Transcript 2-1 - My CCSD

2-1
2-1 Integers
Integers
Warm Up
Problem of the Day
Lesson Presentation
Course
Course
22
2-1 Integers
Warm Up
Compare. Use <, >, or =
1.
7
5
>
2. 32
65 <
3. 82
28 >
4. 64
48 >
Course 2
2-1 Integers
Problem of the Day
Place 4, 5, 6, 7, 8, and 9 in the empty circles so
that each side has the same sum.
1
6
9
5
7
3
Course 2
4
8
2
2-1 Integers
Learn to compare and order integers and
to determine absolute value.
Course 2
2-1 Integers
Vocabulary
opposite
integer
absolute value
Course 2
2-1 Integers
The opposite of a number is the same
distance from 0 on a number line as the
original number, but on the other side
of 0. Zero is its own opposite.
–4 and 4 are opposites
–4
4
•
•
–5–4–3–2–1 0 1 2 3 4 5
Negative integers
Positive integers
0 is neither positive
nor negative
Course 2
2-1 Integers
The integers are the set of whole
numbers and their opposites. By using
integers, you can express elevations
above, below, and at sea level. Sea level
has an elevation of 0 feet.
Remember!
The whole numbers are the counting
numbers and zero: 0, 1, 2, 3, . . . .
Course 2
2-1 Integers
Additional Example 1: Graphing Integers and Their
Opposites on a Number Line
Graph the integer -7 and its opposite on a
number line.
7 units
7 units
–7–6–5–4–3–2–1 0 1 2 3 4 5 6 7
The opposite of –7 is 7.
Course 2
2-1 Integers
Check It Out: Example 1
Graph the integer -5 and its opposite on a
number line.
5 units
5 units
–7–6–5–4–3–2–1 0 1 2 3 4 5 6 7
The opposite of –5 is 5.
Course 2
2-1 Integers
You can compare and order integers by
graphing them on a number line.
Integers increase in value as you move
to the right along a number line. They
decrease in value as you move to the
left.
Course 2
2-1 Integers
Additional Example 2A: Comparing Integers Using a
Number Line
Compare the integers. Use < or >.
4 > -4
–7–6–5–4–3–2–1 0 1 2 3 4 5 6 7
4 is farther to the right than -4, so 4 > -4.
Remember!
The symbol < means “is less than,” and the
symbol > means “is greater than.”
Course 2
2-1 Integers
Additional Example 2B: Comparing Integers Using a
Number Line
Compare the integers. Use < or >.
>
-15
-9
-15 -14 -13 -12 -11 -10 -9 -8 -7
-6
-5
-4 -3 -2 -1
-9 is farther to the right than -15, so -15 < -9.
Course 2
2-1 Integers
Check It Out: Example 2A
Compare the integers. Use < or >.
6 > -6
–7–6–5–4–3–2–1 0 1 2 3 4 5 6 7
6 is farther to the right than -6, so 6 > -6.
Course 2
2-1 Integers
Check It Out: Example 2B
Compare the integers. Use < or >.
-4 > -11
-15 -14 -13 -12 -11 -10 -9 -8 -7
-6
-5
-4 -3 -2 -1
-4 is farther to the right than -11, so -4 > -11.
Course 2
2-1 Integers
Additional Example 3: Ordering Integers Using a
Number Line.
Use a number line to order the integers
from least to greatest.
–3, 6, –5, 2, 0, –8
–8 –7–6 –5–4 –3 –2 –1 0 1 2 3 4 5 6 7 8
The numbers in order from least to greatest
are –8, –5, –3, 0, 2, and 6.
Course 2
2-1 Integers
Check It Out: Example 3
Use a number line to order the integers from
least to greatest.
–5, 4, –3, 2, –1, –2
–8 –7–6–5–4 –3–2 –1 0 1 2 3 4 5 6 7 8
The numbers in order from least to greatest
are –5, –3, –2, –1, 2, and 4.
Course 2
2-1 Integers
A number’s absolute value is its distance
from 0 on a number line. Since distance can
never be negative, absolute values are never
negative. They are always positive or zero.
Course 2
2-1 Integers
Additional Example 4A: Finding Absolute Value
Use a number line to find each absolute value.
|8|
8 units
–8 –7–6–5–4 –3–2 –1 0 1 2 3 4 5 6 7 8
8 is 8 units from 0, so |8| = 8.
Course 2
2-1 Integers
Reading Math
The symbol is read as “the absolute value of.”
For example -3 is the absolute value of -3.
Course 2
2-1 Integers
Additional Example 4B: Finding Absolute Value
Use a number line to find each absolute value.
|–12|
12 units
–12 –11 –10 –9 –8 –7 –6 –5 –4 –3
–2
–1 0 1
–12 is 12 units from 0, so |–12| = 12.
Course 2
2
2-1 Integers
Check It Out: Example 4A
Use a number line to find each absolute value.
|3|
3 units
–8 –7–6–5–4 –3–2 –1 0 1 2 3 4 5 6 7 8
3 is 3 units from 0, so |3| = 3.
Course 2
2-1 Integers
Check It Out: Example 4B
Use a number line to find the absolute value.
|–9|
9 units
–12 –11 –10 –9 –8 –7 –6 –5 –4 –3
–2
–9 is 9 units from 0, so |–9| = 9.
Course 2
–1 0 1
2
2-1 Integers
Lesson Quiz: Part I
Compare. Use <, >, or =.
1. –32
32
<
2. 26
|–26|
=
3. –8
–12
>
4. Use a number line to order the integers –2, 3,
–4, 5, and –1 from least to greatest.
•
• •
–5–4 –3 –2–1 0
Course 2
•
•
1 2 34 5
–4, –2, –1, 3, 5
2-1 Integers
Lesson Quiz: Part II
Use a number line to find the absolute value.
5.
-3
3 units
•
–5 –4 –3 –2 –1 0 1 2 3 4 5
3
Course 2
2-1
2-2 Integers
Adding Integers
Warm Up
Problem of the Day
Lesson Presentation
Course
Course
22
2-1
2-2 Adding
IntegersIntegers
Warm Up
Find each absolute value.
1. |8| 8
2. |–6| 6
3. |–9| 9
4. |–7| 7
5. |–12| 12
6. |53| 53
Course 2
2-1
2-2 Adding
IntegersIntegers
Problem of the Day
Jan’s yearly salary is $30,000, and it will
be increased by $3,000 each year. Phil’s
salary is $20,000, and it will be
increased by $5,000 each year. In how
many years will Jan and Phil both have
the same yearly salary?
5 years
Course 2
2-1
2-2 Adding
IntegersIntegers
Learn to add integers.
Course 2
2-1
2-2 Adding
IntegersIntegers
Additional Example 1A: Modeling Integer Addition
Use a number line to find each sum.
–7 + (–4)
–14
–12
–7
+(–4)
–10
–8
–6
–4
–2
0
2
Start at 0. Move left 7 spaces. Then move left
4 more spaces.
–7 + (–4) = –11
Course 2
2-1
2-2 Adding
IntegersIntegers
Additional Example 1B: Modeling Integer Addition
Use a number line to find each sum.
–12 + 19
19
–12
–12
–10
–8
–6
–4
–2
0
2
4
6
Start at 0. Move left 12 spaces. Then move
right 19 spaces.
–12 + 19 = 7
Course 2
8
2-1
2-2 Insert
Lesson
Title Here
Integers
Adding
Integers
Check It Out: Example 1A
Use a number line to find each sum.
–4 + (–5)
–14
–12 –10
–4
+(–5)
–8
–6
–4
–2
0
2
Start at 0. Move left 4 spaces. Then move left
5 more spaces.
–4 + (–5) = –9
Course 2
2-1
2-2 Insert
Lesson
Title Here
Integers
Adding
Integers
Check It Out: Example 1B
Use a number line to find each sum.
–7 + 12
12
–7
–12
–10
–8
–6
–4
–2
0
2
4
6
Start at 0. Move left 7 spaces. Then move
right 12 spaces.
–7 + 12 = 5
Course 2
8
2-1
2-2 Adding
IntegersIntegers
Adding Integers
To add two integers with the same sign,
find the sum of their absolute values. Use the
sign of the two integers.
To add two integers with different
signs, find the difference of their absolute
values. Use the sign of the integer with the
greater absolute value.
Course 2
2-1
2-2 Adding
IntegersIntegers
Additional Example 2A: Adding Integers Using
Absolute Values
Find each sum.
–4 + 8
The signs are different. Find the difference
of the absolute values.
–4 + 8
4
Course 2
Think: 8 – 4 = 4.
Use the sign of the
integer with the
greater absolute
value.
2-1
2-2 Adding
IntegersIntegers
Additional Example 2B: Adding Integers Using
Absolute Values
Find each sum.
23 + (–35)
The signs are different. Find the difference of
the absolute values.
23 + (–35)
–12
Course 2
Think: 35 – 23 = 12.
Use the sign of the integer with the
greater absolute value.
2-1
2-2 Insert
Lesson
Title Here
Integers
Adding
Integers
Check It Out: Example 2A
Find each sum.
–5 + 3
The signs are different. Find the difference of
the absolute values.
–5 + 3
–2
Course 2
Think: 5 – 3 = 2.
Use the sign of the
integer with the
greater absolute
value.
2-1
2-2 Insert
Lesson
Title Here
Integers
Adding
Integers
Check It Out: Example 2B
Find each sum.
–13 + (–24)
The signs are the same. Find the sum of the
absolute values.
–13 + (–24) Think: 13 + 24 = 37.
–37
Course 2
Use the sign of the two integers.
2-1
2-2 Adding
IntegersIntegers
Additional Example 3: Evaluating Expressions with
Integers
Evaluate x + y for x = –42, y = 71.
x+y
–42 + 71
29
Substitute for x and y.
The signs are different. Think
71- 42 = 29
Use the sign of the integer with the
greater absolute value (positive).
Helpful Hint
When adding integers, think: if the signs are
the same, find the sum. If the signs are
different, find the difference.
Course 2
2-1
2-2 Insert
Lesson
Title Here
Integers
Adding
Integers
Check It Out: Example 3
Evaluate x + y for x = –24, y = 17.
x+y
–24 + 17
–7
Course 2
Substitute for x and y.
The signs are different.
Think: 24 – 17 = 7.
Use the sign of the integer with the
greater absolute value (negative).
2-1
2-2 Adding
IntegersIntegers
Additional Example 4: Application
The jazz band’s income from a bake sale was
$286. Expenses were $21. Use integer
addition to find the band’s total profit or loss.
286 + (–21)
286 – 21
265
Use negative for the expenses.
Find the differences of the
absolute values.
The answer is positive.
The band earned $265.
Course 2
2-1
2-2 Insert
Lesson
Title Here
Integers
Adding
Integers
Check it Out: Example 4
The French Club was raising money for a trip
to Washington D.C. Their car wash raised
$730. They had expenses of $52. Use integer
addition to find the club’s total profit or loss.
730 + (–52)
730 – 52
678
Use negative for the expenses.
Find the differences of the
absolute values.
The answer is positive.
The club earned $678.
Course 2
2-1
2-2 Adding
Integers
Insert Lesson
Integers
Title Here
Lesson Quiz: Part I
Use a number line to find the sum.
1. –7 + (–6)
–14
–12
–13
–10
–8
–6
–4
–2
0
2
Find each sum.
2. –15 + 24 + (–9)
3. –24 + 7 + (–3)
0
–20
4. Evaluate x + y for x = –2 and y = –15.
Course 2
–17
2-1
2-2 Adding
Integers
Insert Lesson
Integers
Title Here
Lesson Quiz: Part II
5. The math club’s income from a bake sale was
$217. Advertising expenses were $32. Use
integer addition to find the club’s total profit or
loss?
$185 profit
Course 2
2-1
2-3 Integers
Subtracting Integers
Warm Up
Problem of the Day
Lesson Presentation
Course
Course
22
2-1
2-3 Subtracting
Integers
Integers
Warm Up
Add.
1. –2 + 6
4
2. –3 + (–4)
–7
3. 7 + (–5)
2
4. 3 + (–4)
–1
6. –6 + 1
–5
5. –6 + (–1)
Course 2
–7
2-1
2-3 Subtracting
Integers
Integers
Problem of the Day
Ray earned $172 shoveling walks and
$188 babysitting. He spent $21 for a
shovel and rock salt and $26 for toys for
children. Which job was more
profitable?
babysitting
Course 2
2-1
2-3 Subtracting
Integers
Integers
Learn to subtract integers.
Course 2
2-1
2-3 Subtracting
Integers
Integers
During its flight to and from Earth, the space
shuttle may be exposed to temperatures as
cold as –250°F and as hot as 3,000°F.
To find the differences in these temperatures,
you need to know how to subtract integers with
different signs.
You can model the difference between two
integers by using a number line. When you
subtract a positive number, the difference is
less than the original number, so you move to
the left. To subtract a negative number, move
to the right.
Course 2
2-1
2-3 Subtracting
Integers
Integers
Helpful Hint
If the number being subtracted is less than the
number it is being subtracted from, the answer
will be positive. If the number being subtracted is
greater, the answer will be negative.
Course 2
2-1
2-3 Subtracting
Integers
Integers
Additional Example 1A: Modeling Integer Subtraction
Use a number line to find each difference.
4–1
–1
4
–2–1 0 1 2 3 4 5 6
Start at 0. Move right 4 spaces. To subtract 1,
move to the left.
4–1=3
Course 2
2-1
2-3 Subtracting
Integers
Integers
Additional Example 1B: Modeling Integer Subtraction
Use a number line to find each difference.
–3 – 1
–1
–3
–6–5–4 –3 –2–1 0 1 2
Start at 0. Move 3 spaces left. To subtract 1,
move to the left.
–3 – 1 = –4
Course 2
2-1
2-3 Subtracting
Integers
Integers
Additional Example 1C: Modeling Integer Subtraction
Use a number line to find each difference.
–2 – (–4)
–(–4)
–2
–4 –3 –2–1 0 1 2 3 4
Start at 0. Move left 2 spaces. To subtract –4,
move to the right.
–2 – (–4) = 2
Course 2
2-1
2-3 Insert
Lesson
Title Here
Integers
Subtracting
Integers
Check It Out: Example 1A
Use a number line to find each difference.
3–2
–2
3
–2–1 0 1 2 3 4 5 6
Start at 0. Move right 3 spaces. To subtract 2,
move to the left.
3–2=1
Course 2
2-1
2-3 Insert
Lesson
Title Here
Integers
Subtracting
Integers
Check It Out: Example 1B
Use a number line to find each difference.
–2 – 4
–4
–2
–6–5–4 –3 –2–1 0 1 2
Start at 0. Move 2 spaces left. To subtract 4,
move to the left.
–2 – 4 = –6
Course 2
2-1
2-3 Insert
Lesson
Title Here
Integers
Subtracting
Integers
Check It Out: Example 1C
Use a number line to find each difference.
–4 – (–2)
–(–2)
–4
–4 –3 –2–1 0 1 2 3 4
Start at 0. Move left 4 spaces. To subtract –2,
move to the right.
–4 – (–2) = –2
Course 2
2-1
2-3 Subtracting
Integers
Integers
Addition and subtraction are inverse
operations—they “undo” each other.
Instead of subtracting a number you
can add its opposite.
Course 2
2-1
2-3 Subtracting
Integers
Integers
Additional Example 2: Subtracting Integers by
Adding the Opposite
Find each difference.
A. 5 – (–2)
5+2
Add the opposite of –2.
7
B. –3 – 7
–3 + (–7)
Add the opposite of 7.
–10
C. – 1 – (–8)
Add the opposite of –8.
–1 + 8
7
Course 2
2-1
2-3 Insert
Lesson
Title Here
Integers
Subtracting
Integers
Check It Out: Example 2
Find each difference.
A. 4 – 2
4 + (–2)
2
Add the opposite of 2.
B. –2 – (–6)
–2 + 6
4
C. –1 – 4
Add the opposite of –6.
–1 + (–4)
–5
Course 2
Add the opposite of 4.
2-1
2-3 Subtracting
Integers
Integers
Additional Example 3: Evaluating Expressions with
Integers
Evaluate x – y for each set of values.
A. x = –3 and y = 2
x–y
–3 – 2 = –3 + (–2)
= –5
Substitute for x and y.
Add the opposite of 2.
B. x = 4 and y = –6
x–y
4 – (–6) = 4 + 6
= 10
Course 2
Substitute for x and y.
Add the opposite –6.
2-1
2-3 Insert
Lesson
Title Here
Integers
Subtracting
Integers
Check It Out: Example 3A & B
Evaluate x – y for each set of values.
A. x = –4 and y = –3
x–y
–4 – (–3) = –4 + 3
= –1
Substitute for x and y.
Add the opposite of –3.
B. x = –4 and y = 5
x–y
–4 – 5 = –4 + (–5)
= –9
Course 2
Substitute for x and y.
Add the opposite of 5.
2-1
2-3 Subtracting
Integers
Integers
Additional Example 4: Temperature Application
Find the difference between 32°F and –10°F.
32 – (–10)
32 + 10 = 42
Add the opposite of –10.
The difference in temperature is 42˚F.
Course 2
2-1
2-3 Insert
Lesson
Title Here
Integers
Subtracting
Integers
Check It Out: Example 4
Find the difference between 8°F and –5°F.
8 – (–5)
8 + 5 = 13
Add the opposite of 5.
The difference in temperature is 13˚F.
Course 2
2-1
2-3 Subtracting
Integers
Insert Lesson
Integers
Title Here
Lesson Quiz: Part I
Use a number line to find the difference.
1. 3 – 9
–6
Find each difference.
2. –7 – 4
3. –3 – (–5)
–11
2
4. Evaluate x – y + z for x = –4, y = 5, and z
–19
= –10.
Course 2
2-1
2-3 Subtracting
Integers
Insert Lesson
Integers
Title Here
Lesson Quiz: Part II
5. On January 1, 2002, the high temperature was
81˚F in Kona, Hawaii. The low temperature
was –29˚F in Barrow, Alaska. What was the
difference between the two temperatures?
110˚F
Course 2