1. Section 1.5
Subtracting Integers

2. Objectives Subtract integers. (NS 1.2)
Simplify expressions and use properties of rational numbers to justify the process used. (AF 1.3)

3. Subtracting Integers
ADD the OPPOSITE
To subtract an integer b from an integer a, add the opposite of b to a.
a – b = a + (-b)
3 – 4 = 3 + (-4) = -1
In Words
In Algebra
In Arithmetic

4. Symbols and Directions+
Addition
Subtraction -
Walk Forward
Turn Around
Always Start At 0 -4 -3 -2 -1 1 2 3 4

5. Symbols and Directions+
Positive
Negative -
Walk Forward
Walk Backwards
Always Start At 0 -4 -3 -2 -1 1 2 3 4

6. Subtracting Integers On a Number Line( ) + + 1
4 - 3 = 1 4 - 3 + =
Add the opposite
Walk Forward 4 Spaces
Walk Backwards 3 Spaces -4 -3 -2 -1 1 2 3 4

7. Subtracting Integers ( ) 1 - 3 - 4 -1 - 3 = -4 - + = Add the opposite
Walk Backwards 1 Space
Walk Backwards 3 Spaces -4 -3 -2 -1 1 2 3 4

8. Subtracting Integers Add the opposite + + ( ) 1 3 4 1- (-3) = 4 + =
Walk Forwards 3 Spaces
Walk Forward 1 Space -4 -3 -2 -1 1 2 3 4

9. Two negatives make a happy face( ) 2 4 - - - -
Smile + 6 =

10. Making Zero Pairs
Positives +
Negatives -
Zero Pair

11. Finding the Difference Using Markers+ ( )
5 - 7 5 - 7 +
Add the opposite
2 Negatives
Zero
Pairs - 2 =

12. Finding the Difference Using Markers( ) -
-5 - 7 5 - 7 +
Add the opposite
12 Negatives 1 2 = -

13. Finding the Difference Using Markers+ ( )
5 - (-7) 5 7 + +
Happy Face
12 Positives + 1 2 =

14. Application
The distance from the high dive to the swimming pool is 10 feet. The pool is 12 feet deep. What is the total distance from the high dive to the bottom of the pool?
10 – (–12)
Subtract the depth of the pool from the height of the high dive.
Add the opposite of –12. 22
It is 22 feet from the diving board to the bottom of the pool.

15. Now You Try Number Line or Markers -17 4 -4 10 31 6 -13 -10 – 7
Hint: rewrite as adding the opposite 
-17
-10 – 7
-5 – (-5)
7 – 9 – (-12)
-5 – 10 – (-2)
19 – 15
5 – 9
23 – (-8)
2 – (-4) 4 -4 10 31 6
-13

16. Lesson Quiz Subtract. 1. –6 – (–4) 3. 4 – (–5) 2. –3 – 3–2
3. 4 – (–5) 9
2. –3 – 3 –6
Evaluate each expression for the given value of the variable.
4. 9 – s for s = –5 14
5. –4 – w + 5 for w = 21
–20
6. Loretta is flying in an airplane and rises an additional 20 feet. Then she descends 190 feet toward the ground. How far below her original height did Loretta go?
170 feet