# A Guide to Simplifying Algebraic Expressions

For many students, variables can complicate a question. Let’s look at an example of what I mean:

**The price of ground coffee beans is d dollars for 8 ounces, and each ounce makes c cups of brewed coffee. In terms of c and d, what is the dollar cost of the ground coffee beans required to make 1 cup of brewed coffee?**

A) d/8c

B) cd/8

C) 8c/d

D) 8d/c

E) 8cd

This question is rated “Hard” by the makers of the SAT. As you can see, there isn’t any mathematically difficult concept here; the problem only requires knowledge of multiplication and division, but the variables (*c, d*) make this harder to comprehend. To fix this, choose numbers to plug in for *c* and *d*. Since the number 8 is mentioned, pick numbers that work well with 8.

I’m going to choose d = 16 and c = 4. Let’s rewrite the problem and see if it becomes easier to comprehend.

**The price of ground coffee beans is 16 dollars for 8 ounces and each ounce makes 4 cups of brewed coffee. What is the dollar cost of the ground coffee beans required to make 1 cup of brewed coffee?**

Now that numbers are given, this is a problem our brains are accustomed to solving. If coffee is 16 dollars for 8 ounces, we just divide to find the price per ounce (16/8 = 2). We know it is $2 for every ounce. Next, we know that each ounce of coffee brews 4 cups of coffee. Again, if we want to know the price per cup, we can divide ($2/4 = $0.50). It costs $0.50 to make 1 cup of coffee. You might be wondering, “How do I find $0.50 in the answers?” Simply plug in d = 16 and c = 4 into the answer choices. The answers now become:

A) 0.5

B) 8

C) 2

D) 32

E) 512

From here, we can spot that the correct answer is A.

A word of warning: This method works for algebraic expressions but not algebraic equations. Once you see an “=” or read the word “equals,” you cannot pick any numbers you’d like. Here is an example:

** If a + 2b is equal to 125 percent of 4b, what is the value of a/b ?**

The values of* a* and *b* have now been greatly restricted because of the “equal” statement. Because this question is not multiple choice, algebra skills become necessary. Because this blog post is not about translating word problems, I’m only going to give a brief overview of this problem:

a + 2b = 1.25(4b)

a + 2b = 5b

a = 3b ** <- *Notice that once the relationship between a and b is established, you are welcome to choose values for a and b and then plug them into the statement for which you are solving (in this case,a/b). **

a/b = 3

A final note: When choosing values to plug in for variables, be wary of choosing 0, 1, or 2. These numbers all have special properties that may affect the problem and steer you into a wrong answer. It is best to avoid these values.