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Comparing Positive and Negative Numbers

One of the first things you’ll be able to do with your new knowledge of positive and negative numbers is compare them using greater than (>), less than (<), and="" equal="" to="" (=")." we’ve="" used="" these="" signs="" in="" the="" past="" to="" compare="" positive="" whole="" numbers,=""> mixed numbers, fractions, decimals, percents, and so on. Now, we can use the same signs to compare positive and negative numbers.

Positive numbers will always be greater than negative numbers. Thus, if you had a problem that looked like this:

-5 ___ 3

You would answer less than (<) because="" negative="" numbers="" are="" always="" less="" than="" positive="" numbers="" (this="" is="" because="" negative="" numbers="" are="" less="" than="" zero,="" and="" all="" positive="" numbers="" are="" greater="" than="" zero).="">

However, you must be careful when comparing two negative numbers. Remember that the higher number you have, the less you have (when the numbers are negative), so a low negative number (like -2) would be greater than a high negative number (like -100). We’ll give you a few examples to make sure you understand.

Let’s go through this. Compare the following:

-4 ___ -2

Normally, your first instinct would be that 4 is greater than 2. However, since these are negative numbers, you have to think about them in a different way. Remember, negative numbers measure how much you do not have. Thus, if you’re only missing 2, you have more than if you’re missing 4. You can also think about this as, which number is closest to zero? That’s the higher number. You can also visualize it like this:

Therefore, in this case, your answer would be -4 <>

Now let’s try another one.

-18 ___ -20

Remember, these are negative numbers again. Which number is closer to zero? We know that -18 is closer to zero than -20 is, so -18 is the bigger number. Thus, our answer is -18 > -20.

Comparing Positive and Negative Numbers Quiz

Problems

1. 3 ___ -5 2. 4 ___ 9 3. -5 ___ -6 4. -8 ___ 4 5. -100 ___ -1000
6. 74 ___ -74 7. -4 ___ -3 8. 9 ___ 10 9. 6 ___ -6 10. -22 ___ -23

Solutions

1. > 2. <> 3. > 4. <> 5. >
6. > 7. <> 8. <> 9. > 10. >