Algebra Honors (Period 6 & 7)

Properties of Rational Numbers 11-1

A real number that can be expressed as the quotient of two integers is called a rational number
A rational number can be written as a quotient of integers in an unlimited number of ways.
3 = 3/1= 6/2 = 12/4 = -15/-5
To determine which of two rational numbers is greater, you can write them with the same positive denominator and compare the numerators
Which is greater 8/3 or 17/7?
the LCD is 21
8/3 = 56/21
17/7 = 51/21
so 8/3 > 17/7

For all integers a and b and all positive integers c and d
a/c > b/d if an only if ad > bc
a/c < b/d if and only if ad < bc This method compares the product of the extremes with the product of the means Thus 4/7 > 3/8 because (4)(8) > (3)(7)

The Density Property for Rational Numbers
Between every pair of different rational numbers there is another rational number
The density property implies that it is possible to find an unlimited or endless umber of rational numbers between two given rational numbers.

If a and b are rational numbers and a< b then the number halfway from a to b is
a + (1/2)(b-a);
the number one third of the way from a to b would be
a + (1/3)(b-a) and so on

Math 6 Honors ( Periods 1, 2, & 3)

Fractions 6-1

The symbol 1/4 can mean several things:
1) It means one divided by four
2) It represents one out of four equal parts
3) It is a number that has a position on a number line.



1/8 means 1 divided by 8 or 1 ÷ 8
A fraction consists of two numbers
The denominator tells the number of equal parts into which the whole has been divided.
The numerator tells how many of these parts are being considered.
we noted that we could abbreviate ...

denominator as denom with a line above it

and numerator as numer

we found that you could add

1/3 + 1/3 + 1/3 = 3/3 = 1
or 1/4 + 1/4 + 1/4 + 1/4 = 4/4 = 1
we also noted that 8 X 1/8 = 8/8 = 1

We also noticed that 2/7 X 3 = 6/7


So we discussed the properties
For any whole numbers a, b,and c with b not equal to zero

1/b + 1/b + 1/b ... + 1/b = b/b = 1 for b numbers added together

and we noticed that b X 1/b = b/b = 1
we also noticed that
(a/b) X c = ac/b

We talked about the parking lot problem on Page 180

A count of cars and trucks was taken at a parking lot on several different days. For each count, give the fraction of the total vehicles represented by
(a) cars

(b) trucks

Given: 8 cars and 7 trucks
We noticed that you needed to find the total vehicles or 8 + 7 = 15 vehicles
so

(a) fraction represented by cars is 8/15
(b) fraction represented by trucks is 7/15


What if the given was: 12 trucks and 15 cars


(a) fraction represented by cars is 15/27
(b) fraction represented by trucks is 12/27

What about
GIVEN:
9cars
35 vehicles
This time we need to find out how many trucks there are
35 -9 = 26
so
(a) 9/35
(b) 26/35

We aren't simplifying YET