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Comparing and Ordering Integers

Why Are Big Negative Numbers Less Than Small Ones?

We are used to big positive numbers meaning a big value – the bigger the number, the more, or higher, or longer, or expensive, or whatever the number represents.

With negative numbers, we have to remember that as the digit gets bigger, the number gets smaller. Think what the number represents. Think what the value is.

  • The amount of money you have gets lower the more you owe.
  • The temperature gets lower, the colder it gets
  • The more you take away, the less you have

Looking at numbers on a vertical number line can be useful.

Negative and positive numbers on a vertical number line

Zero is neither positive or negative

Examples of Comparing Integers

Which is greater, -5 or -3?

Locate both numbers on the number line. Numbers to the right are greater. -3 is to the right of -5 so -3 is greater.

number line showing negative numbers to the left of zero

Put the following numbers in order starting with the least. -23, 17, -32, 2, -4, 0

Start looking at the negative numbers as these are always less than positive numbers. Start with the “biggest” negative number ( -32) as that has the lowest value.

Find the next “biggest” negative number (-23) and continue until the negative numbers are in order.

Zero and positive numbers can then be put into order to give the following complete list:

-32 , -23 , -4 , 0 , 2 , 17

Which of these numbers is greater than -6 but less than 4?
-8, -10, 5, -4, 0

Start be finding all the numbers that are less than -6. This gets rid of -8 and -10 (to the left of -6 on the number line).

Next we’ll get rid of any number that is greater (not less) than 4. This means 5 is out leaving:

-4 and 0

Try these worksheets to practice with using integers.