1-21-2 Adding and Subtracting Real NumbersAdding and...
Transcript of 1-21-2 Adding and Subtracting Real NumbersAdding and...
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Holt Algebra 1
1-2 Adding and Subtracting Real Numbers1-2Adding and SubtractingReal Numbers
Holt Algebra 1
Warm Up
Lesson Presentation
Lesson Quiz
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Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Add real numbers.
Subtract real numbers.
Objectives
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Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Vocabulary
absolute value
opposites
additive inverse
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Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
All the numbers on a number line are called real
numbers. You can use a number line to modeladdition and subtraction of real numbers.
+ • + =
– • – =
+ • – =
– • + =
+(+) =
- (-) =
+(-) =
-(+) =
+
+
―
―
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Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Example 1A: Adding and Subtracting Numbers
on a Number line
Add or subtract using a number line.
Start at 0. Move left to –4.
11 10 9 8 7 6 5 4 3 2 1 0
–4+ (–7) = –11
To add –7, move left 7 units.
–4 + (–7)
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Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Example 1B: Adding and Subtracting Numberson a Number line
Add or subtract using a number line.
Start at 0. Move right to 3.
To subtract –6, move right 6 units.
-3 -2 -1 0 1 2 3 4 5 6 7 8 9
3 – (–6) = 9
3 – (–6)
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Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Add or subtract using a number line.
1a: –3 + 7
Check It Out! Example 1
-3 -2 -1 0 1 2 3 4 5 6 7 8 9
1b: –3 – 7
11 10 9 8 7 6 5 4 3 2 1 0
1c: –5 – (–6.5)
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
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Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
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
210123456 6543- - - - - -
|5| = 5|–5| = 5
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Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
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Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Example 2A: Adding Real Numbers
Add.
Use the sign of the number with the greater absolute value.
The sum is negative.
When the signs of numbers are
different, find the difference of the
absolute values:
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Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Example 2B: Adding Real Numbers
Add.
y + (–2) for y = –6
First substitute –6 for y.
When the signs are the same, find the sum of the absolute values: 6 + 2 = 8.
Both numbers are negative, so the sum is negative.
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Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Add.
2a: –5 + (–7)
Check It Out! Example 2
2b: –13.5 + (–22.3)
2c: x + (–68) for x = 52
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Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
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.
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Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
A number and its opposite are additive inverses.
To subtract signed numbers, you can use additiveinverses.
11 – 6 = 5 11 + (–6) = 5
Additive inverses
Subtracting 6 is the same
as adding the inverse of 6.
Subtracting a number is the same as adding the
opposite of the number.
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Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
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Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Subtract.
–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: 6.7 + 4.1 = 10.8.
Both numbers are negative, so
the sum is negative.
Example 3A: Subtracting Real Numbers
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Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Subtract.
5 – (–4)
To subtract –4 add 4.
Find the sum of the absolute values.
Example 3B: Subtracting Real Numbers
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Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
Subtract.
3a: 13 – 21
Check It Out! Example 3
3b: x – (–12) for x = –14
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Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
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
Minus elevation at bottomof iceberg
–247
75 – (–247)
75 – (–247) = 75 + 247
= 322
The height of the iceberg is 322 feet.
–
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Holt Algebra 1
1-2 Adding and Subtracting Real Numbers
HOMEWORKSec 1-2: (Pg 17) 1-3, 6, 9, 13, 14, 17–25, 28–31, 37-42, 65, 66