LESSON 1MS. LINDSAYJULY 2, 2012
EOP Math
Real Numbers
Natural Numbers are 1,2,3,4…
Integers consists of the natural numbers together with their negatives and …-3,-2,-1,0,1,2,3…
Rational Numbers are constructed by taking ratios of integers
r=m/n where m and n are integers and n is not 0Irrational numbers- numbers that can not be
expressed as a ratio of a ratio Sgrt(2)
Properties of Real Numbers
Commutative Property – When we add or multiply two numbers, order doesn’t matter a+b=b+a ab=ba
Associative Property- When we add or multiply three numbers, it doesn’t matter which two we add first (a+b) + c = a + (b+c) (ab)c = a(bc)
Distributive Property – When we multiply a number by a sum of two numbers, we get the same result as multiplying the number by each of the terms and then adding the results a(b+c) = ab + ac (b+c)a= ab+ ac
Check for Understanding
Is -4 A Rational Number An Irrational Number
Is 2/3 A Rational Number An Irrational Number
Is 3^1/3 A Rational Number An Irrational Number
Property Example
(-1)a = -a-(-a) = a(-a)b=a(-b) = -(ab)(-a)(-b) = ab-(a+b) = -a – b-(a-b) = b-a
(-1)5 = -5-(-5) = 5(-5)7 = 5(-7) = -
(5*7)(-4)(-3) = 4*3-(3+5) = -3-5-(5-8) = 8-5
Properties of Negatives
Check for Understanding
-5*2 =?
5*2=?
5*-2=?
Property Description
a/b * c/d = ac/bda/b / c/d = a/b * d/ca/c + b/c = a+b/c
To multiply fractions, multiply numerators and denominators
To divide fractions, invert (flip) and multiply
To add fractions with different denominators, add the numerators
Properties of Fractions
Property Description
a/b + c/d=(ad + bc)/bd
ac/bc = a/bIf a/b + c/d then
ad=bc
To add fractions with different denom. Find a common denom. Then Add the numerators
Cancel numbers that are common facts in numerator & denom.
Cross multiply
Properties of Fractions
Exponents
If a is any real number and n is a positive integer, then the nth power of a is a^3 = a*a*a
The number a is called the base and n is called the exponent
Check for Understanding
A*A*A = ?
B*B*B*B*B*B= ?
C*C=
D=
Square Roots
Roots (or radicals) are the opposite operation of applying exponents
you can "undo" a power with a radical, and a radical can "undo" a power
The symbol is called the radical symbolTo simplify a square root, you "take out"
anything that is a "perfect square"; that is, you take out front anything that has two copies of the same factor:
Check for Understanding
Sqrt (144) = ?
Sqrt (64) =?
Sqrt (16) = ?
Perfect Squares
Why Perfect Squares?
Check for Understanding
Now with the person sitting next to you. Write down all of the perfect squares you can remember.
You have 20 seconds!
Law of Exponents
Fractions, Decimals and Percents
Fractions and decimals represent the same things: numbers that are not whole numbers.
Step 1: Find a number you can multiply by the bottom of the fraction to make it 10, or
100, or 1000, or any 1 followed by 0s.Step 2: Multiply both top and bottom by that
number.Step 3. Then write down just the top number, putting the decimal point in the correct spot (one space from the right hand side for every
zero in the bottom number)
Examples of Converting Fractions to Decimals
Converting Decimal to Percentages
To convert from decimal to percentage, just multiply the decimal by 100, but remember to put the "%" sign so people know it is per 100.