Proportions

Many word problems ask students to convert units.  Sometimes they explicitly ask how many inches are in 5 feet.  But, the "conversion" part of the question often does not seem that obvious.

Anytime you are given a scale drawing (or the scale for something) in a word problem, you can be fairly sure that you are going to have to use a proportion.

What is a scale drawing?

Ratios show how numbers are related.  When you put two ratios together in a proportion, you show that two sets of numbers are related in the same way.

Ratios can look complicated, but they are just fractions that show the relationship between two numbers that increase and decrease together.  You can write ratios with colons (6:5) or as fractions 6/5. 

Proportions are two fractions (that sometimes represent ratios) that are equal to each other.  Proportions are very helpful because you know that they are equal fractions.  If you know that the fractions are equal you can find missing pieces of information by cross-multiplying.  In the next lesson, we'll talk more about creating proportions, for now, let's look at how to solve them. 

When you have a proportion, you can cross multiply to create an algebraic equation that you can solve.