Download The Set of Real Numbers Set Characteristics Examples Natural

The Set of Real Numbers
Set
Characteristics
Examples
Natural
{1, 2, 3, 4, …..}
(Counting)
Whole
{0, 1, 2, 3, 4, …..}
Integers
{….., -2, -1, 0, 1, 2, …..}
Rational
Fractions, repeating decimals, terminating decimals
Irrational Non-repeating and non-terminating decimals
Real
5
8
, 0.75, 0.236
1.2122....., 14
Set of all rational and irrational numbers
Operations with Signed Numbers
Addition
1)
The sum of two positive numbers is positive.
2)
The sum of two negative numbers is negative.
3)
When adding a positive and a negative:
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
Ignore the signs.

Subtract the number with the smaller absolute value from the number with the
larger absolute value.

The answer has the same sign as the number with the largest absolute value.
Subtraction
Subtracting is the same as adding the opposite - NO DOUBLE SIGNS!!
4 - ( -3 ) = 4 + 3
Multiplication and Division
1)
The product/quotient of two positives is positive.
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2)
The product/quotient of two negatives is positive.
3)
The product/quotient of a positive and a negative is negative.
Simplifying Radical Expressions
1)
Check if the radicand is a perfect square. If so, just simplify!
Example
2)
36 = 6 or
25
81

5
9
If the radicand is not a perfect square, determine the largest perfect square that
divides into the radicand.
Example
44 
4  11
Simplify the square root of the perfect square. That number becomes the
coefficient of the radical.
Example
44  4  11  2 11
Sometimes, it’s difficult to find the largest perfect square. To help you, you could
divide the radicand by 2. Check the perfect squares less than or equal to the
quotient. Starting with the larger numbers is a good way of attacking it.
Example
180 is a big number!!! Where to start?
180
180  2  90
Start with squares less than 90.
81 doesn’t divide into 180, nor 64, nor 49. But,
180  36  5  6 5
3)
If the radical has a coefficient, simplify the radical and multiply the coefficients.
Example
5 90  5 9  10  5  3 10  15 10
The Most Important Thing:
Memorize the Perfect Squares!!