1. Subtraction of REALS
Section 2-3
P. 80
Goal : understand how to
subtraction rational numbers

2. The subtraction rule
 Rule: To subtract -ADD the OPPOSITE.
 Or – Subtracting is the same as ADDING
THE OPPOSITE. Write this down!
 Think about a problem 3 – 6.
 The operation in this problem is
subtraction.
 The 6 is positive.

3. To follow the rule
 Change the subtraction operation to
addition
 and the positive 6 to a negative 6.
 The result is 3 +(-6).
 Now follow the addition rules to get a
result of –3.

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
–3 + (-2) = ____
-5
-5 - 12 = -5 _? _ _? __
-5 + -12 = -17

6.  5 - (-3)
 ADD the OPPOSITE 5 + (+3)
 Notice the use of the rule.
 5 - (-3) = 5 + 3 =
8

7. -8 –(-4)
 ADD the OPPOSITE
 –8 + (+4).
 Now think Down 8 then up 4.
 -8 - (-4) = - 8 + 4 = - 4

8. 3-8
 Think: UP 3 then Down 8 for 5 in the hole.
 3 - 8 = -5
or 3 + - 8 = - 5
 - 81 - 12
 Think Down 81 then Down 12 more.
 -12 -93
–81 –12 = -81 + ____ = _____

9. 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.

10. Try some with the rule
 -8 – (-10) think -8 + ____ = ____
 4 -7 think 4 + ____ = ____
 -9 - 5 think -9
_______________
 -20 – (-4)
 40 – 32
 32 - (-26)
 -32 – (-26)

11. EXAMPLE 3 Evaluate Change
Temperature
One of the most extreme temperature changes in
United States history occurred in Fairfield, Montana,
on December 24, 1924. At noon, the temperature was
63 F. By midnight, the temperature fell to – 21 F. What
was the change in temperature?
SOLUTION
The change C in temperature is the difference of the
temperature m at midnight and the temperature n at
noon.

12. EXAMPLE 3 Evaluate Change
STEP 1
Write a verbal model. Then write an equation.
C = m – n
STEP 2
Find the change in temperature.
C = m–n Write equation.
= – 21 – 63 Substitute values.
= – 21 + (– 63) Add the opposite of 63.
= – 84 Add – 21 and – 63.

13.  Now that you understand “integers”,
let’s do some rational numbers.
 Do you remember how to subtract
fractions?
 Decimals?

14. GUIDED PRACTICE for Example 1
Find the difference.
1. 11.7– (– 5) = 11.7 + 5
= 16.7
1 1
2. –
3 2
–1
=
6

15. 2 1
5 ( 8 )
3 4

16.  Assignment: P. 82 (# 1-14, 26-31)
No Calculators - show the problem
“re-written” as an addition problem
in 3-14
Show how you got your answer in 26-31!!
Study the number properties.

17. Natural