1. 1-2 Adding and Subtracting Real Numbers Warm Up Lesson Presentation
Holt Algebra 1
Warm Up
Lesson Presentation
Lesson Quiz

2. Warm Up Simplify. 1. |–3| 3 2. –|4| –4
Write an improper fraction to represent each
mixed number. 2 14 6 55 3. 4 4. 7 3 3 7 7
Write a mixed number to represent each improper fraction. 2 3 12 2 5 24 5. 6. 5 9

3. Objectives
Add real numbers.
Subtract real numbers.

4. Example 1A: Adding and Subtracting Numbers on a Number line
Add or subtract using a number line.
–4 + (–7)
Start at 0. Move left to –4.
To add –7, move left 7 units.
+ (–7) –4 11 10 9 8 7 6 5 4 3 2 1
–4+ (–7) = –11

5. Example 1B: Adding and Subtracting Numbers
on a Number line
Add or subtract using a number line.
3 – (–6)
Start at 0. Move right to 3.
To subtract –6, move right 6 units. –6
+ 3 -3 -2 -1 1 2 3 4 5 6 7 8 9
3 – (–6) = 9

6. -3 -2 -1 1 2 3 4 5 6 7 8 9 Check It Out! Example 1a
Add or subtract using a number line.
–3 + 7
Start at 0. Move left to –3.
To add 7, move right 7 units. +7 –3 -3 -2 -1 1 2 3 4 5 6 7 8 9
–3 + 7 = 4

7. Check It Out! Example 1b
Add or subtract using a number line.
–3 – 7
Start at 0. Move left to –3.
To subtract 7 move left 7 units. –3 –7 11 10 9 8 7 6 5 4 3 2 1
–3 – 7 = –10

8. Check It Out! Example 1c
Add or subtract using a number line.
–5 – (–6.5)
Start at 0. Move left to –5.
To subtract negative 6.5 move right 6.5 units. –5
– (–6.5) 8 7 6 5 4 3 2 1 1 2
–5 – (–6.5) = 1.5

9. 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

11. Example 2A: Adding Real Numbers
When the signs of numbers are
different, find the difference of the
absolute values:
Use the sign of the number with the greater absolute value.
The sum is negative.

12. 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 the sum of the absolute
values: = 8.
(–6) + (–2) –8
Both numbers are negative, so the sum is negative.

13. 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

14. Check It Out! Example 2b
Add.
– (–22.3)
– (–22.3)
When the signs are the same, find the sum of the absolute values.
–35.8
Both numbers are negative so,
the sum is negative.

15. Check It Out! Example 2c
Add.
x + (–68) for x = 52
First substitute 52 for x.
x + (–68) = 52 + (–68)
When the signs of the numbers are different, find the difference of the absolute values.
68 – 52
Use the sign of the number with the greater absolute value.
–16
The sum 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.

18. Example 3A: Subtracting Real Numbers
–6.7 – 4.1
–6.7 – 4.1 = –6.7 + (–4.1)
To subtract 4.1, add –4.1.
When the signs of the numbers
are the same, find the sum of the
absolute values: = 10.8.
= –10.8
Both numbers are negative, so the sum is negative.

19. Example 3B: Subtracting Real Numbers
5 – (–4)
5 − (–4) = 5 + 4
To subtract –4 add 4. 9
Find the sum of the absolute
values.

20. Example 3C: Subtracting Real Numbers
First substitute
for z.
To subtract
, add
Rewrite with a denominator
of 10.

21. Example 3C Continued
When the signs of the numbers are
the same, find the sum of the
absolute values:
Write the answer in the simplest form. Both numbers are negative, so the sum is negative.

22. Check It Out! Example 3a
Subtract.
13 – 21
13 – 21
= 13 + (–21)
To subtract 21 add –21.
When the signs of the numbers are different, find the difference of the absolute values: 21 – 13 = 8. –8
Use the sign of the number with the greater absolute value.

23. Check It Out! Example 3b
Subtract.
To subtract add –3 1 2 3
When the signs of the numbers are the same, find the sum of the absolute values: = 4. 3 1 2 + 4
Both numbers are positive so, the sum is positive.

24. Check It Out! Example 3c
Subtract.
x – (–12) for x = –14
x – (–12) = –14 – (–12)
First substitute –14 for x.
–14 + (12)
To subtract –12, add 12.
When the signs of the numbers are different, find the difference of the absolute values: 14 – 12 = 2.
Use the sign of the number with the greater absolute value. –2

25. elevation at top of iceberg
Example 4: Oceanography Application
An iceberg extends 75 feet above the sea. The bottom of the iceberg is at an elevation of –247 feet. What is the height of the iceberg?
Find the difference in the elevations of the top of the iceberg and
the bottom of the iceberg.
elevation at top of iceberg 75
elevation at bottom
of iceberg
–247
Minus –
75 – (–247)
75 – (–247) =
To subtract –247, add 247.
Find the sum of the absolute values.
= 322
The height of the iceberg is 322 feet.

26. elevation at top of iceberg
Check It Out! Example 4
What if…? The tallest known iceberg in the North Atlantic rose 550 feet above the oceans surface. How many feet would it be from the top of the tallest iceberg to the wreckage of the Titanic, which is at an elevation of –12,468 feet?
elevation at top of iceberg
550
Minus
elevation of the
Titanic –12,468 –
550 – (–12,468)
To subtract –12,468,
add 12,468.
550 – (–12,468) = ,468
Find the sum of the absolute values.
= 13,018
Distance from the iceberg to the Titanic is 13,018 feet.

27. 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 5.
6. The temperature at 6:00 A.M. was –23°F.
At 3:00 P.M. it was 18°F. Find the difference
in the temperatures.
41°F