Greater than and less than
We often use the greater than and less than signs to record comparison of numbers.
NOTE: To remember the difference between less than and greater than, remember that the smaller pointy end always points to the smaller number.
Example 1: Decide whether to use the > or < sign in the following examples.
You may want to draw a number line to help.
Bigger or smaller
People often get confused when comparing negative numbers.
For example, which number is smaller -5 or -17?
You could draw a quick number line to remind you (as we have done above) or another easy way to think of this problem is to think of the numbers as temperatures. Which temperature is colder (lower), -5° C or -17° C?
Example 2: Arrange the following numbers in order from smallest to largest.
Absolute value is an alternative meaning of size.
You may not think it is sensible to say that a 'big' number like -16 is less than a 'small' number like -3. For example, more money is involved in a debt of $16m than a debt of $3m. A town 16 km south of where I am is further away from me than a town that is 3 km south.
This second idea of size is called 'absolute value'. The absolute value of -16 is +16 and is written |-16|. The absolute value of +16 is written |+16| and is just equal to 16. The absolute value of a number is the distance that it is from zero.
So -16 < -3 but |-16| > |-3| .
On the one hand -16 < -3 because -16 is to the left of -3 on the number line. Later, we will show that if we subtract -16 from -3, the answer is positive, which is the formal definition of one number being greater than another.
But |-16| > |-3| because 16 is further away from zero than 3. |-16| = 16 and |-3| = 3.
Answer true or false to the following statements:
As we have mentioned a positive sign (or no sign) or a negative sign in front of a number indicates its direction from zero, i.e. that it is positive or negative. We can think of a number's direction as being an attribute or property of the number. A negative number has the property of being negative while a positive number has the property of being positive.
-4, +5, +8, -7, 12, -43, 560, -941
is the number 4 with the property of being negative. We call it negative
When we use a positive or negative sign in this sense we call it a unary sign because it applies to one number.
Unfortunately we also use the same symbols to mean subtraction or addition. When we use a sign in this sense we call it a binary sign because it signifies an operation connecting two numbers.
For example, 10 - 4 = 6
Here the symbol means 'subtract', 10 take away 4 equals 6.
The example below includes both negative numbers and subtraction.
For example, (-4) - 6 = (-10)
We read this example as "negative 4 subtract 6 equals negative 10".
The '-' sign in front of the 4 indicates that the 4 is negative while the '-' between -4 and 6 means subtract.
Confusion can arise because we use the same symbol to mean 2 different things. Some people also use the same terminology. We could have read the above example as minus 4 minus 6 equals minus 10 yet the word minus clearly has two different meanings. Minus means the number it is in front of has the property of being negative whereas minus means take away. This is not good practice.
For example, (-4) - (-6) = 2
Here we have three occurrences. The '-' in front of the 4 and 6 indicate that they are negative numbers and the '-' sign between the two numbers means 'subtract'. We read the example as 'negative 4 subtract negative 6 equals 2'.
To differentiate between the two meanings we often hand write the signs for positive and negative in a smaller font raised above the level of the text. This difference is not always maintained and cannot always be adhered to in printed or electronic documents. We are using brackets to make the meanings clear.
You do not use the subtraction button on a calculator to enter a negative number. Calculators have separate buttons for the unary and binary sign.
Most simple calculators have a change of sign button, which enables you to enter positive and negative integers.
Example: Do you know how to type in the following numbers in your calculator?
On most simple calculators, in order to indicate that a number is negative we must first key in the number and then change the sign of the number via the '+/-' key. You will notice that if you repeatedly press the '+/-' key the number displayed will alternate between being displayed as negative and positive. Experiment on your own calculator. What happens when you press the change of sign key when you have zero displayed on the screen?
Example: (-49) - 786
Answer on screen display: -835
Example: -34 + (- 57) - (- 22)
Answer on screen display: -69
For more information on using a calculator see Whole Numbers, Multiplication, Using a Calculator or Percent, Ratio and Rates, Percent Examples,Calculator Shortcuts.
To view the quiz answers, click here.
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