Question

Ruth is making a banner for her little sister's birthday party. She tapes together pieces of construction paper until the banner is 3 feet long. Each piece of paper is 9 inches long. How many pieces of paper does Ruth need?

Answer 1

4 papers

Explanation:

You know that the final amount of paper needs to be 3 ft long, but each paper is only 9 in.

In order to solve this, you first would convert everything into the same units. This is technically called "dimensional analysis", but in this case, it's just simple multiplication.

Since I prefer to keep everything in whole numbers, I'm converting 3 ft into inches.

You start with your given number:

3 ft

Then multiply by the conversion factor. The units need to cancel out until you have the end goal.

×
`(12 in)/(1 ft)` = 36 in

So as you can see, since there is a "ft" on top, and on the bottom, they'd "cancel out", leaving you with inches (and the numbers, of course).

That's the drawn out version of converting 3 ft into 36 inches.

Now that you know how much total paper you need, you can just divide that by the length of each paper.

36 inches / 9 inches = 4.

You need 4 pieces of paper.

Also, the dimensional analysis is almost useless for this kind of problem, but it becomes important in more complicated conversions you would use in Chemistry, or AP Environmental Science. I hope this helps!