The document explains the rules for subtracting integers, emphasizing that subtraction can be transformed into addition by changing the sign of the number being subtracted. It includes various examples illustrating the application of these rules, along with practice problems. Additionally, it discusses evaluating variable expressions with given values.

1. Subtraction of Integers
I can subtract positive and
negative numbers.

2. Focus Question
■ What is the rule for subtracting positive
and negative numbers?

3. The subtraction rule
■ Rule: To subtract ADD the OPPOSITE.
■ Or – Subtracting is the same as
ADDING THE OPPOSITE.
■ 5 + (-7) =
■ 5 – 7 =
-2
-2

4. Example: -5 - (-3)
■ ADD the OPPOSITE –5 + (3) = -2
■ Notice the subtraction operation
changed to addition, and
■ the opposite of –3 becomes 3.
■ NOTE: only the number behind
the subtraction sign gets
changed.

5. - 3 – 2
- ADD the OPPOSITE

6. - 3 – 2
- ADD the OPPOSITE
–3 + (-2) = -
_
5

7. Two Negatives
■ 5 - (-3)

8. Two Negatives
■ 5 - (-3)
■ ADD the OPPOSITE 5 + (+3)
■ Notice the use of the rule.
■ 5 - (-3) = 5 + 3 = 8

9. -8 –(-4) + 2
■ ADD the OPPOSITE

10. -8 –(-4) + 2
■ ADD the OPPOSITE
■ –8 + (+4) + 2.
■
■ -8 - (-4) +2
■ - 8 + 4 + 2 = - 2

11. Try some with the rule
■ -8 – (-10)=
■ 4 - 7 =
■ -9 - 5 =
■ -20 – (-4) =
■ 40 – 32 =

12. Try some with the rule
■ -8 – (-10)=
■4 - 7 = 4 + (-7)=
■ -9 - 5 =
■ -20 – (-4) =40 + (-32)=
■ 40 – 32 =
-8 + 10 = 2
-9 + (-5)= -14
-20 + 4= -16
-3
8

13. Example:
-7 – 9 - (-4) – 3 + 9 - (-4)=

14. Example:
-7 – 9 - (-4) – 3 + 9 - (-4)=
■ Changes on paper to
–7 + -9 + 4 + - 3 + 9 + 4 =
■
■ Then think DOWN 7, Down 9 more,
then UP 4, Down 3, UP 9, and UP 4.
■ The result is –2.

15. EXAMPLE 2
Evaluate
Evaluating a Variable Expression
15 – a – b when a = 24 and b = – 36

16. EXAMPLE 2 Evaluating a Variable Expression
Evaluate 15 – a – b when a = 24 and b = – 36
15 + (–24) + 36 =
–9 + 36 =
27
15 – a – b =
15 – 24 – (–36)
= Add the opposite of 24 and
of –36.
Add 15 and –24.
Add –9 and 36.
Substitute 24 for a and –36 for b.

17. GUIDED PRACTICE for Examples 1, 2, and 3
a – b – (–6) a = 8, b = –15

18. GUIDED PRACTICE for Examples 1, 2, and 3
8 – (–15) – (-6)
8 + 15 + 6
29
Substitute 8 for a and –15 for b.
Add the opposite of –15 and
of –6.
Add.
a – b – (–6) a = 8, b = –15

19. ■ In the Sahara Desert one day it was
136°F.
■ In the Gobi Desert a temperature of
-50 F was recorded.
■ What is the difference between
these two temperatures?
■ Write a subtraction expression to
represent this situation.

20. ■ Assignment:
No Calculators - show your work