Advice on Translating Word Problems into Algebra?

Ah, great question! This is one of my favorite topics...so many sentences actually embed the equation right in them, and it comes down to the "language of mathematics":

These words translate directly into symbols:

Is (or any form of "to be") --> =
Of --> * (multiplication)
Per --> / (division)
Greater than --> > (in an inequality) or + (in an equation)
What --> x (your variable)



So...if a sentence says:

What is 20% of 15?

You can directly translate that to:

x = 20/100 * 15
x = 1/5 *15
x = 3


Or if it asks:

15 is what percent of 75?

That translates to:

15 = x/100 * 75
15 = 3/4 x
x = 20


The key with percents is that the percentage must be taken "of" something, so if it asks:

What is 30% greater than 40?

Then you have to determine what the % change is in terms of. Here, you'd increase 40 by a percentage of itself:

x = 30/100 * 40 + 40

x = 1200/100 + 40

x = 52



To me, the important terms in these words-to-equations are usually "is" and "of". "Is" sets up your equation, and when fractions or proportions are present that word "of" may be inferred ("of itself"), so you'll need to be careful about that. but try this on a set of word problems and I think it will give you a great start...

Key to handling word problems is to break them down. Don't try to take a "big picture" view from the start. Go phrase by phrase through the problem making sure you translate one point at a time. Most of my students get lost by trying to force all the information into a single expression from the start.

It is also important to recognize the variety of terms that can be used to represent math terms in a word problem. Watch for "non-math" words such as "combined", "together", "older than" or "excluding" that may mean the same as "+" or "_".