1. Objectives
Add real numbers.
Subtract real numbers.

2. The absolute value of a number is the distance from zero on a number line. The absolute value of 5 is written as |5|.
5 units
5 units - 6 - 5 - 4 - 3 - 2 - 1 1 2 3 4 5 6
|–5| = 5
|5| = 5

4. Check It Out! Example 2a
Add.
–5 + (–7)
–5 + (–7) = 5 + 7
When the signs are the same, find the sum of the absolute values.
5 + 7 = 12
Both numbers are negative, so the sum is negative.
–12

5. Check It Out! Example 2b
Add.
– (–22.3)
When the signs are the same, find how many TOTAL NEG we have.
– (–22.3)
–35.8
Both numbers are negative so,
the sum is negative.

6. Check It Out! Example 2c
Add.
x + (–18) for x = -32
First substitute -32 for x.
x + (–18) = (–18)
–50
The sum is negative.

7. Check It Out! Example 2b
Add.
11 + (–8)
When the signs are the same, find how many TOTAL NEG we have.
11 + (–8) 3
Both numbers are negative so,
the sum is negative.

8. Example 2B: Adding Real Numbers
y + (-2) for y = -6
y + (2) = (-6) + (2)
First substitute -6 for y.
When the signs are the same,
Find how many TOTAL NEG
we have.
(-6) + (2) -4
Both numbers are negative, so the sum is negative.

9. Check It Out! Example 2b
Add.
8 + (–21)
When the signs are the same, find how many TOTAL NEG we have.
8 + (–21)
-29
Both numbers are negative so,
the sum is negative.

10. Additive inverses 11 – 6 = 5 11 + (–6) = 5
A number and its opposite are additive inverses.
To subtract signed numbers, you can use additive
inverses.
Subtracting 6 is the same
as adding the inverse of 6.
Additive inverses
11 – 6 = 5
11 + (–6) = 5
Subtracting a number is the same as adding the
opposite of the number. (The both have a NEG sign
right next to them)

11. Example 3A: Subtracting Real Numbers
–6.7 – 4.1
–6.7 – 4.1 = –6.7 + (–4.1)
Minus 4.1 is the same as -4.1
How many TOTAL NEG do you
have?
= –10.8
Both numbers are negative, so the sum is negative.

12. Check It Out! Example 3a
Subtract.
13 – 21
Minus 21 is the same as -21
13 – 21
= 13 + (–21)
When the signs of the numbers are different, see if you have more positives or more negatives. HOW MANY MORE ARE THERE? –8
The sum is negative.

13. Example 3B: Subtracting Real Numbers
5 – (–4)
Two NEG signs are next to each
Other so you can “blip blip” them
to both be positive signs.
5 + (+4) = 5 + 4 9
Find the sum.

14. Example 3B: Subtracting Real Numbers
16 – (–10)
Two NEG signs are next to each
Other so you can “blip blip” them
to both be positive signs.
16 + (+10) = 26
Find the sum.

15. Check It Out! Example 3c
Subtract.
x – (–12) for x = –14
x – (–12) = –14 – (–12)
First substitute –14 for x.
–14 + (+12)
Two NEG signs are next to each
Other so you can “blip blip” them
to both be positive signs. –
Are there more NEG or more POS? How many more? –2
The answer is negative.

16. Two numbers are opposites if their sum is 0
Two numbers are opposites if their sum is 0. A number and its opposite are on opposite sides of zero on a number line, but are the same distance from zero. They have the same absolute value.

17. Lesson Quiz
Add or subtract using a number line.
2. –5 – (–3) –2
1. –2 + 9 7
Add or subtract.
3. – 19
– (–3.7)
8.2