Abook shelf is 2 feet long. each book on the shelf is 5/8 inches wide. how many books will fit on the shelf?

we will need four cases and a bookend

Step-by-step explanation:

STEP 1 - How many books fit on 1 shelf?

We divide 2%263%2F4 feet by 1%2F4 feet.

We could use fractions, or decimals.

We could even transform both measurements to inches.

The result is that 2%263%2F4 feet divided by 1%2F4 is 11 exactly.

It divides evenly, so we can fit 11 books per shelf, tightly packed, with no room to spare.

Calculation using fractions:

2%263%2F4=2%2B3%2F4=8%2F4%2B3%2F4=11%2F4 (transforming mixed number into improper fraction)

11%2F4�1%2F4=11%2F4�4%2F1=11

Calculation using decimals:

If we know that 2%263%2F4=2.75

and we know that 1%2F4=0.25

and we can use a calculator, it is to divide

2.75%2F0.25=11

If we prefer to measure in inches we would think that

the shelf width is 33 inches

and each book is 3 inches wide,

so we divide 33%2F3=11 to find that 11 books fit on each shelf.

STEP 2 -How many shelves will be used?

We divide the 35 books into piles of 11 books.

We find that we can make 3 piles of 11 books, and we will have 2 books left over.

We will need highlight%284%29 shelves (and a bookend).

Three (3) shelves could have 11 books (full shelves),

but you need at least one more shelf, for a total of 4 shelves.

If the first 3 shelves are filled with 11 books each,

the fourth shelf could hold the remaining 2 books.

Or you could arrange the books differently, but you need at least 4 shelves.

The calculation:

1 pile = 1 x 11 books = 11 books

2 piles = 2 x 11 books = 22 books

3 piles = 3 x 11 books = 33 books

4 piles = 4 x 11 books = 44 books

Obviously, we can make 3 piles of 11 books, and we will have 2 books left over.

35 - 33 = 2

The teacher would say that 35 divided by 11 is 3 with a remainder of 2.

When we do long division, we do exactly the calculations above.

THE WRONG WAY:

Someone could figure that 35 books at 1%2F4 foot per book require

35%281%2F4%29=35%2F4 feet of shelf space.

Then, dividing the space needed by the space per shelf,

35/4 feet divided by 2%263%2F4 feet,

that person could find that 3&2/11 shelves are needed,

and round up to 4 shelves.

The result is the same in this case, but the approach is wrong,

because if the measures of book and shelf width were different,

you might find a number of shelves that could not hold the books,

unless we cut some of the books in pieces.

New! FREE algebra solver that shows work:

3x-x+2=4

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step-by-step explanation:

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