Transcript Adding Integers PPT (2015)

Adding Integers
•Workbook pgs. 19-26
•On-line textbook:
Chapter 1 (lesson 2)
The integers are the set of whole
numbers and their opposites. Including
zero.
Remember!
The whole numbers are the counting
numbers and zero: 0, 1, 2, 3, . . . .
The opposite of a number is the same
distance from 0 on a number line as the
original number. 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
A number’s absolute value is its distance
from 0 on a number line.
They are always positive or zero.
Reading Math
The symbol is read as “the absolute value of.”
For example -3 is the absolute value of -3.
Ex # 1: Modeling Integer Addition on the Number Line
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
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Example # 2: Modeling Integer Addition on the Number Line
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
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8
Ex # 3: Modeling Integer Addition on the Number Line
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
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Insert Lesson Title Here
Ex # 4: Modeling addition integers on the number line
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
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8
Adding Integers
Adding Integers (OMG)
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.
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Adding Integers
Ex # 5: Adding Integers Using Absolute Values
Find each sum.
–4 + 8
The signs are different. Find the difference
of the absolute values.
–4 + 8
4
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Think: 8 – 4 = 4.
Use the sign of the
integer with the
greater absolute
value.
Ex # 6: 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.
Ex # 7: Adding Integers using absolute values
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.
Ex # 8: Adding integers using absolute values
Find each sum.
–13 + (–24)
The signs are the same. Find the sum of the
absolute values.
–13 + (–24) Think: 13 + 24 = 37.
–37
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Use the sign of the two integers.
Ex # 9 : 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.
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Ex # 10: Adding integers using absolute values
Evaluate x + y for x = –24, y = 17.
x+y
–24 + 17
–7
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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).
Ex # 11 (Word Problems: Adding Integers)
“Application”
A roller coaster starts at point A. It goes up 20 feet, down 32
feet, and then up 16 feet to point B. Write an addition
sentence to find the height at point B in relation to point A.
Find the sum and explain its meaning. .
20 + (-32) + 16 =
36 + (-32) =
4
Add positive integers
Find the differences of the
absolute values.
The answer is positive.
Point B is 4 feet higher than point A.
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Ex # 12 (Word Problems: Adding Integers)
“Application”
Max owes his brother $20. He gives his brother $ 10 one week
and then the next week he gives $5. Write an addition
sentence to describe this situation. Then find the sum and
explain its meaning. .
(-20) + 10 + 5 =
15 + (-20) =
-5
Add positive integers
Find the differences of the
absolute values.
The answer is negative.
Max still owes his brother $5.
Course 2
Ex # 13 (Word Problems: Adding Integers)
“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
Ex # 14 (Word Problems: Adding Integers)
“Application”
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
Adding
Insert Lesson
Integers
Title Here
Now you try a few problems (summary) pg. 1
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.
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–17
Homework (differentiated)
Tues 8-11
•If you got 4 problems correct, complete pg.
23-24 in workbook #’s 11-18
•If you got 3 problems correct, complete pg.
23-24 in workbook #’s 11-14 & # 18
•If you 1 or 2 problems correct, complete
pg. 23-24 in workbook #’s 1-11, 13,14,18
•HINT…….Use the properties on pg.
21 to help you answer question # 14.
Adding
Insert Lesson
Integers
Title Here
Now you try a few problems (summary) pg. 2
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