Dividing with Integers

1
Dividing with Integers
Lesson 1.2.2
2
Lesson 1.2.2
Dividing with Integers
California Standard Number Sense 2.3 Solve
addition, subtraction, multiplication, and
division problems, including those arising in
concrete situations, that use positive and
negative integers and combinations of these
operations.
What it means for you Youll learn what to do
when you see positive and negative integers in
division questions.

• Key words
• integer
• quotient
• positive
• negative

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Lesson 1.2.2
Dividing with Integers
You already know how to divide by positive whole
numbers.
Now youre going to see how a number line can be
helpful in answering division questions with
positive and negative integers.
This is similar to what you saw in the previous
Lesson with multiplication.
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Lesson 1.2.2
Dividing with Integers
Division Means Breaking a Number into Equal Parts
Divide is another way of saying share out
equally.
10 2
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Lesson 1.2.2
Dividing with Integers
Example 1
A large bag contains 12 apples. The apples are
shared equally among 4 students. How many apples
does each student get?
Solution
You can see from the picture that if the apples
are shared out equally, each student will get 3
apples.
Solution follows
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Lesson 1.2.2
Dividing with Integers
You can also think of division as the opposite of
multiplication.
Example 1 asked you to find 12 4.
When you do a division, the result is called the
quotient.
You can rewrite that as
12 4 ?
which is the same as saying
4 ? 12
Then you can use guess and check to work out
what the question mark must represent
Try substituting 1 4 1 12
Try substituting 2 4 2 12
Try substituting 3 4 3 12
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Lesson 1.2.2
Dividing with Integers
Guided Practice
Solve without a calculator
18 3 21 7 12 6 26 2 100 4
1.
3 6 18, so 18 3 6
2.
7 3 21, so 21 7 3
3.
6 2 12, so 12 6 2
4.
2 13 26, so 26 2 13
5.
4 25 100, so 100 4 25
Solution follows
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Lesson 1.2.2
Dividing with Integers
Guided Practice
Solve without a calculator
6.
54 9 88 11 70 5 48 12
9 6 54, so 54 9 6
7.
11 8 88, so 88 11 8
8.
5 14 70, so 70 5 14
9.
12 4 48, so 48 12 4
Solution follows
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Lesson 1.2.2
Dividing with Integers
Division Can Also Be Shown on a Number Line
Here is a number line showing the multiplication
4 6 24.
You can think about this line in another way
It shows that the number 24 can be divided into 4
equal parts, each of size 6.
It also shows that the number 6 is one-fourth of
the way from 0 to 24.
So the number line also shows that 24 4 6
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Lesson 1.2.2
Dividing with Integers
Example 2
Use this number line to solve 35 5.
Solution
The number line shows the line from 0 to 35
divided into 5 equal parts. You can see that 7
is one-fifth of the way from 0 to 35, so the
answer must be 35 5 7.
Solution follows
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Lesson 1.2.2
Dividing with Integers
Guided Practice
Use this number line to answer Exercises 1012
102 2 102 3 85 5
10.
When 102 is divided into 2 equal parts, each part
has a size of 51.
11.
When 102 is divided into 3 equal parts, each part
has a size of 34.
12.
When 85 is divided into 5 equal parts, each part
has a size of 17.
Solution follows
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Lesson 1.2.2
Dividing with Integers
Guided Practice
Use this number line to answer Exercises 1318
13. 24 4 14. 60 5 15. 54
3 16. 36 2 17. 36 3 18.
48 4
6
12
18
18
12
12
Solution follows
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Lesson 1.2.2
Dividing with Integers
Negative Numbers Can Be Used in Division
Dividing with negative integers is similar to
dividing with positive integers. You still have
to work out how many equal parts go into the
number.
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Lesson 1.2.2
Dividing with Integers
Example 3
Calculate 42 7 using the number line.
Solution
The number 6 is one-seventh of the way from 0 to
42 on the number line. So the answer is 6.
You can check this by working out 7 (6) 42
Solution follows
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Lesson 1.2.2
Dividing with Integers
Guided Practice
Use this number line to answer Exercises 1922
19. 64 8 20. 64 2 21. 40
5 22. 48 3
32
8
8
16
Solution follows
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Lesson 1.2.2
Dividing with Integers
The rules for dividing integers are really
similar to the multiplication rules you saw in
the last Lesson.
Rules for dividing integers
For example
positive positive positive
For example
positive negative negative
For example
negative positive negative
For example
negative negative positive
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Lesson 1.2.2
Dividing with Integers
Example 4
Calculate (42) (7).
Solution
You can use a number line to work out that 42
divides into 7 equal groups of 6, so 42 7 6.
Then using the rules for dividing integers shown
above, you can see that 42 (7) 6
Solution follows
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Lesson 1.2.2
Dividing with Integers
Example 5
Calculate 120 (40).
Solution
You can use the rules for dividing integers
instead of the number line.
You are dividing a negative by a negative, so the
answer is positive.
The answer will be the same as 120 40 120
(40) 120 40 3
Check 40 3 120
Solution follows
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Lesson 1.2.2
Dividing with Integers
Guided Practice
Say whether the following will give positive or
negative answers. (You dont need to work out the
actual solutions.)
23. 18 3 24. 27 (9) 25. 17
(1) 26. 625 (25) 27. 363
11 28. 1008 (24)
negative
positive
positive
negative
negative
positive
Solution follows
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Lesson 1.2.2
Dividing with Integers
Independent Practice
Solve
1. 16 2 2. 45 5 3. 36 12
4. 66 (11) 5. 27 (9)
6. 126 9
8
9
3
6
3
14
Solution follows
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Lesson 1.2.2
Dividing with Integers
Independent Practice
Use a number line to solve
7. 63 7 8. 371 7 9. 40
(5)
9
53
8
Solution follows
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Lesson 1.2.2
Dividing with Integers
Independent Practice
Use a number line to solve
10. 126 6 11. 188 (4) 12. 64
(4)
21
16
47
Solution follows
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Lesson 1.2.2
Dividing with Integers
Independent Practice
The Garcias are going to the store. Mrs. Garcia
is going to divide 42 equally among her three
children so they have pocket money. How much
money does each child get?
13.
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14.
A submarine is 400 m from the surface of the
ocean. It rises to half of this depth. At
what depth is the submarine now?
200m
15.
Emmas bank account is overdrawn. Her balance
is 240. She pays some money into the account
so that her overdraft is reduced to one-third of
the old balance. What is the new balance on
Emmas account?
80
Solution follows
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Lesson 1.2.2
Dividing with Integers
Round Up
Youve now learned rules for adding, subtracting,
multiplying, and dividing integers.
In the next Lesson, youll see these rules
applied in real-life situations.