Jenn asked in Science & MathematicsMathematics · 4 months ago

# How many 9 x 9“ tiles are needed to cover a floor that is 8‘ x 10‘? Got answer but why do I have to convert first ?

I figured out the answer but was wondering why you can’t find the area first in ft then convert that to inches.  The work in pink is wrong but I don’t understand why.

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• Jim
Lv 7
4 months ago

8ft (12in/ft) (1tile width/9in) x 10ft (12in/ft) (1tile length/9in) = 142.22222 tiles

Rounds to 143 tiles <<<<

Of course, irl you buy 10% (or 1 box) more for wastage.

The technique used is Unit Cancellation, and is bar far the easiest way to work the problem!

• 4 months ago

feet are not the same as inches. so you need to make the units the same before doing the division. Either express the tiles in square feet or the area in square inches

one square foot = 12*12 square inches

9 inches by 9 inches = 81 square inches or 81/144 = 9/16 square feet

so:

80 square feet ==> 80 /(9/16) tiles = 80*16/9 tiles = 142.222... tiles

or floor = (8 * 12) * (10*12) square inches

==> (8*12/9) * (10*12/9) tiles = 96 *120 /81 tiles = 142.222... tiles

• RockIt
Lv 7
4 months ago

If you've ever done tile work before you will know to grab an extra box of tiles anyway regardless how many it takes to cover it because you will use more.  Some will be cracked, you will break some, you will cut some incorrectly, etc.

• 4 months ago

Square conversions are 2 times the rate. 80ft² = 80*12*12 = 11520 inche²

Height = 8ft *12 = 96in / 9 = 10.6666 tiles

Width = 10ft *12=120in / 9 = 13.3333 tiles

One column of the Height can be filled with the splitted row from the Width.

So you need 11*13=143 tiles, and will have a spare of 0.89 tiles ( 3*24 inches)

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• 4 months ago

how may children are required on one side of a seesaw

to balance their father on the other side

• 4 months ago

You convert first in order to get everything into identical units.  That makes it possible to proceed.

8' = 96 inches

10' = 120 inches

96 * 120 square inches / (9 * 9 square inches) =>

(96/9) * (120/9) =>

(32/3) * (40/3) =>

(10 + 2/3) * (13 + 1/3) =>

130 + 10/3 + 26/3 + 2/9 =>

130 + 36/3 + 2/9 =>

130 + 12 + 2/9 =>

142 + 0.2222222

You can't purchase partial tiles, so you'd need 143.  Add another 10% for waste and you're looking at around 160 tiles altogether.

But even the initial method of dividing area by area was wrong.  In reality, we'd have a grid of 11 tiles by 14 tiles, for 154 tiles total when they're purchased.

• ted s
Lv 7
4 months ago

1st comments : it is not 80 ft , rather 80 sq ft.....2nd : a 9in by 9 in is (3/4) ft by (3/4) ft = 9 / 16 ths sq ft....80 / ( 9 / 16)  = 142 & 2/9ths tiles....8 ft = 96 in and 96 / 9 = 10 + and 10 ft = 120 in and 120 / 9 = 13 & 1/3 tiles ...so 130 whole tiles fit into the space & the rest is partial tiles

• rotchm
Lv 7
4 months ago

Hint: your 8*10 = 80 ft is wrong. Take care of your UNITS. See it now?

• 4 months ago

your units are wrong.

8' x 10' = 80 ft²

(square feet, NOT feet)

80 ft² x (12 in/ft)² = 80•144 in² = 11520 in²

tiles are 9x9 = 81 in²

11520 in² / 81 in²/tile = 142+ tiles

• 4 months ago

You didn't use the right conversion factor.

When you multiply 8 ft. by 10 ft. you get 80 *square* feet.

A square foot is 12 inches by 12 inches = 144 *square* inches.

So you should have multiplied by 80 * 144 = 11,520 *square* inches

Yes, you can do it in the order you did in pink, but you must use the conversion of 1 sq. ft = 144 sq. inches, not just 1 ft = 12 inches.

Summary:

Always use the correct conversion factor.

Always use the correct units (e.g. *square* units) for area.

In reality, you would never calculate it this way saying you need 142 2/9 tiles. First you are going to end up trying to patch in with partial tiles making for a messy job. Second, you are inevitably going to break a tile, cut it wrong, have a damaged tile, etc. So you should generally buy about 10% more than you need.

I'd solve it by figuring out how many tiles were needed in each direction.

8 ft. = 96 inches --> 96/9 = 10 2/3 tiles

10 ft. = 120 inches --> 120/9 = 13 1/3 tiles

I'd probably just round up to 11 by 14 = 154 tiles, and then get another 5-10% on top of that. I'd also consider how many tiles are in each box and round to a whole number of boxes.

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