2-2 adding & subtracting rational numbers
TRANSCRIPT
2-2 Adding & Subtracting Rational Numbers
Class Assignment
Evaluate the following if a =5, b= -8 and c = -3:
1. |b| + 72. a - |c|3. |a| + |b|4. 6|b|
Activity For this activity each circle is worth “one” is positive is negative You can represent a number by drawing
that amount of counters on your paper.
+
-
Your Turn On your paper use the counters to
represent the following numbers1. -8 2. +23. -64. +10
-- -- -- --
+ +
+ + + + +++ ++ +
-- ----
+
Zero Pairs When adding the counters together you
remove zero pairs to get the solution A zero pair is 1 red counter and 1 yellow
counter
Example: - 3 + 2 =Draw 3 negative counters and 2 positive counters on your paper like this:
-
-
-
+
+
These are zero pairs. The positive and negative cancel each other out. Cross them out. Whatever is left is the answer.
The answer is -3 + 2 = -1
Draw the counters to illustrate the problem5 + (-2)
Draw 5 positive counters on your paper Draw 2 negative counters on your paper Remove the zero pairs to get your answer
And the answer is…
+
+
+
+
+
-
-
5 + (-2) = 3
Use the counters to illustrate the problem7 + (-5)
Draw 7 positive counters on your paper Draw 5 negative counters on your paper Remove the zero pairs to get your answer
And the answer is…
+
+
+
+
+
+
+
-
--
--
=2
Your Turn Draw the counters to illustrate the
problem- 1 + 1
And the answer is…
The discovery you should have made during this activity is…When adding integers, if the signs are the same you add and keep the sign…
If the signs are different you actually subtract and KEEP THE SIGN OF THE LARGER NUMBER…
…or in other words, whichever has the higher Absolute Value
Opposites
Before we can go on to subtracting integers, I need to make sure that we all understand “what is the opposite”?.
Raise you hand if you know the answer to the question… What is the opposite of 5? What is the opposite of 12? What is the opposite of -8? What is the opposite of -35?
-5
-12
8
35
Subtracting Integers The rule for subtracting integers is:
To subtract integers, just add its opposite
Here is what that looks like…
3 – 5 =First you have to know what the
opposite of 5 is…in this case -5Second you need to add the opposite,
therefore the equation changes to3 + (-5) =
Then you follow the rules for adding integers
Example
7 – (-15) =
When SUBTRACTING…
…just ADD THE OPPOSITE !!!!
7 + 15 = 22
Example # 4
-30 – (-20) =-30 + 20 =
When SUBTRACTING…
…just ADD THE OPPOSITE !!!!
-10
Your Turn1. 6 – (-7) =2. - 5 – (-19) =3. - 14 – (-2) =
ObservationsYou might have already made
the observation that when see a
double negative you change it to a plus.
8 – (-8) = 8 + 8 = 16