Operations with Integers

1
Operations with Integers Lesson Objective To
add, subtract, multiply and divide rational
numbers.
Created By Ms. Marques Mrs. Nelson
2
What is an Integer?

• A whole number that is either greater than 0
  (positive) or less than 0 (negative) can be
  visualized on a number line

3
What is a Number Line?

• A line with arrows on both ends that show the
  integers with slash marks
• Arrows show the line goes to infinity in both
  directions ( and -)
• Uses a negative sign (-) with negative numbers
  but no positive sign () with positive numbers
• Zero is the origin and is neither negative nor
  positive

0
1
2
3
4
5
6
-1
-2
-3
-4
-5
-6
4
What are Opposites?

• Two integers the same distance from the origin,
  but on different sides of zero
• Every positive integer has a negative integer an
  equal distance from the origin
• Example The opposite of 6 is -6
• Example The opposite of -2 is 2

0
1
2
3
4
5
6
-1
-2
-3
-4
-5
-6
5
What is Absolute Value?

• A numbers distance from zero on a number line is
  always a positive number
• Indicated by two vertical lines
• Every number has an absolute value
• Opposites have the same absolute values since
  they are the same distance from zero
• Example -8 8 and 8 8
• Example 50 50 and -50 50

6
Negative Numbers Are Used to Measure Temperature
7
Negative Numbers Are Used to Measure Under Sea
Level
30
20
10
0
-10
-20
-30
-40
8
What Can We Do to Integers?

• Integers are numbers, so we can add,
  subtract, multiply, and divide them
• Each operation has different rules to follow

9
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.

-
0
1
2
3
4
5
6
-1
-2
-3
-4
-5
-6
10
One Way to Add Integers Is With a Number Line
3 -5
-2

0
1
2
3
4
5
6
-1
-2
-3
-4
-5
-6
-
11
One Way to Add Integers Is With a Number Line
3 -7
-4

0
1
2
3
4
5
6
-1
-2
-3
-4
-5
-6
-
12
One Way to Add Integers Is With a Number Line
6 -4
2

0
1
2
3
4
5
6
-1
-2
-3
-4
-5
-6
-
13
One Way to Add Integers Is With a Number Line
-3 7
4
-
0
1
2
3
4
5
6
-1
-2
-3
-4
-5
-6

14
One Way to Add Integers Is With a Number Line
-5 3
-2
-
0
1
2
3
4
5
6
-1
-2
-3
-4
-5
-6

15
Solve the Problems below using a number line.
-3 -5 4 7 3 - 4
-8
11
-1
16
Solve the Problems below using a number line.
-6 -7 5 9 -9 -3
-13
14
-12
17
but we cant always use a number line,
especially if the numbers are very large
(-123456) or very small (-23467). We need a
rule to help us when a number line is not
feasible.
18
Adding Rules Same Signs

• If the integers have the SAME signs ADD the
  numbers keep the same sign!
• Positive Positive Positive Answer
• Negative Negative Negative Answer

• Examples -3 (-10) ? ? -13
• 6 (8) ? ? 14

19
Adding (Same Signs) - Examples
1. -3 (-10) Step 1 13 Add the
s Step 2 -13 Keep same sign (Both
s are negative Answer is
negative!) 2. 6 (8) Step 1
14 Add the s Step 2 14 Keep same sign
(Both s are positive Answer is
positive!)
20
Adding Rules Different Signs

• If the integers have the DIFFERENT signs
  SUBTRACT the numbers use sign of the BIGGER
  number!
• Bigger is Positive Positive Answer
• Bigger is Negative Negative Answer

• Examples -13 (7) ? ? -6
• 23 (-8) ? ? 15

21
Adding (Different Signs) - Examples
1. -13 (7) Step 1 6
Subtract the s Step 2 -6 Use sign
of bigger (Bigger is negative -
Answer is negative!) 2. 23 (-8)
Step 1 15 Subtract the s Step
2 15 Use sign of bigger (Bigger is
positive - Answer is positive!)

22
Subtracting Rules

• Put ( ) around second number its sign
• Change SUBTRACTION sign to an ADDITION sign
• Change sign of 2nd number to its opposite
• Follow the rules for ADDITION
  
  
• -SAME signs Add keep the same sign
  -DIFFERENT signs
  Subtract use sign of bigger

• Examples -5 -10 ? ? 5
• 9 - 23 ? ? -14

23
Subtracting - Examples

• 1. -5 -10 2. 9 - 23
• Step 1 -5 (-10) Insert ( ) 9
  (23)
• Step 2 -5 (-10) Change to 9
  (23)
• Step 3 -5 (10) Change 2nd sign 9
  (-23)
• Step 4 5 Follow adding rules
  -14 d

24
Multiplying Rules

• Multiply the numbers like usual
• If the integers have the SAME signs ANSWER will
  be POSITIVE
• If the integers have DIFFERENT signs ANSWER will
  be NEGATIVE

• Examples -3 (-5) ? ? 15
• -9 (-10) ? ? 90
• -7 7 ? ? -49
• 6 -6 ? ? -36

25
Multiplying - Examples

• 1. -3 (-5) 2. -9
  (-10)
• 15 Multiply the numbers 90
• 15 Same signs Positive Answer
  90

3. -7 7 4. 6
-6 49 Multiply the numbers
36 -49 Different signs Negative
Answer -36
26
Dividing Rules

• Divide the numbers like usual
• If the integers have the SAME signs ANSWER will
  be POSITIVE
• If the integers have DIFFERENT signs ANSWER will
  be NEGATIVE

• Examples -33 (-3) ? ? 11
• -90 (-10) ? ? 9
• -20 2 ? ? -10
• 6 -6 ? ? -1

27
Dividing - Examples

• 1. -33 (-3) 2. -90
  (-10)
• 11 Divide the numbers 9
• 11 Same signs Positive Answer
  9

3. -20 2 4. 6
-6 10 Divide the numbers
1 -10 Different signs
Negative Answer -1
28
Mixed Practice
Solve the following problems
-9 - 9 -18
7 -4 3
-10 (-19) -29
-35 -7 -42
15 -25 -10
-23 9 -14
29
Review

• Visit the website below for additional
  information on integers
• http//www.math.com/school/subject1/
  lessons/S1U1L10GL.html
• Click on the signs below to review the rules for
  each operation

30
Review

• Visit the website below for additional
  information on integers
• http//www.math.com/school/subject1/
  lessons/S1U1L10GL.html
• Click on the signs below to review the rules for
  each operation