Numbers & Operations
Positive/Negative/Undecided
Here’s an example of a number line:
Negative numbers can mess with your head. Looking at the number line, you can see that –2 is greater than –5, but your mind doesn’t like this because it’s used to positive numbers, and 5 is greater than 2. The SAT loves to set traps like this using negative numbers. Be vigilant.
You also need to know how multiplying and dividing negative numbers affect an equation. Study this chart and memorize the eight possible combinations:
Multiplication Division
positivepositive = positive positivepositive = positive
negativenegative = positive negativenegative = positive
positivenegative = negative positivenegative = negative
negativepositive = negative negativepositive = negative
Negative Numbers
An item that includes negative numbers and parentheses can be tricky:
1. 4 + 2 – (2 – 6) =
When you see a negative sign before parentheses, you need to distribute the negative across the parentheses. So –(2 – 6) becomes –2 + 6:
4 + 2 – (2 – 6) =
4 + 2 – 2 + 6 = 10
Absolute Value
The cure to negative numbers is absolute value. The absolute value of a number is the distance between any given number on the number line and zero. This distance is never negative. If you’re traveling from 3, the distance from 3 to zero is three spaces. If you’re traveling from –3 to zero, the distance is also 3 spaces, so the absolute value of –3 is 3. So for positive numbers, the absolute value is the same as the number itself. For negative numbers, the absolute value is the positive version of that number.
Absolute value is written using two thin bars:
In an equation, absolute value brackets work like positive parentheses. You have to work whatever’s inside the absolute value brackets first, but if you get a negative number, you have to convert it to a positive number when taking it out of the absolute value brackets.
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