Operation "Stop the Slimy Aliens."

I was about to go to bed on a peaceful night when I heard a loud "thud!" that sounded like it came from far away. Then paparazzis were throwing rocks on my bedroom window. "We need your help! The aliens are here to kill us all unless you teach them about proportions!", they said. "I knew one day would come in where you would need my brains," I replied.

To explain what proportion is to the aliens, I used 3 questions.

First of all, a proportion is a relationship that says that two ratios or two rates are equal. It can be solved in two ways; chart form and fraction form.

1) Six chairs are always placed with every two tables at McNeill higschool. Supposing a room has 72 chairs, how many tables does it have?

Proportion problems always (or usually) has 3 important facts/numbers given. In this case, they are written un purple. Let's solve this problem using the Tchart.

As you see all I did was to set up a chart, labeling each side "chairs" and "tables". I put the numbers (6, 2 and 72) in the column where they belong. In order to know what the missing spot is, we have to figure out how 6 became 72. In this case, it was multipled by 12. The simple rule we follow is that whatever we do to one side, we do to the other. Therefore we multiply 2 with 12 as well. We get 24.

The room has 24 tables.

2) If two pencils costs $1.50, how many pencils can you buy with $9.00?

As you see, I set up the two columns again. Except this time I labelled them differently, according to the given facts from the question. I put the numbers (1.50, 2, and 9.00) in the columns where they belong. To find the missing value. we have to figure out how 1.50 became 9. Then we follow "the rule" which I stated in the first question. We multiply 2 by 6 to get 12.

You can buy 12 pencils with $9.00.

3) Sally has to make rectangle boxes. The proportion of it's length and width had to be the same. A big box has a length of 21 m. and a width of 14 m. A small box has to have a width of 6 m. What will it's length be?

We will now solve this problem in fraction form.

All i did was to set up all 3 given numbers in fraction form, labelling them as length and width. To find the missing value, we have to figure out how 14 meters became 6 meters, as shown in the diagram. Then we we the same for the other side. So if 14 meters was divided by 2.333, then we divide 21 meters by 2.333 as well. And we get 9 meters.

The length of the small box should be 9 meters.