Embedded Files
Learning Targets
- I can find the difference between two rational numbers.
- I understand how to subtract positive and negative numbers in general.
Notes
Notes
When we talk about the difference of two numbers, we mean, “subtract them.” Usually, we subtract them in the order they are named. For example, the difference of +8 and - 6 is 8 - ( - 6 ).
The difference of two numbers tells you how far apart they are on the number line. 8 and -6 are 14 units apart, because 8 - ( - 6 ) = 14:
Notice that if you subtract them in the opposite order, you get the opposite number:
( - 6 ) - 8 = - 14
In general, the distance between two numbers a and b on the number line is |a - b|. Note that the distance between two numbers is always positive, no matter the order. But the difference can be positive or negative, depending on the order.
Activities
Activities
6.2 Expressions with Altitude
6.2 Expressions with Altitude
A mountaineer is changing elevations. Write an expression that represents the difference between the final elevation and beginning elevation. Then write the value of the change. The first one is done for you.
6.3 Does the Order Matter?
6.3 Does the Order Matter?
- Find the value of each subtraction expression.
- What do you notice about the expressions in Column A compared to Column B?
- What do you notice about their values?
Add To Your Notes
Add To Your Notes
The difference between two numbers can be positive or negative, depending on their order…
(a − b) = -(b − a)
(a − b) = -(b − a)
The distance between two numbers is always positive. It does not depend on their order, because it is the magnitude (absolute value) of the difference:
|a − b| = |b − a|
|a − b| = |b − a|
Example:
- What is the difference between 12 and 10? 12 - 10 = 2
- What is the distance between 12 and 10? |2| = 2
- What is the difference between 10 and 12? 10 - 12 = 2
- What is the distance between 10 and 12? |-2| = 2
Notice that for every way, the difference is 2!
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