Math CentralQuandaries & Queries


Question from Lesley, a teacher:

If I have a board 12 feet long and am building shelves 2 1/4 feet in length, how many inches are left?

Hi Lesley,

In order to determine how many inches are left over you will have to do some converting - from feet to inches. You can choose to convert your feet right off the bat and then you can just simply subtract the number of shelves (their length) from the total board.

To do a conversion, there are 12 inches in a foot, so we would take let's say 10 feet and we set up a proportion:

Our proportion reads 10ft/xin = 1ft/12in and we solve for the unknown by cross multiplying. Make sure your proportion is set up proper and you'll have your conversion.

Hope that helps!

Hi Lesley,

Here is another way to approach the problem.

Each shelf is 2 1/4 feet long so 4 shelves will require $2 \times 4 = 8$ plus $\frac14 \times 4 = 1$ feet so 4 shelves will require $8 + 1 = 9$ feet. (I choose to look at 4 shelves since $\frac14 \times 4$ gives me an integer, not a fraction.)

After cutting 4 shelves I have $12 - 9 = 3$ feet left. Cut one more shelf. How many feet are left? How many inches is that?


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