COMPASS Test (Pre-Algebra Section)Page 1 of 2

For official information, visit: http://www.act.org/compass/. Be sure to determine if you will be allowed to use a calculator, and if so, what models are acceptable. The information and tips on this page is based on a COMPASS study guide. I have not taken this test first hand. As always, make sure you find out exactly what will be on your college's test.

This is a quick study guide. For more information about these topics, please review the related lessons on this site.

Basic Operations with Integers

Addition:

Make sure you feel comfortable working with a number line, in both the positive and negative directions. Adding two positive numbers yields a positive. Adding two negatives yields a negative (think about adding debts). To add a positive and negative, think of the positive as how much money you have, and the negative as how much you owe. Compute the difference. If you owe more than you have, the answer is negative (you are still in debt, but less so). If you have more than you owe, the answer is positive (you paid your debt, and you still have money left over).

Subtraction:

Change the subtraction sign to an addition sign. Change the sign of the second number, remembering that a positive number will often have no sign at all. Then proceed as above.

Multiplication:

Pos * Pos = Pos
Pos * Neg = Neg
Neg * Neg = Pos

Remember, like signs yield positive, unlike signs yield negative.

Division:

Follow the exact same rules as multiplication.

Basic Operations with Fractions

The top number is the numerator, and the bottom number is the denominator.

Adding and Subtracting:

The fractions must have a common denominator. If they do, just add/subtract the numerators, and leave the denominator the same. If the denominators are not the same, determine the LCM of the denominators, i.e., the LCD. Write out multiples of each of the denominators, and pick the lowest multiple that is common to both denominators. Convert each fraction so that it has that denominator by multiplying numerator and denominator as needed. Whatever you do to the numerator must also be done to the denominator.

Multiplying:

Multiply the numerators straight across, and the denominators straight across. To multiply a fraction times a whole number, first put the whole number over a denominator of 1.

Dividing:

Change the division sign to a multiplication sign, and change the section fraction to its reciprocal (i.e., flip it upside down). Then multiply as above.

Simplifying:

Find the GCF of the numerator and denominator. Divide numerator and denominator by the GCF. If you're having trouble finding the GCF. Find some number that divides both numerator and denominator, and do so. Repeat (in some cases dividing by a different small number) until you can't reduce anymore.

Basic Operations with Decimals

Almost certainly, your test will allow the use of a calculator, so I will omit the manual procedures for doing computations with decimals. Remember that if you see what looks like a fraction, it is really a division problem. What you are doing is numerator divided by denominator. That means the numerator gets entered into your calculator first.

Square Roots (Radicals)

To find the square root of a number, ask yourself what number times itself equals that number. For example, √81 = 9, because 9 times itself equals 81.

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