Transcript Positive and Negative Numbers

Adding and Subtracting Integers
Additive Inverse
Additive Inverse - two numbers with
a sum of zero.
-4 + 4 =
0
-
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
Additive Inverse
Additive Inverse - two numbers with
a sum of zero.
6 + (-6) =
0
+
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-
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.
+
-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
+
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
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
-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
- 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
-
Integer Addition Rules
• Rule #1 – If the signs are the same,
pretend the signs aren’t there. Add the
numbers and then put the sign of the
addends in front of your answer.
9 + 5 = 14
- 9 + (- 5) = -14
(+8) + (+13) = ?
1.
2.
3.
4.
5
21
-5
+5
(-22) + (-11) = ?
1.
2.
3.
4.
+33
-11
+11
-33
Integer Addition Rules
• Rule #2 – If the signs are different pretend
the signs aren’t there. Subtract the smaller
number from the larger one and put the
sign of the one with the larger absolute
value in front of your answer.
-9 + 5 =
9 - 5 = 4 Answer = - 4
Larger abs. value
(-12) + (+6) = ?
1.
2.
3.
4.
+6
-6
+18
-18
12 – 6 = 6
Number with larger
absolute value is -12
So we put a negative
sign in front of answer
(-16) + (+5) = ?
1.
2.
3.
4.
11
21
-21
-11
16 – 5 = 11
Number with larger
absolute value is -16
So we put a negative
sign in front of answer
- 3 + 18 = ?
1.
2.
3.
4.
11
15
-15
-11
18 – 3 = 15
Number with larger
absolute value is 18
So we put a positive
sign in front of answer
Integer Subtraction Rule
To Subtract an Integer add it’s
opposite
2 – 7
becomes
2 + (-7)
2 + (-7) = -5
Integer Subtraction Rule
To Subtract an Integer add it’s
opposite
8 – 15
becomes
8 + (-15)
8 + (-15) = -7
Integer Subtraction Rule
To Subtract an Integer add it’s
opposite
12 – (-8)
becomes
12 + (8)
12 + 8 = 20
Integer Subtraction Rule
To Subtract an Integer add it’s
opposite
-3 – (-11)
becomes
-3 + (11)
-3 + 11 = 8
15 – (7) = ?
1.
2.
3.
4.
17
-17
8
-8
12 – (-10) = ?
1.
2.
3.
4.
22
-22
2
-2
(-3) – (-11) = ?
1.
2.
3.
4.
14
-14
8
-8
(+12) - (+8) = ?
1.
2.
3.
4.
-4
+4
20
-20
Solve the Problems
• -3 + -5 =
•4+7=
• (+3) + (+4) =
• -6 + -7 =
•5+9=
• -9 + -9 =
-8
11
7
-13
14
-18
Solve the Problems
• -7 – 4 =
• -19 + 11 =
• -16 - (-21) =
• 32 – (-16) =
• -18 + 9 =
• -9 + 1 =
-11
-8
5
48
-9
-8
Range
Range - the difference between the
greatest and the least values
In other words,
biggest minus smallest
Range is always positive because
it is measuring the distance
between two numbers
Range
In Alaska, temperatures have ranged from a low
of -47 degrees to a high of 53 degrees. Find the
temperature range.
53 - (-47)
53 + (47)
53 + 47 = 100
Range
Find the range between 97 and 56.
97 - 56
97 - 56 = 41
Range
Find the range between -16 and -6.
-6 - (-16)
-6 + (16)
-6 + 16 = 10