INTEGER NUMBERS€¦ · INTEGER NUMBERS Integer numbers : Positive numbers, negative numbers and...
Transcript of INTEGER NUMBERS€¦ · INTEGER NUMBERS Integer numbers : Positive numbers, negative numbers and...
INTEGER NUMBERS
Almudena Casares Fernández www.matematicasalmudena.com
INTEGERS IN THE REAL WORLD
VIDEO https://www.youtube.com/watch?v=NX3mNjSfERo
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POSITIVE AND NEGATIVE NUMBERS
Positive numbers: These numbers are greater than zero.
Sometime, positive numbers have a plus sign in front of them.
Negative numbers: These numbers are lower than zero.
Negative numbers have a minus sign in front of them.
Where are they used?
- Altitudes below sea level
- Winter temperatures (below freezing point)
- …
Zero is neither positive nor negative.
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INTEGER NUMBERS
Integer numbers : Positive numbers, negative
numbers and zero.
We use the number line to represent numbers
Z N
0, 1, 2, 3, ...
-1, -2, -3, ...
Venn Diagram
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ABSOLUTE VALUE
The absolute value is the number without its sign.
Absolute value represents the distance from zero in the
number line.
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OPPOSITE NUMBERS
The opposite number is obtained by changing its sign.
They have the same absolute value.
Op 3 3 Op 3 3
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ORDERING NUMBERS
Ordering numbers: The number line also shows the
order of numbers. For negative numbers you count
backwards from zero on the number line.
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ADDING AND SUBTRACTING
We can add and subtract negative numbers using the
number line to help us.
When adding, move to the right.
When subtracting, move to the left.
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5 8 3
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ADDING AND SUBTRACTING. RULE
a) If integers have the same sign before them,
add their absolute values and give the result
with the same sign as the integers.
b) If integers have different sign before them,
find the difference between their absolute
values and give the result with the same sign
as the integer with the greater absolute
value.
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RULE OF SIGNS TOGETHER
+ + = +
+ - = -
- + = -
- - = +
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REMOVING BRACKETS
1st) Remove all the brackets.
2nd) Joint similar numbers (with the same sing in front of them).
3rd) Do the operations with the similar numbers.
4th) End up the operation.
5 6 2 4 3 1
5 2 3 6 4 1
10 11
10 1 11
5 6 2 4 3 1
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ADDING AND SUBTRACTING. BRACKETS
Brackets inside out. Removing brakets.
5 4 10
5 6
5 6
11
5 4 10
5 4 10
5 10 4
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11
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BRACKETS. RULE
+ Nothing changes - Change all the
signs
5 4 10
5 4 10
9 10
1
5 4 10
5 4 10
5 10 4
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11
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MULTIPLYING AND DIVIDING
Use the rule of the signs:
+ + = +
+ - = -
- + = -
- - = +
+ : + = +
+ : - = -
- : + = -
- : - = +
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OPERATIONS REVIEW
PLAY AND LEARN
www.math-play.com/Integers-Jeopardy/Integers-
Jeopardy.html
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POWERS OF INTEGER NUMBERS
Rule:
If the base is positive then the result is always
positive.
If the base is negative then we look at the index.
If the index is an even number then the result is
positive.
If the index is an odd number then the result is
negative.
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POWERS OF INTEGER NUMBERS
Rule:
( )
( )
positive
posit
negativ
i
e
ve
n odd
n
n even
a
a
a
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POWERS OF INTEGER NUMBERS
Rule:
( )
( )
positive
posit
negativ
i
e
ve
n odd
n
n even
a
a
a
3
2
3
3 3 · 3 · 3 27
4 4 · 4 16
5 5 · 5 · 5 125
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POWERS. PROPERTIES
0
·
1) 1
2) ·
3) :
4)
5) · ·
6) : :
n m n m
n m n m
mn n m
nn n
nn n
a
a a a
a a a
a a
a b ab
a b a b
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ROOTS OF INTEGER NUMBERS
Negative numbers don’t have square root.
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Non-exis n9 te t
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ORDER OF OPERATIONS
1st) Parentheses
2nd) Powers and roots
3rd) Multiplications and divisions
4th) Additions and subtractions
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EXAMPLES
Example 1
Example 2
5 · 2 2 · 3 1· 7
10 6 7
10 13 3
14 : 7 2· 3 5
14 : 7 2· 8
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