IN THIS CHAPTER

Overlooking signs

Confusing similar formulas and terms

Freaking out over fractions

Knowing how to perform certain types of math operations is a big part of solving problems correctly, but it isn’t everything. Caution is also important. Avoiding common math errors involves both. Think back to times when you saw what you missed on math tests and thought, “Oh yeah, I had this mixed up with that!” This chapter helps you avoid that exact situation. Errors are always a threat. Don’t let them get you.

Misusing Negative Signs

In our observations, math mistakes occur most frequently when negatives are involved. Negatives are to math problems what land mines are to war zones, except they’re only dangerous to math scores. That’s the good news. When you see a negative sign, you should turn your level of caution up a notch or two. Such a small symbol has so much power to transform a quantity. Imagine being told that you have $1 million in a bank account and then being told, “Oh, I’m sorry. I didn’t see the negative sign. You have –$1 million. You are that much in debt.” It’s a completely different picture. One misuse of a negative sign will usually wreck an entire answer. See Chapter 4 for the lowdown on negative numbers.

Multiplying by an odd number of negative factors results in a negative product, and multiplying by an even number of negative factors results in a positive product. Also keep in mind that the sum of two negatives is a negative and the sum of a negative and a positive has the sign of the number with the greater absolute value.

You will have a calculator to use on the Praxis Core exam. When you work with negative numbers, you should use the calculator even when you feel like you don’t need it. Safety is a big issue in math.

Confusing Perimeter and Area

Many people mix up the formulas for perimeter and area. Remember that perimeter is the distance around something. If it is expressed in units, it’s expressed in one-dimensional units, such as meters (m), centimeters (cm), feet (ft.), and inches (in.). Area is two-dimensional. It is the amount of a plane inside a two-dimensional figure. When area is expressed in units, the units are two-dimensional and have an exponent of 2. Such units include m², cm², ft.², and in.². For more details on calculating perimeter and area, turn to Chapter 6.

The perimeter of a circle is also called the circumference. Mixing up the formula for circumference with the formula for the area of a circle is common. Both formulas involve only , r, and 2, but in different arrangements. The formula for the circumference of a circle is . The formula for the area of a circle is . So you see how they’re especially easy to confuse — it happens all the time. Be very careful with the formulas for area and perimeter.

Incorrectly Combining Like Terms

Only like terms can be combined, and terms have to meet certain conditions to be like terms. They have to either have no variables or have exactly the same variables with the same exponent per corresponding variable. Remember that when no variable is shown with an exponent, its understood exponent is 1. 5xyz and 4xyz can be added to get 9xyz, and 4x²y³z⁴ can be subtracted from 5x²y³z⁴ to get x²y³z⁴. However, can’t be simplified because the two terms are not like terms. z does not have the same exponent in both terms. Take a look at Chapter 4 for a review of exponents and Chapter 5 to see how they work in algebraic terms and equations.

Messing Up when Moving Decimals

Some really common math errors involve calculations and rewritings that require moving a decimal to the right or left. The two major areas of math that entail decimal movement are using scientific notation and converting between decimals and percents. Both involve doing something and then making up for it by undoing it. You can do this smoothly if you keep in mind that multiplying by a multiple of 10 can be done by moving a decimal to the right and dividing by a multiple of 10 can be accomplished by moving a decimal to the left. Decimals and percents are reviewed in Chapter 4.

Not Solving for the Actual Variable

Solving an equation or inequality involves stating what a variable equals or could equal. A mistake people commonly make is saying what something that almost looks like a variable could equal. For example, you may think an equation is solved by the conclusion . That’s not a solution. It shows a value for the opposite of the variable. To solve for x, you need a statement about x at the end, not –x. Solving for x (or any other variable) is all about the value of x (or whatever the variable is). Your final statement must be about what x equals, not about what 3x, or , equals, for example. Chapter 5 tells you everything you need to know about solving for variables.

Misrepresenting “Less Than” in Word Problems

When an operation is described with English words instead of mathematical symbols, part of your challenge is to represent the operation correctly. The most common mistake made in doing that is incorrectly representing a certain amount less than a number. The quantities are often falsely reversed. For example, “6 less than a number” can be represented by x – 6, but it cannot be represented by 6 – x. The latter represents a certain amount less than 6, not 6 less than a certain amount. Check out Chapter 5 for a more detailed review of this concept.

The confusion that commonly exists here results from the fact that the subtracted quantity is mentioned in the description before the quantity from which it is subtracted. Be careful with that. 4 less than 7 is 7 – 4, not 4 – 7.

Mixing Up Supplementary and Complementary Angles

The words “supplementary” and “complementary” are often confused. Preparing ahead of time to avoid that confusion will help keep your work safer. Complementary angles have measures that add up to , and supplementary angles have measures that add up to . Here’s a silly but effective mnemonic statement to help you remember the difference: If you live to be 90, you deserve a complement. If you live to be 180, you are super. You can find out all about angles in Chapter 6.

Finding the Wrong Median

The most common mistake that happens in finding a median of a set of data is failing to put the data in order. The median is the middle number or mean of the two middle numbers of a set of data when the data is in order. Getting that for a set of data that is not in order is not very likely to result in the actual median. Get the lowdown on determining the median, mean, and mode in Chapter 7.

Fearing Fractions

So “fearing fractions” isn’t a specific mistake, but fraction problems create all sorts of opportunities for errors, and that scares people.

Common denominators are necessary for adding and subtracting fractions, not for multiplying or dividing them. The distinction is extremely important.

Multiplying fractions involves multiplying the numerators and multiplying the denominators, and dividing by a fraction is the same as multiplying by its reciprocal. Adding and subtracting fractions involves getting a common denominator and then operating with only the numerators. The denominator doesn’t change unless the sum or difference has to be simplified. You can review computing with fractions in Chapter 4.

Forgetting about Fractions in Formulas

Some of the formulas you need to know have in them, and the is often neglected. That can wreck your answer. For example, the formula for the area of a triangle is . That is half of bh, so calculating just bh won’t give you the area of a triangle. The area of a parallelogram is bh because a parallelogram can be split into two congruent triangles. The topic of area is covered in Chapter 6.