BIGGER, SMALLER, GREATER, LESSER

There are different words that can be used to compare real numbers: bigger, smaller, greater, lesser.
Bigger and greater do NOT mean the same thing!
Smaller and lesser do NOT mean the same thing!

Bigger and smaller have to do with distance from zero.
Thus, the words big and small are used to compare the sizes (absolute value) of numbers.

Greater and lesser have to do with left/right positioning.
The verbs ‘[beautiful math coming... please be patient]$\,>\,$’ (greater than) and ‘[beautiful math coming... please be patient]$\,<\,$’ (less than) are used to talk about this left/right ordering.

Bigger means farther away from zero.
Smaller means closer to zero.

Greater means farther to the right on a number line.
The sentence   [beautiful math coming... please be patient] $\,a > b\,$   is read aloud as “$\,a\,$ is greater than $\,b\,$”.
The sentence   [beautiful math coming... please be patient]$\,a > b\,$   is true precisely when $\,a\,$ lies to the right of $\,b\,$ on a number line.

Lesser (or less than) means farther to the left on a number line.
The sentence   [beautiful math coming... please be patient] $\,a < b\,$   is read aloud as “$\,a\,$ is less than $\,b\,$”.
The sentence   [beautiful math coming... please be patient]$\,a < b\,$   is true precisely when $\,a\,$ lies to the left of $\,b\,$ on a number line.

Memory devices:

EXAMPLES:
Question: Compare the numbers [beautiful math coming... please be patient] $\,-10\,$ and $\,7\,$. Which is bigger? Why?
Solution: The number [beautiful math coming... please be patient] $\,-10\,$ is bigger, because it is farther away from zero.
Question: Compare the numbers [beautiful math coming... please be patient] $\,-10\,$ and $\,7\,$. Which is greater? Why?
Solution: The number [beautiful math coming... please be patient] $\,7\,$ is greater, because it is farther to the right on a number line.
Question: Compare the numbers [beautiful math coming... please be patient] $\,-10\,$ and $\,7\,$. Which is smaller? Why?
Solution: The number [beautiful math coming... please be patient] $\,7\,$ is smaller, because it is closer to zero.
Question: Compare the numbers $\,-10\,$ and $\,7\,$. Which is lesser? Why?
Solution: The number [beautiful math coming... please be patient] $\,-10\,$ is lesser, because it is farther to the left on a number line.
Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
Practice with the Phrases ‘at least’ and ‘at most’

 
 
On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.
(an even number, please)