Transcript 4 + 3 Operations with Signed Numbers Multiplication and Division

The Set of Real Numbers
Set
Natural
(Counting)
Whole
Characteristics
{1, 2, 3, 4, …..}
{0, 1, 2, 3, 4, …..}
Integers
{….., -2, -1, 0, 1, 2, …..}
Rational
Fractions, repeating decimals, terminating decimals
Irrational
Real
Examples
Non-repeating and non-terminating decim als
Set of all rational and irrational numbers
5
8
, 0.75, 0.236
1.2122.....,
14
Operations with Signed Numbers
Addition
1) The sum of two positive numbers is
positive.
2) The sum of two negative numbers is
negative.
Operations with Signed Numbers
Addition
3) When adding a positive and a negative:



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 larger absolute value.
Operations with Signed Numbers
Subtraction
Subtraction is the same as adding the
opposite - NO DOUBLE SIGNS!!
4 - (-3) = 4 + 3
Operations with Signed Numbers
Multiplication and Division
1)
The product/quotient of two positives is
positive.
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
36  6
or
25
81

5
9
Simplifying Radical Expressions
2)
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
Simplifying Radical Expressions
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
180  2 = 90
180 is a big number!! Where to start?
Start with squares less than 90.
Simplifying Radical Expressions
81 doesn’t divide into 180, nor 64, nor 49.
But,
Example
180 
36  5  6 5
Simplifying Radical Expressions
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!!
Operations with Fractions
• Addition and Subtraction Rules
The first step when adding and
subtracting fractions is to find a
common denominator.
Adding and Subtracting
Fractions
3 1
 
4 2
3 1(2)
 
4 2(2)
3 2
 
4 4
1

4
Here, my least common denominator will be 4.
Change the second fraction by multiplying numerator and
denominator each by 2.
Watch signs when adding numerators.
Make sure your final answer is in simplest form.
Multiplying Fractions
7 5

10 14
1 1

2 2
1

4
Cross simplify if possible.
Multiply across.
Dividing Fractions
• Take the reciprocal of the second
fraction and the problem becomes a
multiplication problem. Then, follow the
rules for multiplication.
 4  2  4  3  2   3 6
                 
 5   3   5   2   5   1 5