When is an Answer Negative?
This can trip you up because depending on what operation is in play ( +, -, *, /), your answer can be positive or negative when negative numbers are in the game. How do you know when the answer should be negative? Let’s break down each operation.
Is There a Difference Between 5 – 3 and -3 – (-5)?
Do not let the parenthesis intimidate you. The parenthesis is just there to make the problem easier to read. If the problem was written like -3 – -5, it looks messy and might be harder to work. Whenever you have two signs side by side, the first thing you need to do is break that down so:
- + beside + or written as +(+) will always be positive (+). Example: + (3) = 3
- – beside – or written as -(-) will also always be positive (+). Example: – (-3) = 3
- – beside + or vice versa +(-) will always be negative (-). Example: – (3) = -3
Addition and Subtraction
When adding or subtracting involves a negative number, it doesn’t necessarily matter which number comes first, but your first step will be determining the sign of the larger number. That will be the sign in your answer.
Ok, let’s examine the question asked earlier. Is there a difference between the two problems: 5 – 3 and -3 – (-5)? The answer is no. Both problems yield 2 as the answer.
When starting out working these problems, you might find it helpful to draw out a number line with the numbers that are in the problem. For example with -3 + 5, you can visually work out the problem now by starting at 5 and going back three spaces to land at 2. This is also helpful to verify that your answer is a positive because you didn’t go to the left of zero on the number line.
Important! If the problem does not contain a parenthesis and is something like -6 – 7, then apply your own parenthesis rule if you aren’t sure if the answer will be -13 or 1. If we put a parenthesis around the second number, -6 – (7), then it might make it clearer that the 7 is a positive. Remembering that -(+) makes a negative, then you can see that you will be starting at -6 and moving left seven spaces. Therefore, the answer is -13.
If the problem was -6 – (-7), then you would use the parenthesis rule to make the problem -6 + 7. Then, starting at -6 you would move right along the number line seven spaces and land on 1.
Multiplication and Division
Working these problems are really straightforward. First, multiply or divide like you would a problem with no negative numbers. Then, follow the same rules as the parenthesis rules listed above.
- If you are multiplying or dividing two positive numbers, your answer will be positive. Example: 2 * 2 = 4
- If the two numbers are both negative, your answer will be positive. Example: -2 * -2 = 4
- If one number is positive and the other is negative, your answer will be negative. Example : 2 * -2 = -4
Second Reminder!
Do not mistake these rules when simply adding or subtracting numbers. Example: The problem -10 – 8 equals -18 not -2. If that doesn’t make sense when working the problem, use the parenthesis rule and draw it out on a number line. Starting at -10 you would move to the left eight spaces because you are subtracting 8 from -10.
If the problem was set up as -10 – (-8), then the answer would be -2 because first you would be modifying the problem to be -10 + 8. Referring back to the number line you can start at -10, then move right eight spaces this time. You would stop on -2.
Note: Some problems may be too big to draw out a number line, but, if helpful, you can at least draw a portion of it, if it helps you to decide whether to move left or right.