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```These are all the real numbers.
If a number doesn’t fall into any of those categories – but you
can write it as a fraction, it’s just called a rational number
If you can’t
write the
number as
a fraction,
it’s an
irrational
number.
4.561…
π
18
numbers, and you start calling
them integers.
Then, around 1st
zero, and you
started calling
them whole
numbers.
-2, -1, 0, 1, 2…
0, 1, 2, 3, …
The first kind of
rational number you
learned was called a
natural number.
1, 2, 3, …
CLASSIFYING RATIONAL NUMBERS
W,Z,Q
Q
N,W,Z,Q
N,W,Z,Q
Q
N,W,Z,Q
Q
Q
Z,Q
Q
Z,Q
N,W,Z,Q
Q
Q
Z,Q
rational
irrational
integer
whole
natural
200
0
-11
rational
irrational
integer
whole
natural
-1.08
1
-87
rational
irrational
integer
whole
natural
π
1
4
7
rational
irrational
integer
whole
natural
144
rational
irrational
integer
whole
natural
ABSOLUTE VALUE
Watch this:
http://vn2.me/AQKD
For each value, write it opposite, then its
absolute value.
opposite absolute value
1) -3
+3
3
2) 4
-4
4
3) 15
-15
4) -7
+7
7
5) 0
0
0
6) 1
-1
1
7) -1
+1
1
8) -50
+50
50
9) 10
-10
10
10)-2.5
+2.5
2.5
15
ABSOLUTE VALUE
17
– │14│
–14
16 - │ 10 │
16 - 10
6
4 – 19
–15
– 15
+ 16
+1
1
16 – 5
11
-│7│
–7
8
– │2│+
19
– 2 + 19
17
1.
–3
+9
problem.
2.
2 + –7
problem.
3.
–6
+ –4
problem.
The first integer, -3, is
the location,
The first integer, 2, is
the location,
The first integer, -6, is
the location,
The second integer, 9,
is the movement.
The second integer, –7,
is the movement.
The second integer, –4,
is the movement.
-3 + 9 = 6
2 + –7 = -5
-6 + –4 = -10
1.
–3
+9
9–3
6
+6
1.
2.
3.
4.
Signs are DIFFERENT.
SUBTRACT the absolute values.
Write down that number.
The answer is POSITIVE because the bigger
absolute value (9) is positive.
2. 5 + –8
8–5
3
–3
1.
2.
3.
4.
Signs are DIFFERENT.
SUBTRACT the absolute values.
Write down that number.
The answer is NEGATIVE because the bigger
absolute value (-8) is negative.
3. –2 + –6
2+6
8
–8
1.
2.
3.
4.
Signs are SAME.
Write down that number.
The answer is NEGATIVE because both
integers are negative.
= –34
= –15
=1
=6
= –7
= 14
= –11
=6
= –31
= –7
= –12
= 65
= –26
= –28
=9
= –8
= 25
= –31
=–80
= 41
Integer Subtraction - Number Line
1.
3–9
It’s a subtraction
problem.
2.
–2
– –7
It’s a subtraction
problem.
3.
–6
–3
It’s a subtraction
problem.
The first integer, +3, is
the location,
The first integer, –2, is
the location,
The first integer, –6, is
the location,
The subtraction sign
means move
to the left...
The subtraction sign
means move
to the left...
The subtraction sign
means move
to the left...
...the second integer,
+9, means
move 9 spaces.
...but, the second
integer, –7, means
reverse direction, then
move 7 spaces.
...the second integer,
+3, means
move 3 spaces.
3 – 9 = -6
–2
– –7 = 5
–6
–3
= -9
Integer Subtraction - The Rules
1.
4 – 10
4 + –10
10 – 4
6
–6
2.
–7
–1
– 7 + –1
7+1
8
–8
3.
–1
– –3
– 1 + +3
3–1
2
+2
1.
2.
3.
4.
5.
6.
Change the subtraction to addition, then...
...change the sign of the 2nd integer.
Signs are DIFFERENT.
SUBTRACT the absolute values.
Write down that number.
The answer is NEGATIVE because the bigger
absolute value (–10) is negative.
1.
2.
3.
4.
5.
6.
Change the subtraction to addition, then...
...change the sign of the 2nd integer.
Signs are SAME.
Write down that number.
The answer is NEGATIVE because both
integers are negative.
1.
2.
3.
4.
5.
6.
Change the subtraction to addition, then...
...change the sign of the 2nd integer.
Signs are DIFFERENT.
SUBTRACT the absolute values.
Write down that number.
The answer is POSITIVE because the bigger
absolute value (+3) is positive.
Integer Subtraction - Practice
1.
2.
3.
= –85
= – 15
= 60
4.
= –54
7.
5.
= – 84
8.
6.
= 93
9.
= –65
– 16 – ( – 95)
10.
= –56
= 79 11. – 5 – ( – 9) = 4
= 98
12.
= 97
13.
14.
15.
= –59
= –37
= 36
Integer Multiplication
Watch this:
http://nlvm.usu.edu/en/nav/frames_asid_322_g_1_t_1.html?from=topic_t_1.html
1. –7(8) =
There’s a number
smashed next to
parenthesis.
Why is this multiplication?
When you multiply or divide integers, it’s easy:
7•8
Step 1: Multiply (or divide) the absolute values.
Step 2: Now, look the signs:
– 56
• If they match...
it’s positive
• If they’re different...
it’s negative
Integer Division
2.  90 =
9
Why is this division?
+10
or
10
Fractions are division.
When you multiply or divide integers, it’s easy:
Step 1: Multiply (or divide) the absolute values.
Step 2: Now, look the signs:
• If they match...
it’s positive
• If they’re different...
it’s negative
Integer Multiplication and Division - Practice
1.
2.
= –48
= 168
5.
= –50
9.
6.
= –105
10.
= – 24
= 70
11.
= – 96
3.
= – 70
7.
4.
=288
8.
13.
= – 21
15.
= – 11
17.
14.
= –5
16.
= – 20
18.
= 24
= 143
12.
=– 200
= 17
= 13
Integers Operations
4
-10
1
7
-50
-125
-1
-5
-8
-3
4
3
1
-3
-9
-1
-7
96
-4
-3
Integers Operations
1. The change in elevation from the top to the
bottom of the Grand Canyon is -1.83 km. A
tour guide hikes down to the bottom every
day for a week, but rides an ATV back up. For
the week, what is the total change in elevation
that he hiked?
-12.81 km
2. Lina started the week with a checking account
balance of \$496. During the week, she wrote a
check in the amount of \$58.50, another check in
the amount of \$147.29, and then made a deposit
in the amount of \$180.00.
What was her
checkbook balance after this deposit? \$470.21
3. The temperature at 10 P.M. one evening
o
was 7 C. At 4 A.M. the next morning the
o
temperature was - 3 C . What was the change
in temperature from 10 P.M to 4 A.M.? -10oC
4.
Samantha has \$688.52 in her checking
account. If she makes a withdrawal of \$127.78,
what will be the new balance?
\$560.74
5. Jared and Natalie were playing basketball. After playing for a long time, Jared was losing by six
points. Then he scored ten points in a row, but Natalie scored the next five points. Then they had to
Natalie won by a point.
stop playing. Who won and by how many points?
6. Gertrude plays bingo every Tuesday. In the last 5 weeks, she has lost \$7, lost \$4, won \$8, lost
\$9, and won \$2. What was her average weekly gain or loss?
\$-2 or \$2 loss
```
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