Download 1 - Number Sets and Integers

MPM1DE – Review
565328971
Date: _________________________
Number Sets and Integers
Symbol
Name
Definition
Natural
Numbers
The counting numbers starting from 1.
Whole
Numbers
All the natural numbers and 0.
Integers
All the whole numbers and their
opposites.
Rational
Numbers
Irrational
Numbers
Numbers that can be written as a
fraction whose denominator is not 0.
In decimal form, rational numbers
terminate or repeat.
Numbers that cannot be written as a
fraction.
In decimal form, irrational numbers do
not terminate or repeat.
Real
Numbers
All rational and irrational numbers.
Imaginary
Numbers
The result of square-rooting a
negative number.
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Examples
MPM1DE – Review
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Integers
Numbers like +5, -7 and -10 are called integers. These numbers are used to show
direction above or below some zero point.
Integers can be shown on a number line:
When two integers are compared on a number line, the integer to the right is the greater
one. When comparing two values, we used specific language and symbols. For
example, since +3 is to the right of -4, we say “+3 is greater than -4” and we write
 3  4 . We can also say “-4 is less than +3” and write  4  3 .
Note:
A positive integer can be written without the + sign. However, a negative integer must
always be written with the – sign.
Here’s a list of the symbols that we use when comparing two values:
Symbol
Description
Greater than
Less than
Equal to
Not equal to
Greater than or equal to
Less than or equal to
Opposite Integers - integers with the same "number" but have different signs. Every
integer, except 0, has an opposite.
Examples:
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MPM1DE – Review
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Adding and Subtracting Integers
On a number line, think of positive integers as trips to the right and negative integers as
trips to the left.
Evaluate 2   3  8   5 .
To subtract an integer, you must add its opposite.
Evaluate 3   6  2 .
We can evaluate expressions like the ones above without using a number line. Just
replace all the double signs with single signs, and then add or subtract from left to right.
Remember the following rules:
 Two positives make a positive.
 Two negatives make a positive.
 A positive and a negative make a negative.
Addition
Evaluate.
a) 7  2
b) 5   3
e)  5   3
f)
Subtraction
Evaluate
a) 8  3  
b) 5  7
e) 5  11
f)
 10   2
34
c)  4   6
d)  8   1
g) 7   3
h)  8  4
c) 1 6
d) 10  4
g)  3  7
h) 3  9
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MPM1DE – Review
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Multiplying and Dividing Integers
We can use the same rules as above to multiply and divide integers.
Examples
Evaluate the following expressions.
a) ( 3)( 4)
b) ( 6)  ( 4)  3
c) 11(2)
d) ( 10)  5
e) ( 12) / ( 3)
f)
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20( 3)
( 6)( 2)
MPM1DE – Review
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Integers – Addition and Subtraction
To be completed without a calculator.
1. Find each sum.
a)  3   2
_____
b)  8   8
_____
c)  4   5
_____
d) 5   7
_____
e)  9  2
_____
f)
 4   6
_____
g)  8   4
_____
h)  5  (  5)
_____
i)
43
_____
2. Find each difference.
a) 4  (  3)
_____
b)  5  (  2)
_____
c) 6  (  6)
_____
d) 4  (4)
_____
e)  7  (  8)
_____
f)
 7  (3)
_____
g)  4  (  7)
_____
h)  4  3
_____
i)
4  (  7)
_____
3. Simplify.
a) 5  (  3)  4
c)
b)  4  (  3)  5
 6 4 3
d)  4  7  5
4. Which choice would make each statement true: >, <, =?
a)  3  4  5  3 _____  4  3  1  ( 2)
b) 4  7  6  8 _____  3  5  ( 7)  4
c) 5  13  7  2 _____ 4  5  ( 3)  5
d) 7  3  ( 15)  11 ___  7  3  ( 11)  15
5. In each row, which expression has the greatest value? The least value?
a)  5  3  4, 4  3  ( 4), 5  ( 3)  10
b) 9  ( 2)  7, 5  ( 7)  ( 9),  5  3  6
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Integers – Multiplication and Division
To be completed without a calculator.
1. Find each product.
a) (3)(2)
b) ( 4)( 9)
c) (4)(3)
d) (5)(4)
e)  4(9)
f)
a)  2 ( 7)
b)  3(8)
c) 5(7)
d)  5(7)
e) ( 3)( 7)
f)
(2)(7)
 4(9)
2. Simplify.
3. Find each quotient.
a)  18  ( 6)
b) 51  ( 17)
c)  18  (18)
d) 60  ( 12)
4. Simplify.
a)
 50
5
b)
 15
5
c)
48
6
d)
 16
16
e)
 18
9
f)
 81
27
5. Evaluate.
a) (4) 2
b)  2 4
c)  3 3
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d) (2) 5