 inches by 8 inches. Find the number of tiles needed to cover the bathroom.
I am gonna convert to a single unit. i have chosen inches
so 1ft=12 in
so the dimension of the bathroom floor are now
96 in by 72 in
i have been told that each tile measures 8 in by 8 in so
96 in /8in=12 in^2 ....................................................................................Incorrect
72 in/ 8 in= 9^2 ...... ...................................................................................Incorrect
72 in/ 8 in= 9^2 ...... ...................................................................................Incorrect

12in^2 * 9^2=180 tiles needed to tile the bathroom floor.........Incorrect
Click to expand...
Eddy your solution has multiple missteps. Can you please correct your working and repost the correct solution?
 
Okay, let's see. I am gonna checkmark what i think i did right so you can rectify me later and drop me a hint if i am not so right.
I am gonna convert to a single unit. I have chosen inches
so 1ft=12 in ?
so the dimension of the bathroom floor are now
96 in by 72 in
I have been told that each tile measures 8 in by 8 in so
96 in /8in=12 in^2 ......................................Incorrect ..........................96 in /8 in = 96 in /8 in = 96 / 8 = 12
72 in/ 8 in= 9^2?......................................Incorrect .......................... 72 in/ 8 in= = 72 in /8 in = 9
so far so good, i guess.

12in^2 * 9^2=108 ......................................Incorrect .......................... What are you doing Eddy?

Please do it again Eddy and I'll delete this response.

tiles needed to tile the bathroom floor. ( Dr P rectified me here)
The area, in square tiles, is 12 tiles * 9 tiles = 108 square tiles.?

108 tiles needed. each one has a dimension of 8 in by 8 in.
 
Last edited by a moderator:
another approach could be this one and I thin it is easier and applies a little bit of the mason's logic to it.
same thing I did : get everything into the same units, whether feet or inches. I chose inches, so i can say that the floor is 96 inches by 72 inches.
now, to find how many tiles are needed, I need to find out how many time 8 fits into each of the floor's dimensions.
So
[math]96/8 = 12[/math][math]72/8=9[/math]we can say that the bathroom floor will have 12 rows and each row will have 9 tiles.
that will give us 108 tiles needed to tile the entire area of the floor.
 
Sorry!
I am gonna convert to a single unit. I have chosen inches
so 1ft=12 in
so the dimension of the bathroom floor are now
96 in by 72 in
I have been told that each tile measures 8 in by 8 in so
96 /8=12
72 / 8 = 9

12 * 9=108 tiles needed
 
eddy2017 said:
Sorry!
I am gonna convert to a single unit. I have chosen inches
so 1ft=12 in
so the dimension of the bathroom floor are now
96 in by 72 in
I have been told that each tile measures 8 in by 8 in so
96 /8=12
72 / 8 = 9

12 * 9=108 tiles needed
Click to expand...
I would add a note about 96 /8=12 and 72 / 8 = 9. The calculation is correct, but why are you doing it?
 
I need to fit tiles of 8 by 8 into an area of 96 by 72 inches.
I need to find out how many tiles fit into this space and I am using division to find out.
 
eddy2017 said:
I need to fit tiles of 8 by 8 into an area of 96 by 72 inches.
I need to find out how many tiles fit into this space and I am using division to find out.
Click to expand...
I don't think this is what you are doing. You divided bathroom side lengths by the length of the tile.
If you calculated the area of the bathroom and then divided it by the area of one tile - then, yes, it would be finding how many tiles fit into the area of the bathroom using division.
 
lev888 said:
I don't think this is what you are doing. You divided bathroom side lengths by the length of the tile.
If you calculated the area of the bathroom and then divided it by the area of one tile - then, yes, it would be finding how many tiles fit into the area of the bathroom using division.
Click to expand...
So, what am I doing wrong then?. Isn't it the area of the bathroom floor 8ft by 6ft?.
And each tile 8 by 8 inches.
6912 inches is the total area if the floor in inches. The area of the tile is 64 in
So 6912÷ 64= 108 tiles.
I think this is what you are talking about. I understand now.
 
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eddy2017 said:
So, what am I doing wrong then?.
Click to expand...
I wrote that the calculation was correct. If I were your teacher I would've liked an explanation for those 2 divisions.
What did you find by doing this: 96/8=12?
 
One dimension of the room.
Then the other dimension by doing the other division.
 
eddy2017 said:
One dimension of the room.
Then the other dimension by doing the other division.
Click to expand...
If we consider the resulting tile arrangement as rows and columns, then I would say one division gives us the number of rows and the other gives us the number of columns. Then we multiply the 2 numbers to get the total number of tiles.
 
lev888 said:
If we consider the resulting tile arrangement as rows and columns, then I would say one division gives us the number of rows and the other gives us the number of columns. Then we multiply the 2 numbers to get the total number of tiles.
Click to expand...
I appreciate the way you explained it mathematically but it is exactly what did at #9.
 
eddy2017 said:
I appreciate the way you explained it mathematically but it is exactly what did at #9.
Click to expand...
I wrote twice already that your calculation was correct. I agree that you did exactly the same calculation. But it seemed strange to me that you explained each step in your solution but not the 2 divisions.
 
Okay, lev, it was a good question to ask. I like that. Probing questions to see if something is done with a logic in mind and not mechanically. Thanks. I appreciate that.
 
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