# Avoid the Pitfalls

Common Math Mistakes:

Watch the operations. Read the problems carefully and pay attention to what the test writer wants you to do. Be sure you don’t divide when you should be multiplying. Make sure you are converting word problems to the appropriate math operation. Be very careful with signs (negative times negative is positive and a positive minus a negative is addition).

Percents of percents. When the question asks you to calculate a final percent by doing two percentages (either two increasing, or two decreasing, or one of each) from an initial value, be sure the second calculation is based on the result of the first calculation. For example, if a price went up 10% and then another 20%, the final price is not 130% of the original price. It is 132%. (If you start with 100 and raise that 10%, you get 110. When you raise the 110 another 20%, the increase is 22. That’s why you end up at 132.)

Weighted averages. When calculating averages of unequally sized groups or rates, be sure you “weight” the information you are given. Do not treat the two groups equally. If a group of 5 has an average of 82 and a group of 15 has an average of 90, the average for all 20 is NOT 86. It is 88.

Proportions and Ratios: Be careful to read the question and the possible answers to compare the right groups (parts and whole). Some questions compare parts to parts. Others compare a part to the sum of other parts.

Interval Counting. Remember the distance between two values on the number line is the difference of the two values. However, the number of integers involved is the difference plus one. For example, how many interstate mile markers are there between Orlando (mile marker 272) and Ft. Lauderdale (mile marker 58)? Remember this question doesn’t ask how many miles it is. Think about a number line. If you start at 0 and stop at 5, how many integers are there? Now subtract 0 from 5. Why is there a difference? Try this: If I print pages 21 through 36 of a research paper, how many pages did I print? Hint: It isn’t 15! It’s 16 (the difference plus 1). If you don’t get it, try an easier one. What if I printed pages 21 through 22? It is still the difference plus 1. “The world of math is a world of patterns.”

Assuming the Sequence. Sometimes on questions about lines, the order of the points is not indicated and there is no diagram provided. Be sure to draw ALL POSSIBLE sequences before you answer the question. For example: X, Y, and Z are points on a line. X is 1 unit from Y and Y is 2 units from Z. How many different ways can you sequence these point on a line?

Length’s Effect on Area. For squares and circles doubling the length of a side or radius DOES NOT double the area. For example, a square with a side of one has one-fourth the area of a square with a side of two. Draw a picture and see why this is true. The same is true for a radius of one versus a radius of two. You can do the whole calculation when confronted with these problems. You can also do something very clever: square the ratio of the lengths. For example, if you triple the side of a square the area becomes nine times as large!

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