What you need to know

Things to remember:

  • The number on the left of > is bigger than the one on the right

6 > 3                6 is bigger than 3

  • The number on the left of < is less than the one on the right

3 < 6                3 is less than 6

  • The “pointy end” of the inequality “points” to the smaller number.

There are 5 symbols we need to learn to allow us to solve inequalities:

 

< less than                            > greater than                                    = equals

\leq less than or equal to       \geq greater than or equal to

Write “three is less than five” using inequalities and numbers.

We can break this up into parts:

Three                                      3

Three is less than                  3 <

Three less than five                3 < 5

So, to write this as an inequality with numbers, we’d just write:

3 < 5

Write “12 is greater than 7” using inequalities and numbers.

 

Twelve                                    12

Twelve is greater than          12 >

Three is greater than seven   12 > 7

So, to write this as an inequality with numbers, we’d just write:

12 > 7

Sometimes though, we aren’t told what the symbol is, and we need to find out what it is.

What is the missing symbol?

 

8 ___ 3

To do this we, read it from left to right and ask three questions until we answer yes:

Is it less than?

Is it greater than?

Is it equal?

So, let’s answer these.

Is 8 less than 3? No

Is 8 greater than 3? Yes

Is 8 equal to 3? No

Because we answered “yes” to question 2, this must be our answer!

8 > 3

Note: We could also use \geq because 8 is greater than OR equal to 3.

 

What is the missing symbol?

 

2 ___ 7

Is 2 less than 7? Yes

Is 2 greater than 7? No

Is 2 equal to 7? No

 

Because we answered “yes” to question 1, this must be our answer!

2 < 7

Note: We could also use \leq because 2 is less than OR equal to 7.

This gets slightly more difficult with decimals, but we know how to do these, so let’s try a couple.

What is the missing symbol?

 

5.67 ___ 5.234

Hint: Remember, when we compared and ordered decimal before, we added 0s to the end, so that they had the same number of decimal places. Then, if they had the same “whole number part” all we had to do was compare the decimal.

 

5.670 ___ 5.234

These have the same whole number part, so we just have to compare the decimal.

Is 670 less than 234? No

Is 670 greater than 234? Yes

Is 670 equal to 234? No

Because we answered “yes” to question 2, this must be our answer!

5.67 > 5.234

Note: We could also use \geq because 5.67 is greater than OR equal to 5.234.

What is the missing symbol?

 

13.24 ___ 11.544

Note: Because the “whole” number parts are different, we just need to compare these.

 

Is 13 less than 1? No

Is 13 greater than 11? Yes

Is 13 equal to 11? No

Because we answered “yes” to question 2, this must be our answer!

13.24 > 11.544

Note: We could also use \geq because 13.24 is greater than OR equal to 11.544.

Example Questions

Question 1: What is the missing symbol?

 

3 ___ 121

Answer

Is 3 less than 121? Yes

Is 3 greater than 121? No

Is 3 equal to 121? No

 

Because we answered “yes” to question 1, this must be our answer!

 

3 < 121

 

Note: We could also use \leq because 3 is less than OR equal to 121.

Question 2: What is the missing symbol?

 

13.245 ___ 13.82

Answer

13.245 ___ 13.82

13.245 ___ 13.820

 

These have the same whole number part, so we just have to compare the decimal.

 

Is 820 less than 245? No

Is 820 greater than 245? Yes

Is 820 equal to 245? No

 

Because we answered “yes” to question 2, this must be our answer!

 

13.820 > 13.245

13.82 > 13.245

Note: We could also use \geq because 13.82 is greater than OR equal to 13.245.