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
    1 month 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!

  • 1 month 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
    1 month 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.

  • 1 month 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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  • 2 months ago

    how may children are required on one side of a seesaw

    to balance their father on the other side

  • 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
    2 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
    2 months ago

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

  • 2 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

  • 2 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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