LESSON 1 MS. LINDSAY JULY 2, 2012 EOP Math. Real Numbers Natural Numbers are 1,2,3,4… Integers...

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.