Download 2-2 - Laurel County Schools

Name Class 2-2
Date Adding Integers
Connection: Rational Numbers
Essential question: How can you add rational numbers?
A rational number is a number that can be written as a ratio of two integers a
and b, where b is not zero. All integers are rational numbers.
video tutor
CC.7.NS.1b
1
EXample
A
Andrea has 6 cups of fruit punch in a bowl. She adds 3 cups of fruit
punch to the bowl. How many cups of punch are there altogether?
Find 6 + 3.
Start at 6.
Move ∣3∣ = 3 units to the right because the
second addend is positive.
. There are
The result is
B
© Houghton Mifflin Harcourt Publishing Company
Adding Rational Numbers with the Same Sign
0
1
2
3
4
5
6
7
8
9
10
cups of punch.
Selina removes 32 pounds of stones from a pile to make a walkway.
Then she removes another 28 pounds on her next trip. How many
pounds does she remove altogether?
Use negative numbers to represent amounts that are removed
from the pile.
Find -32 + (-28). Start at -32.
Move -28 = 28 units to the left because
the second addend is negative.
The result is
|
-60
|
. Selina removes
-40
0
-20
pounds.
TRY THIS!
Use a number line to find each sum.
1a. 3 + 1 =
0
1b. -2 + (-4) =
1
2
3
4
5
-7
-6
-5
-4
-3
-2
-1
0
REFLECT
1c. Conjecture Work with other students to make a conjecture about the sign of the
sum when the addends have the same sign.
Chapter 2
47
Lesson 2
To add two rational numbers with the same sign, find the sum of their
absolute values. Then use the same sign as the sign of the two rational numbers.
CC.7.NS.1c
2
EXample
A
Adding Rational Numbers with Different Signs
A football team gains 4 yards on their first play. Then they lose 7 yards
on their next play. What is the team’s overall gain or loss on the two plays?
Use a positive number to represent a gain and a negative number to represent a loss.
Find 4 + (-7).
Start at 4.
Move ∣-7∣ = 7 units to the
because the second addend is
The result is
The team gains / loses
B
-5 -4 -3 -2 -1
0
1
2
3
4
5
.
.
yards.
A school band decides to hold a bake sale to raise money. They withdrew
$50 from the band’s account for ingredients. The deposit they made back
into the account from the sale was $140. What was the overall increase
or decrease in the band’s account?
Use a positive number to represent a deposit and a negative number to represent a
­withdrawal.
Find -50 + 140.
Start at -50.
Move ∣140∣ = 140 units to the
because the second addend is
The result is
The account balance increases / decreases by $
–60 –40 –20 0
20 40 60 80 100 120 140
© Houghton Mifflin Harcourt Publishing Company
.
.
.
TRY THIS!
Use a number line to find each sum.
2a. -8 + 5 =
-8 -7 -6 -5 -4 -3 -2 -1
2b. 2 + (-3) =
0
1
2
-4
0
4
REFLECT
2c. Conjecture Work with other students to make a conjecture about the sign of the
sum when the addends have different signs.
Chapter 2
48
Lesson 2
To add two rational numbers with different signs, find the difference of
their absolute values. Then use the sign of the rational number with the greater
absolute value.
CC.7.NS.1a
3
Example
A
Abby takes 5 gallons of water out of an aquarium. Later, she adds
5 gallons of water to the aquarium. What is the overall increase
or decrease in the amount of water in the aquarium?
Use a positive number to represent water added to the aquarium and a
negative number to represent water taken out of the aquarium.
Find -5 + 5. Start at
Move ∣5∣ = 5 units to the
because the second addend is
The result is
This means
B
© Houghton Mifflin Harcourt Publishing Company
Finding the Additive Inverse
.
-5 -4 -3 -2 -1
0
1
2
3
4
5
.
.
.
Kendrick adds 2 cups of chicken stock to a pot. Then he takes 2 cups
of stock out of the pot. What is the overall increase or decrease in
the amount of chicken stock in the pot?
Use a positive number to represent chicken stock added to the pot and
a negative number to represent chicken stock taken out of the pot.
Find 2 + (-2). Start at
Move -2 = 2 units to the
because the second addend is
The result is
This means
.
∣ ∣
0
.
1
2
.
.
REFLECT
3a. Conjecture Work with other students to make a conjecture about the sum
of a number and its ­opposite.
3b. What is the opposite of 50? What is the opposite of -75?
The opposite, or additive inverse, of a number is the same distance from
0 on a number line as the original number, but on the other side of 0. The sum
of a number and its additive inverse is 0. Zero is its own additive inverse.
Chapter 2
49
Lesson 2
practice
Use a number line to find each sum.
1. 3 + (-8) =
-5 -4 -3 -2 -1
2. -2 + (-2) =
0
1
2
3
4
-5 -4 -3 -2 -1
5
3. -4 + 9 =
-5 -4 -3 -2 -1
0
1
2
3
4
5
4. 5 + (-7) =
0
1
2
3
4
0
-4
5
4
Tell what sum is modeled on each number line. Then find the sum.
5.
6.
0
-5 -4 -3 -2 -1
1
2
3
4
5
-5 -4 -3 -2 -1
7.
8.
-4
0
4
1
2
3
4
5
-2
0
-1
0
Find each sum without using a number line.
10. -15 + (-12) =
11. 24 + (-54) =
12. -40 + (-18) + 40 =
13. 15 + (-22) + 9 =
14. -1 + 1 + (-25) =
15. Describe a real-world situation that can be represented by the expression -10 + (-2).
Then find the sum and explain what it represents in terms of the situation.
16. A contestant on a game show has 30 points. She answers a question correctly
to win 15 points. Then she answers a question incorrectly and loses 25 points.
What is the ­contestant’s final score?
17. Error Analysis A student evaluated -4 + x for x = -9 and got an answer of 5.
What might the student have done wrong?
Chapter 2
50
Lesson 2
© Houghton Mifflin Harcourt Publishing Company
9. -31 + 16 =
Name Class 2-2
Date Name ________________________________________ Date __________________ Class __________________
Integers and
Rational Numbers
Additional
Practice
2
LESSON
Practice B: Adding Integers
Use a number line to find each sum.
1. 1 5
2. 4 (6)
________________________________________
________________________________________
Find each sum.
3. 51 (9)
4. 27 (6)
________________
7. 50 (7)
5. 1 (30)
________________
_______________
8. 19 (15)
________________
11. 17 11
________________
9. (23) 9
________________
10. 19 (21)
_______________
12. 20 (8)
________________
6. 15 (25)
________________
13. (15) (7)
________________
14. 12 (14)
_______________
________________
Evaluate e f for the given values.
9, f
24
________________________
© Houghton Mifflin Harcourt Publishing Company
© Houghton Mifflin Harcourt Publishing Company
15. e
18. e
15, f
15
________________________
16. e
17, f
7
_______________________
19. e
20, f
20
_______________________
17. e
32, f
19
________________________
30, f
20. e
12
________________________
21. The temperature rose 9 °F in 3 hours. If the starting temperature
was 5 °F, what was the final temperature?
_________________________________________________________________________________________
22. Matt is playing a game. He gains 7 points, loses 10 points, gains
2 points, and then loses 8 points. What is his final score?
_________________________________________________________________________________________
Chapter 2
51
Practice and Problem Solving
7
Holt McDougal Mathematics
Name ________________________________________ Date __________________ Class __________________
Integers
and Rational Numbers
Problem
Solving
LESSON
2
Problem Solving: Adding Integers
Write the correct answer.
1. The temperature dropped 12 °F
in 8 hours. If the final temperature
was 7 °F, what was the starting
temperature?
2. At 3 P.M., the temperature was 9 °F.
By 11 P.M., it had dropped 31 °F.
What was the temperature at 11 P.M.?
________________________________________
3. Tad owes John $23 and borrows
$12 more. How much does Tad
owe John now?
________________________________________
4. New Orleans, Louisiana, is 6 feet
below sea level. The highest point
in Louisiana, Driskill Mountain, is
541 feet higher than New Orleans.
How high is Driskill Mountain?
________________________________________
________________________________________
6. An airplane at 20,000 ft drops
2,500 ft in altitude. What is the
new altitude?
5. A submarine submerged at a depth
of 40 ft dives 57 ft more. What is
the new depth of the submarine?
________________________________________
________________________________________
7. Last week, Jane made deposits of
$64, $25, and $37 into her checking
account. She then wrote checks for
$52 and $49. What is the overall
change in Jane’s account balance?
8. In Indianapolis, Indiana, the coldest
recorded temperature was 23 °F.
The hottest recorded temperature
was 127 °F higher. What was the
hottest temperature in Indianapolis?
A $99
C $126
F 150 °F
H 104 °F
B $25
D $227
G 127 °F
J 150 °F
9. Helena borrowed $189 from her
parents to buy an electric bass. She
paid back $56 last week and $64 this
week. How much does Helena still
owe her parents?
10. The Aral Sea and the Caspian Sea
are actually lakes. The elevation of
the Caspian Sea is 92 feet below sea
level. The Aral Sea is 217 feet higher.
What is the elevation of the Aral Sea?
A $133
C $69
F 125 ft
H 309 ft
B $120
D $29
G 309 ft
J 125 ft
Chapter 2
527
Practice
Problem
Solving
Holtand
McDougal
Mathematics
© Houghton Mifflin Harcourt Publishing Company
© Houghton Mifflin Harcourt Publishing Company
Choose the letter for the best answer.