There are 420 books on a bookcase with 7 shelves. each shelf has the same number of books. how many books are on 4 shelves? 28 60 120 240

If we have 420 books for every 7 shelves and are looking for how many books are on 4 shelves, we need to set up fractional proportions.

We have 7 shelves for every 420 books, so we will have our first fraction like this:
7/420.
We also have 4 shelves for every x books, so our second fraction will be 4/x.

Set these fractions up as an equation.
7/420 = 4/x

To solve for x, we need to cross multiply the numerators of one fraction with the denominators of the other fraction.
In other words, multiply the top number of one fraction by the bottom number of the other question.

It should look like this:
7(x)
420(4)

7(x) = 7x
420(4) = 1680

Set your products up as an equation.
7x = 1680

Now to solve for x, we need to simplify.
Currently, x is being multiplied by 7.
To get x alone, divide 7x by 7.
Remember, what you do to one side of an equation, you must do to the other, so divide 1680 by 7.

7x / 7 = x
1680 / 7 = 240

You are left with:
x = 240.

For every 4 shelves you have 240 books.

I hope this helps!