Adding And Subtracting Negative Numbers
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Adding and subtracting negative numbers is part of our series of lessons to support revision on negative numbers. You may find it helpful to start with the main negative numbers lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:
Within the study of mathematics, after learning how to add and subtract positive numbers, negative numbers are introduced. Adding and subtracting negative numbers is different from adding and subtracting positive numbers, and we have a nice set of rules that we can use to add and subtract negative numbers that make the process run much more smoothly.
Let's consider an example of each case. First, consider adding two negative numbers, -12 and -15, or calculating -12 + (-15). To add -12 and -15, we first ignore the negative signs, and we add 12 and 15 to get 12 + 15 = 27. Now, we just make 27 negative to get the following:
Now for the subtraction of negative numbers. Suppose we want to calculate -5 - (-22). To perform this calculation, we are going to turn this into an addition problem by adding the opposite. We leave -5 as it is, we change the subtraction to addition, and we change -22 to 22 to get the following:
Numbers higher than zero are called positive numbers, and numbers lower than zero are negative numbers. That means they fall at either side of the number line. However, just because they're on the same line doesn't mean they follow the same rules! Keep reading for a list of the basic rules for using positive and negative numbers in math.
Notice that equations with two positive numbers have positive sums, and equations with two negative numbers have negative sums. If you're using a number line to solve the problem, adding two positive numbers will go farther to the positive side, and adding two negative numbers will go farther on the negative side.
Subtracting positive and negative numbers means that you add the opposite numbers, or additive inverse. Change the subtraction sign to addition and change the sign that follows to its opposite. Then follow the steps for addition. For example:
It seems like multiplication and division would be more complicated than addition and subtraction, but they're actually much simpler. The rule for multiplying positive and negative numbers with the same sign (two positive or two negative) is that the product will always be positive. For example:
In all of these cases, you first need to multiply or divide the numbers. Then decide whether the product or quotient is positive (two positives or two negatives in the equation) or negative (one positive and one negative in the equation).
Another way to think about adding positive and negative numbers is to look at the signs in a row. Two like signs in a row (++ or --) mean you add the numbers, while two unlike signs in a row (+- or -+) mean that you subtract. For example:
This method follows the same rules as above but might help you solve the problem more quickly if you prefer to work out the signs beforehand. Once you understand positive and negative numbers conceptually, you can decide which method works best for you.
Problems with negative numbers may look difficult, but there's still only one right answer and with practice you can learn to find it quickly. There are at least two ways you can think your way through these problems. Most people start by learning on a number line. 5376163bf9
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