Have you ever looked at a thermometer on a cold winter morning? If you have, you might have noticed a negative number. In many places, it’s normal for a winter morning to be -15° F or even -20° F. In Antarctica, it gets as low as -128° F!

Does this make you WONDER how it is even possible to have a negative temperature? How can negative numbers exist?

You’re not the first to ask that question! European mathematicians rejected the idea of negative numbers for a long time. They didn’t think negative numbers made any sense. However, people in India and China have been using negative numbers for thousands of years. Eventually, the Europeans changed their minds, and now we use negative numbers everywhere today.

Negative numbers make more sense if we look at a number line. On a number line, all the numbers to the right of zero are positive. If we move to the left of zero, they become negative:

We get a negative number by subtracting a smaller number from a larger one. For example, if we subtract nine from eight, it looks like this:

8 – 9 = -1

There are many other rules for using negative numbers in math. Have you heard the saying that two wrongs don’t make a right? That may be true, but two negatives do make a positive! When we subtract a negative number, the subtraction sign is right next to the negative sign. That means we can replace them with an addition sign. Here’s what it looks like when two negatives make a positive:

0 – -3 = 0 + 3 = 3

This rule also applies in multiplication. When we multiply two negative numbers, the answer is always positive:

-5 × -2 = 10

Negative numbers might seem mysterious in math problems. For many people, negative numbers in the real world make more sense. Remember that cold morning when you read the thermometer? The negative numbers helped you understand how cold the weather was. Think of the thermometer as a number line. If the thermometer was in degrees Fahrenheit, then the freezing point was 32° F. If the temperature was -15° F, then it was 47 degrees below freezing. In Celsius, the freezing point is 0° C. That means -15° C would be 15 degrees below freezing.

Have you ever studied maps or geography? If so, you may have heard of altitude. Altitude tells us how far above or below sea level a place is. For example, the peak of Mount Everest is 29,029 feet above sea level. Badwater, California is the lowest point in the United States. Its altitude is -282 feet! That means that if Badwater Basin were closer to the ocean, it would be under water.

One last way to think about negative numbers is to look at a bank account. When a person spends money, banks use negative numbers to record transactions. If a person spends $10.50 on a movie ticket, the movie ticket will show up on his or her bank account as a negative number (-10.50). That way, the bank knows to subtract $10.50 from the account.

Negative numbers are sometimes confusing when we first learn about them. The rules can be difficult to remember! Like everything else, understanding negative numbers becomes easier with practice. Can you think of any other real-world examples of negative numbers?

Try It Out

Make sure you find a friend or family member to help with these activities!

Exploring Negative Numbers

If you’re still struggling to understand negative numbers, don’t worry! We have a helpful tool for you – the Interactive Number Line. Take a look and make sure to test your knowledge by answering the questions provided at the bottom.

Ready to practice using negative numbers? Try playing Orbit Integers, a fun game that allows you to practice addition and subtraction with negative numbers. As you play, make a note of any problems you struggle with. Later, you can discuss these problems with a friend, family member, or teacher for further clarification.

Feeling confident in your understanding of negative numbers? Remember that they can be challenging for many people. Take the opportunity to assist a friend or family member by sharing your knowledge about negative numbers. If they have any questions that you can’t answer, consider searching for the answers together.

Useful Sources

• https://nrich.maths.org/9958 (accessed on January 31, 2019)
• https://www.purplemath.com/mod… (accessed on January 31, 2019)
• https://nrich.maths.org/5961 https://nrich.maths.org/5961 (accessed on January 31, 2019)