Book review: Math Doesn’t Suck

Last week, I finally managed to get my hands on Danica McKellar’s book Math Doesn’t Suck, and now I’m recommending all of my girl students read it.

In the book, McKellar offers explanations, tips and practice problems for some of the topics that give most kids fits in math class- factors, fractions, decimals, percents, proportions, and encountering variables for the first time, and she frames it all in stories just about any girl can relate to.

Along the way, she offers insight into her own experiences with math and being a smart girl, and encourages the reader to find their own confidence and to not give that up for anyone.

The book also has an accompanying website that offers full explanations of the practice problems in the book, and provides a forum where students can gather to talk about math education, math and science careers for girls, and being both beautiful and smart in this day and age.

Maybe the stick figure in the second panel above should read it, if only to get a clue!

Combining like terms

To make your math life simpler, we’re going to attack combining like terms. Let’s start by defining what we mean when we talk about terms. A term is a mathematical unit that can be acted upon by other units through the four basic operations.

Okay, that sounds pretty scary. It’s not really that bad. A term is simply each bit of an expression or equation. Terms can look like 7, 5y, 2b², or x³y⁴.

So, now that we know what a term is, what makes terms “like”? Like terms have the exact same variables, raised to the exact same powers. For example, 2b² and 6b² are like terms because they both have b² in them. 7 and 5y, however, are not like terms because 7 has no variable.

Why would we want to combine like terms, anyway? Imagine you had the following expression to deal with:

2b² + 7 + 6b²That’s pretty messy. If we combined those b² terms together, the expression would look a lot neater, and would be easier to work with. So let’s combine them.

We can’t work with the 7 because it doesn’t have a b² term, so we’ll just ignore it for now. Instead, we’ll focus on combining 2b² and 6b². What we really have here is:

2b² + 6b²which can also be looked at as:

(b² + b²) + (b² + b² + b² + b² + b² + b²)We’re essentially just adding b² terms together. How many b² terms do we have all together?

There are 8 b² terms, so we can combine 2b² and 6b² into 8b². Our simplified expression now reads:

8b² + 7 which looks far less scary to work with.

The order of operations

The order of operations tells us how to handle complex expressions to make sure we get the correct answer. This order is: parentheses, exponents, multiplication and division, addition and subtraction. We remember this order through the acronym PEMDAS.

For example, the expression (5 + 3) * 4 would become 8 * 4, which equals 32. If those parentheses weren’t there, the problem would be 5 + 3 * 4, which would become 5 + 12, which equals 60. It’s an entirely different problem.

You might notice that I have multiplication and division in a group together in the list, and I’ve also grouped addition and subtraction in the same group. This is because multiplication and division are done together as they occur starting from the left.

Let’s look at the problem 28 / 7 * 4. Your first instinct might be to multiply 7 and 4 together, which would give you 28, thereby making the answer 1. However, because the division comes first, you have to divide 28 by 7 to get 4, and then multiply that 4 by 4 to get 16. Not exactly the same as 1, is it?

The same is true for addition and subtraction. Look at 9 – 3 + 2. Again, you might try to start by adding the 3 and 2 together to end up with 9 – 5, which leads to the answer 4. But, you should start by subtracting 3 from 9. This gets you an answer of 6, which you then add to 2 to get the correct answer of 8.

It would be very confusing to try to show this in our acronym, though, so you’ll have to remember this on your own.