Why Dividing Two Negatives Leads to a Positive Outcome

When dividing a negative number by a negative number, what is the result?

• A. A positive number
• B. A negative number
• C. Zero
• D. Undefined

Answer: (A)

When you divide a negative number by another negative number, the result is a positive number. This is based on the rules of arithmetic regarding the signs of numbers. Specifically, when you divide two numbers with the same sign (both negative in this case), the result is always positive. For example, if you take -10 and divide it by -2, the calculation looks like this: -10 ÷ -2 = 5. Here, both numbers are negative, and the result is positive. This rule holds true no matter what the negative values are, as long as the divisor (the number you're dividing by) is also negative. Thus, the outcome of dividing a negative by a negative leads to a positive result, confirming that the correct answer is indeed a positive number.

When it comes to math, some rules can really throw us for a loop—especially when we start dealing with negatives. You might be sitting there wondering, “What happens when I divide two negative numbers?” Well, prepare yourself for a pleasant surprise: the answer is a positive number!

Let’s consider this concept a little deeper. Why does dividing a negative number by a negative number give us a positive result? It all boils down to the basic rules of arithmetic and the nature of numbers. Remember those signs? Positive and negative signs are like a dance—when two negatives come together, they tango their way to positivity!

So, for instance, take -10 and divide it by -2. If you do some quick math, you’ll find:

-10 ÷ -2 = 5.

Both of our original numbers are negative, but once we divide them, our result is a cheerful positive 5. A classic case of negative numbers playing nice together!

You might be thinking, “But why does it work this way?” Well, imagine you owe your friend $10 (that's a negative for you). If they forgive you that debt (the second negative), suddenly you’re in the green. You’ve moved from negative to positive. That’s the essence of the math rule right there!

This isn’t just a fun fact for trivia night. Understanding why we get a positive number from dividing two negatives can significantly help simplify complex equations during your studies, especially if you’re prepping for tests and placement exams, like the ALEKS Basic Math Placement Test. It’s all about getting comfortable with the rules and making them work for you.

To make it even more intuitive, think about temperatures. If it’s -10 degrees (really chilly!) and you turn the heat up by 2 degrees (that’s essentially taking away the chill, right?), you end up at a comfortable 5 degrees. That’s the charm of negatives.

Now, you might run into some tricky problems or feel a bit stuck when tackling algebra or other advanced math topics, but hang in there! The idea that two negatives make a positive will serve you well. Practice this rule until it clicks—literally turn your frown upside down!

In summary, dividing two negative numbers results in a positive number. When you grasp this concept, you not only gain confidence in your math skills but also build a solid foundation for more complicated mathematical operations. So next time you find yourself scratching your head over negatives, remember this little gem: two negatives make a positive! And who couldn’t use a little more positivity in their math journey?