Transcript One Way to Add Integers Is With a Number Line - Math GR. 6-8

Integers and the
Number Line
Definition
Positive number:
A number greater than zero.
0 1 2 3 4 5 6
Definition
Negative number:
A number less than zero.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
Definition
Opposite Numbers:
Numbers that are the same
distance from zero in the opposite
direction
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
Definition
Integers:
Integers are all the whole numbers
and all of their opposites on the
negative number line including
zero.
-7
opposite
7
Adding Integers
Using the
Number Line
One Way to Add Integers Is
With a Number Line
•When the number is positive count
to the right.
•When the number is negative count
to the left.
Always start at zero!
-
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
One Way to Add Integers Is
With a Number Line
+3 + (-5) = -2
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-
One Way to Add Integers Is
With a Number Line
+6 + (-4) = +2
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-
One Way to Add Integers Is
With a Number Line
+3 + (-7) = -4
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-
One Way to Add Integers Is
With a Number Line
-3 + 7 = +4
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
+
One Way to Add Integers Is
With a Number Line
-5 + 3 = -2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
+
One Way to Add Integers Is
With a Number Line
-2 + 8 = +6
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
+
One Way to Add Integers Is
With a Number Line
-5 + 2 = -3
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
+
One Way to Add Integers Is
With a Number Line
-4 + (-2) = -6
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-
One Way to Add Integers Is
With a Number Line
-2 + (-3) = -5
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-
One Way to Add Integers Is
With a Number Line
-1 + (-4) = -5
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-
One Way to Add Integers Is
With a Number Line
4+1= 5
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
+
One Way to Add Integers Is
With a Number Line
1+5= 6
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
+
Subtracting
Integers Using
the Number Line
One Way to Subtract Integers
Is With a Number Line
•Subtraction on the number line
can become tricky without the
introduction of some rules.
•Before we introduce the rules,
let’s look at some scenarios that
involve integer subtraction.
Accounting
Say I borrow $5 from you and buy lunch since I
forgot my wallet. I owe you $5 so on my
balance sheet I have -5. Later I get my wallet
and pay you the $5 back so I can subtract
what I owe. So we have:
-5 -(-5) = -5 +5 = 0
Driving
You are driving with cruise control set at 65 mph,
which we will call your reference speed. You see a sign
stating that you are entering a 55 mph zone so you
slow down 10 mph ( -10). After a few miles a new sign
informs you that you are entering a 65 zone again so
you resume your original speed, thus removing
(subtracting) the -10 mph modification. We thus have:
-10 - (-10) = 0
or no speed modification (thus you are moving at the reference
speed of 65 again).
Books
You borrow 3 books from a library. You thus
owe three books (-3). You read one and
discover it does not cover what you want, so
you return (subtract) it (a borrowed book is a minus,
thus a -1) and thus you have subtracted one
book you owe, and now owe only two. And
we have:
-3 -(-1) = -3 + 1 = -2
Behavior
Johnny swears and fights a lot (two negatives). He
feels he wants to get better so he decides to
stop (thus removing or subtracting) fighting (a negative).
Thus he now has:
-2 - (-1) = -2 + 1 = -1
or 1 negative behavior he does a lot.
Integer Subtraction Rule
Subtracting a negative number is the
same as adding a positive. Change
the signs and add.
2 - (-7) is the same as 2 + (+7)
and 2 + 7 = 9!
How do we know that
“Subtracting a negative number
is the same as adding a positive”
is true?
We can use the same method we
use to check our answers when
we subtract.
Suppose you subtract a – b and it
equals c:
a–b=c
5–2=3
To check if your answer is correct,
add b and c:
a=b+c
5=2+3
Here are some examples:
a–b=c
9–5=4
a=b+c
9=5+4
a–b=c a=b+c
20 – 3 = 17 20 = 3 + 17
If the method for checking
subtraction works, it should
also work for subtracting
negative numbers.
If a – b = c, and….
2 - (-5) is the same as
2 + (+5), which equals 7,
Then let’s check with the negative
numbers to see if it’s true…
a-b=c
2 - (-5) = 7
a=b+c
2 = -5 + 7
It works!
a-b=c
-11 - (-3) = -8
a=b+c
-11 = -3 + (-8)
YES!