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Number Basics for SAT Math

This may be the most basic of all the SAT Math reviews you read on TestSherpa – but take nothing for granted. You must know the basics about numbers in order to interpret the questions correctly.

Number Basics for SAT Math

Number Basics for SAT MathThe SAT Math section will use various words about numbers. This module will help you understand the basic math lingo so that you won’t be intimidated when you see it on test day. You have seen these terms before, but it may have been a while since you had to really know what they mean.

Here’s a quick refresher:  

Whole Numbers also called Integers: Numbers you could count on your fingers and toes and also zero (i.e., 0, 1, 2, 3, 4, 5, etc.). Positive or negative. . No fractions or decimals

Natural Numbers: Positive whole numbers without zero.

Integers: All positive and negative whole numbers, and zero.

Rational Numbers: Also called fractions. A ratio or quotient of two integers, usually written in the form a/b, where b is not zero and a and b are both integers.

Irrational Numbers: Numbers that cannot be expressed as a rational number (a fraction). In other words, the decimal places keep going, and going, and going without repeat or end…reductio ad absurdum is the fancy Latin term mathematicians throw around. Try the square root of the number 2. A little irrational number trivia for you next dinner conversation – any root of any natural number is either a natural number or irrational.

Real Numbers: Any number you could place somewhere on the number line. This includes all rational and irrational numbers.

Dealing with Odd and Even Numbers

Multiples of two (2) are even numbers. All other integers are Odd. Odd numbers have a remainder of 1 when divided by 2. This includes negative numbers.

It is helpful on the SAT Math section to understand the behavior of even and odd numbers when they are added, subtracted or multiplied. Division isn’t so easy, as you won’t necessarily get an integer as an answer when you divide one integer by another (e.g., 6 ÷ 4 = 1.5)

The rules are easy to remember.:

  • Add or subtract the same you get even (even + even = even, odd + odd = even)
  • Add or subtract mixed you get odd (even + odd = odd).
  • Multiply by the same you get the same (even x even = even, odd x odd = odd)
  • Multiply by mixed you get even (even x odd = even).

This should help you by making it easier to eliminate answer choices. 

Positives and Negatives

Anything greater than zero is a positive number. Anything less than zero is a negative number. Zero is neither positive nor negative. On the SAT (and in most places in your life) a positive number is simply expressed as the number itself (e.g., 9). Negative numbers have a negative sign before the number (e.g., -9).

Positive numbers are straightforward enough, but negative numbers sometimes cause our students some grief. Negative numbers have different behavior when you add, subtract, multiply and divide them.

When you add a negative, it is like subtracting. For example:

15 +(-3) = 12

Conversely, if you subtract a negative number, you are essentially adding. For example:

15 – (-3) = 18

Two wrongs don’t make a right, but two negatives do make a positive. This is also the case in multiplication and division. Thus, if you have an even number of negative numbers in your problem, your answer will be positive. If you have an odd number of negatives in your problem, the answer will be negative. So, if you multiply two positives or two negatives together, you will get a positive number as the answer. If you have a positive and a negative, the answer is negative. For example:

3 x 6 = 18

3 x (-6) = -18

(-3) x (-6) = 18

12 ÷ 2 = 6

12 ÷ (-2) = -6

(-12) ÷ (-6) = 2

(-3) x (-4) x 2 = 24

3 x (-4) x 2 = -24

And what are the parentheses about?

Anything in the parenthesis relates to the number inside the parenthesis itself. Anything outside of the parenthesis is an operand and relates to everything else inside of the parenthesis. The fancy SAT Math way of saying that is that the negative sign outside of a parenthesis is “distributed” to each number inside the parenthesis.

To solve these types of problems, you may have been taught the mnemonic “PEDMAS.” That stands for the order you should solve these problems in:  parenthesis, exponents, division, multiplication, addition and subtraction. For example:

5 – 4 + (2 – 8) – (3 + 6 – 11) =

Simplify the parenthesis first…

5 – 4 + (- 6) – (- 2) =

Adding a negative is the same as subtracting (-6), subtracting a negative is the same as adding (+2)

5 – 4 – 6 + 2 =

-3

Absolute Values

Technically, the absolute value of a number is the distance on the number line from itself to zero. Since -7 is 7 numbers from zero, so the absolute value of -7 is 7. Most students just think of the absolute value of any number as the positive value of that number. The way absolute numbers are written on the test is with two surrounding vertical lines like this: |a|.

Now return to our SAT page to read another lesson.

Treat anything within the lines like you would a parenthesis – that is, do the math inside the bars and then take the absolute value. Thus, | 4 – 8 | = 4, not 12 (you don’t make the -8 positive, you take the value and make that the absolute value).