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Negative & Positive Numbers Review

Negative and positive numbers can be tricky. We have to remember some basic rules and apply some skills when solving equations with negative and positive numbers.

What is a negative number?

- A negative number is a number that is less than zero.
- A positive number is a number that is greater than zero.
- Zero is neither positive nor negative.
- Negative numbers are used to describe values that go below zero, such as temperature.

Using the Number Line for Addition and Subtraction


Looking at the number scale, we recall that negative numbers are to the left of zero, and positive numbers are to the right

number line
When subtracting you move to the left and when adding you move to the right. Later on when you get better at working with negative numbers you will be able to picture the number line in your head while doing calculations.

If we are given the question 5 - 7, what would our answer be?
Since we want to subtract 7 from 5, you start at 5 and move 7 spaces to the left. You then land on - 2. Therefore, our answer is - 2.

A trick to keep in mind when adding and subtracting negatives and positives is the following:
When we are given a question like - 5 + 8, you look for the greater number. In this case, 8 is greater than - 5 and 8 is also positive. Therefore we know our answer must be positive because adding 8 to -5 would bring you to the right side of the number line. Whenever we have a negative sign before the smaller number we would subtract the smaller number from the greater number. So, 8 - 5 is 3. (Note: when the greater number is negative, the answer will be negative).

Examples:
14 + 8 = in this case, 14 is greater and positive. 14 + 8 = 22

14 - 8 = in this case, 14 is greater and positive but it is a subtraction question. 14 - 8 = 6

-6 + 12 = in this case, 12 is greater than 6 and it is positive, so our answer will be positive because adding 12 to -6 will bring you to the positive side of the number line. Now you know the answer will be positive. Then, you simply subtract the smaller number from the greater number and apply the appropriate sign (positive, which was previously determined) to your answer. 12 -6 = 6 and you determined previously that the answer will be positive, therefore 6 is the correct answer.

-15 + 2 = in this case, 15 is greater than 2 and it is negative so we know our answer will be negative. The reason for this is because adding 2 to a number that is negative and greater than 2 will not bring you to the positive side of the number line. Again, now you know the answer will be negative. Then, you simply subtract the smaller number from the greater number and apply the appropriate sign (negative, which was previously determined) to your answer. 15 -2 is 13 but remember you determined that the answer is negative, therefore the answer is - 13.

Steps that will help you solve addition/subtraction questions with negative numbers:

If you get an addition/subtraction question with two different signs like -6+12 or +6-12:

1. Think logically using the number line to determine if the sign of your answer will be positive or negative.

If you are adding a positive number to a negative number (i.e. -6+12), you have to determine if adding 12 to -6 will bring you over from the negative side (because -6 is on the negative side) of the number line to the positive side. In any case, you would only need to add 6 to bring -6 to 0; therefore, adding anything greater than 6 to -6 will bring you to the other side of the 0 (positive side of the number line). Hence, adding 12 to -6 will give you a positive number. If the number you are adding to the negative number is less than the negative number itself (i.e. -6+5), then that will not bring you to the positive side of the number line and hence, your answer will be negative.

If you are subtracting a number from a positive number (i.e. +6-12), you have to determine if subtracting 12 from 6 will bring you from the positive side (because +6 is positive) to the negative side of the number line. In any case, you would only need to subtract 6 from 6 to get to 0; therefore, subtracting anything greater than 6 from 6 will give you something less than zero, bringing you to the negative side of the number line. Hence, subtracting 12 from +6 will give you a negative number.

Remember: in this first step you are only trying to determine which sign the answer will be and not what value/number it will be. One step at a time!

2. Once you've determined the sign of your answer, you can now ignore all signs in the question and do the following:

a. Determine which number is greater than the other in value (ignoring the sign). In this case, 12 is greater than 6.

b. Then, simply subtract the smaller number from the greater number (i.e. 12-6=6).

c. Add the appropriate sign, which you determined in step 1, to the number you obtained from step b and that will be your final answer!

If you get an addition/subtraction question with two negative signs like -3-7:

1. Determine what sign the answer will have: When you have a question like -3-7 the answer will always be negative, because if you subtract from a negative number you are moving to the left of that number on the number line (which will always be negative).

2. Ignore all signs and simply add the two numbers together (3+7=10).

3. Your answer will have the sign determined in step 1 and the number determined in step 2 (final answer: -10).

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