Along with multiplication, addition, and subtraction, division is one of the four basic operations of mathematics. Of the four, it is the operation that causes the most angst amongst students as it is widely regarded as the most complex. A cause of even greater angst in the student population is division problems involving negative numbers.
But do not fear! As you will come to see, dividing negative numbers is simple, and there are some easy-to-remember tips and tricks you can apply to any question you face that will help you on your way to the correct answer.
So, how do you divide negative numbers?
We are going to show you how to approach division questions with negative numbers in them and demonstrate the rules we introduce with plenty of examples.
When dividing negative numbers, if both numbers are negative, the answer will be positive. If one number is positive and the other negative, you will get a negative answer.
As you may have noticed, you divide negative numbers in the same way as when multiplying negative numbers. The exact same rules apply for negative division as negative multiplication.
So let's jump in and take a closer look at some of the rules for dividing negative and positive numbers.
The rules for dividing two numbers together change when using positive and negative numbers, so let's look at each possible scenario:
Positive ÷ negative
A positive number divided by a negative number will always result in a negative number. For example, 10 ÷ -5 = -2. You can follow the same principles as if you were dividing the positive forms of both numbers and then turn the answer into a negative by adding the negative sign (-).
Negative ÷ positive
The rule for this scenario is the same as the above: it will always result in a negative number. As with multiplication, the position of the negative number doesn't affect the result. This is not the same when undertaking addition and subtraction problems.
Negative ÷ negative
A negative number divided by another negative number will always result in a positive answer. In this scenario, the negativity of both numbers cancels each other out, so you can treat the question as if you were dealing with positive numbers. Again, this is the same rule as it is when multiplying negative numbers together.
Positive ÷ positive
Dividing two positive numbers together always results in a positive answer. No matter how much bigger the divisor is than the dividend, dividing two positives always yields a positive result.
|Negative -||Positive +|
Now we know the rules of dividing negative numbers, let's look at some examples that will illustrate how each possibility works.
Positive numbers divided by negative numbers:
- 20 ÷ -5 = -4. We know that 20 ÷ 5 = 4. Therefore, because one of the numbers in the question is negative, we need to make our answer negative too.
- 5 ÷ -10 = -0.5. In this example, the positive number has a smaller value than the (positive iteration of the) negative number; the divisor is larger than the dividend. However, the answer remains the same as it would be if both numbers were positive, only it is turned into a negative.
Negative numbers divided by positive numbers:
- -4 ÷ 2 = -2. As with the above examples, the positioning of the negative number does not impact the fact that the answer must still be negative. 4 ÷ 2 = 2. Therefore, the presence of a negative number only means the answer is the same but negative.
- -10 ÷ 30 = -0.3. The same principle applies when the divisor is larger than the dividend.
Negative numbers divided by negative numbers:
- -8 ÷ -4 = 2. When you divide a negative number by a negative number, it always makes a positive. 8 ÷ 4 = 2. Therefore, dividing -8 by -4 also equals 2.
- -6 ÷ -12 = 0.5. Again, the same principle applies when the divisor is larger than the dividend.
Positive numbers divided by positive numbers:
- 15 ÷ 3 = 5. When you divide positive numbers by other positives, the result will always be a positive answer.
- 6 ÷ 60 = 0.1. The same rules apply even if the divisor is larger than the dividend, no matter the size difference.
The thought of seeing the negative sign (-) and the division sign (÷) in the same question is enough to instill terror in even the bravest student that is new to negative division. But, as we have seen, there is nothing to be afraid of when dividing negative numbers. Whether it is negatives with negatives or negatives with positives, there are simple rules that apply and work in every situation.
So learn the rules to make sure you are prepared for when any negative division question pops up in your exams!