Section 15 Goals Goal To find sums and differences of real numbers Rubric Level 1 Know the goals Level 2 Fully understand the goals Level 3 Use the goals to solve simple problems ID: 523970
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Slide1
Adding and Subtracting Real Numbers
Section 1-5Slide2
Goals
Goal
To find sums and differences of real numbers.
Rubric
Level 1 – Know the goals.
Level 2 – Fully understand the goals.
Level 3 – Use the goals to solve simple problems.
Level 4 – Use the goals to solve more
advanced problems
.
Level 5 – Adapts and applies the goals to different and more complex
problems
.Slide3
Vocabulary
Absolute value
Opposite
Additive inversesSlide4
The set of all numbers that can be represented on a number line are called
real numbers
.
You can use a number line to model addition and subtraction of real numbers.
Addition
To model addition of a positive number, move right. To model addition of a negative number, move left.
Subtraction
To model subtraction of a positive number, move left. To model subtraction of a negative number, move right.
Real NumbersSlide5
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
+ (–7)
–4 + (–7) = –11
To add –
7,
move left 7 units
.
–4
–4 + (–7)
Example: Adding & Subtracting on a Number LineSlide6
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
3 – (–6) = 9
3 – (–6)
–
(
–
6)
Example: Adding & Subtracting on a Number LineSlide7
Add or subtract using a number line.
–3 + 7
Start at 0. Move left to
–
3.
To add 7, move right 7 units.
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
–3
+7
–3 + 7 = 4
Your Turn:Slide8
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
0
–3 – 7 = –10
Your Turn:Slide9
Add or subtract using a number line.
–5 – (–6.5)
Start at 0. Move left to
–
5.
To subtract
–
6.5, move right 6.5 units.
8
7
6
5
4
3
2
1
0
–5
–5 – (–6.5) = 1.5
1
2
–
(
–
6.5)
Your Turn:Slide10
Definition
Absolute Value
– The distance between a number and zero on the number line.
Absolute value is always nonnegative since distance is always nonnegative.
The symbol used for absolute value is | |.
Example: The |-2| is 2 and the |2| is 2.Slide11
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
2
1
0
1
2
3
4
5
6
6
5
4
3
-
-
-
-
-
-
|5| = 5
|–5| = 5
Absolute Value on the Number LineSlide12
Rules For AddingSlide13
Add.
Use the sign of the number with the greater absolute value.
Different signs: subtract
the
absolute values.
A.
B.
–6
+
(–2)
(6 + 2 = 8)
–
8
Both numbers are negative, so the sum is negative.
Same signs: add the absolute values.
Example: Adding Real NumbersSlide14
Add.
–5 + (–7)
–12
Both numbers are negative, so the sum is negative.
Same signs: add the absolute values.
a.
(5 + 7 = 12)
–
13.5 + (
–
22.3)
b.
(13.5 + 22.3 = 35.8)
–
35.8
Both numbers are negative, so the sum is negative.
Same signs: add the absolute values.
Your Turn:Slide15
c.
52
+ (–68)
(68 – 52 = 16)
–16
Use the sign of the number with the greater absolute value.
Different signs: subtract
the
absolute values.
Add.
Your Turn:Slide16
Definition
Additive Inverse
– The negative of a designated quantity.
The additive inverse is created by multiplying the quantity by -1.
Example:
The additive inverse of 4 is -1 ∙ 4 = -4.Slide17
Opposites
Two numbers are
opposites
if their sum is 0.
A number and its opposite are
additive inverses and are the same distance from zero.
They have the same absolute value.Slide18
Additive Inverse PropertySlide19
Subtracting Real Numbers
To subtract signed numbers, you can use additive inverses.
Subtracting a number is the same as adding the opposite of the number.
Example:
The expressions 3 – 5 and 3 + (-5) are equivalent.Slide20
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.
Subtracting Real NumbersSlide21
Subtracting Real
Numbers
Rules For SubtractingSlide22
Subtract.
–6.7 – 4.1
–6.7
– 4.1
= –6.7
+ (–4.1)
To subtract 4.1, add –4.1.
Same signs: add absolute values.
–10.8
Both numbers are negative, so the sum is negative.
(6.7 + 4.1 = 10.8)
Example: Subtracting Real NumbersSlide23
Subtract.
5
–
(
–
4)
5
− (–4)
= 5
+ 4
9
To subtract –4, add 4.
Same signs: add absolute values.
(5 + 4 = 9)
Both numbers are positive, so the sum is positive.
Example: Subtracting Real NumbersSlide24
On many scientific and graphing calculators, there is one button to express the opposite of a number and a different button to express subtraction.
Helpful HintSlide25
Subtract.
13 – 21
13
– 21
To subtract 21, add
–
21.
Different signs: subtract absolute values.
Use the sign of the number with the greater absolute value.
–8
= 13
+ (–21)
(21
–
13 = 8)
Your Turn:Slide26
–14
– (–12)
Subtract.
–14
– (–12)
= –14
+ 12
(14 – 12 = 2)
To subtract –12, add 12.
Use the sign of the number with the greater absolute value.
–2
Different signs: subtract absolute values.
Your Turn:Slide27
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
minus
elevation
at
bottom
of
iceberg
75 – (–247)
75
– (–247)
= 75
+ 247
= 322
To subtract –247, add 247.
Same signs: add the absolute values.
–
75
–
247
Example: Application
The height of the iceberg is 322 feet.Slide28
What if…?
The tallest known iceberg in the North Atlantic rose 550 feet above the ocean's 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
minus
elevation
of the
Titanic
–
550 – (–12,468)
550
– (–12,468)
= 550
+ 12,468
To subtract –12,468,
add
12,468.
Same signs: add the absolute values
.
= 13,018
550
–
12,468
Your Turn:
Distance from the top of the iceberg to the Titanic is 13,018 feet.Slide29
Joke Time
What’s brown and sticky?
A stick.
What happened when the wheel was invented?
It caused a revolution.
Why was the calendar depressed?Because it’s days were numbered.Slide30
Assignment
1.5 Exercises Pg. 41 – 43: #10 – 76 even