OBJECTIVES:
1. To understand fractions
2. To reduce fractions
3. To compare fractions
4. To find fractions between two given
fractions
Solve:
1. x + 2 = 5
2. x + 4 = 3
3. 6x = 3
A fraction is an ordered pair of numbers a and b (not
necessarily integers), b≠ 0, written
The number a is called the numerator of the fraction , and
the number b is called the denominator of the fraction.
If a and b are integers, we call the fraction a rational
numbers (Q). Q = { a and b are integers,
b≠0}
Example:
Classify each of the expressions above as rational
numbers,
fractions or both?
Any integer x is view as
VENN DIAGRAM:
OF THE REAL
NUMBERS
N: Natural Numbers
W: Whole Numbers
I: Integers
Q: Rational Numbers
R: Real Numbers
TRUE OR FALSE:
Assign page 297 Preliminary Problem
MODELS FOR FRACTIONS
1. Colored Regions Model
What fraction is shaded? ____ What fraction is
shaded?______


What fraction of the balls are shaded? 
Shade 2/5 of the balls. 
3. Number Line Model
Shade 5/6 of the unit segment
TRY THESE
Draw a number line and include the following points.
4. Fraction Strip Model page A29 Act Book
When students are asked to show and understanding of the
concept
of a fraction, the area model is preferred over the set model
because the total area is more flexible.
Fraction strips can be folded into parts so that the
resulting strip
is equal in length to the given fraction. Folds may be made
ONLY on the lines of the strips.
Some of the English words for rational numbers are the
same as
the words for position:
the third person in line and one third for 1/3.
This causes confusion for students. The Chinese read 1/3 as “out of
three parts, (take) one.
Proper fraction A fraction
where
A proper fraction is a fraction greater than 0 but less
than 1.
Examples of proper fractions
Improper fractionA fraction a/b , where
An improper fraction is a fraction that is greater than 1.
Examples of improper fractions
Equivalent Fractions
Paper Folding
Fold in half
Fold in half
represent the same
rational number and are
equivalent fractions or equal fractions.
Notice that the value of the fraction does not change when
the numerator and denominator are multiplied by the same
number.
TRY THESE: Name four rational numbers equivalent to 1/4 .
Remember: Fractions that express the same quantity are
called equivalent fractions.
Fundamental Law of Fractions
Let a/b be any fraction and n be a nonzero whole number,
then
Actually, n can be any nonzero number.
This law show us that
We can use this law to “build up” fractions and also to
simplify “reduce” them.
SIMPLIFY:
Definition of Simplest Form  (lowest terms)
A rational number a/b is in simplest form if a and b have no
common factors greater than 1, that is a and b are relatively
prime. (that is, the GCD (a, b) = 1).
TRY THESE: Write each of the following in simplest
form.
Equality of Fractions
Methods to determine if two fractions are equal
A. Reduce to simplest form.
B. Rewrite both fractions with the same least
common denominator.
C. Write both fractions with any common
denominator
Let’s use method 3 to explain our next Property.
When are equivalent?
therefore thus
if and only if ad = bc.
Property
Two fractions are equal if, and only if, ad
= bc.
Use the above property to determine if the following
fractions are equal:
Ordering Fractions
Methods to order fractions
A. Like Denominators : It is simple to compare fractions
that have like denominators; just compare the numerators.
The one with the greater numerator is the greater fraction
Theorem 5.1 If a, b, and c are integers and
and only if, a > c.
Insert <, >, or =.
B. Unlike Denominators:
1. Area Model or Fraction Strips
Compare
2. Getting the LCD and comparing
3. Using Cross Products
THEOREM 5.2 If a, b, c, and d, are integers and b > 0,
d> 0, then if, and only if, ad > bc.
Therefore, because
3(12) > 5(7).
because 3(13) > 4(9)
because 15(9) > 16(8)
TRY THESE
TRY THESE Arrange each of the following in ascending
order. Do not convert the fractions to decimals.
Denseness of Rational Numbers
Property Given rational numbers
there is a
rational number between these two numbers
1. Find a fraction between 1/3 and 1/2 .
Rewrite with a common denominator.
2. Find a fraction between 7/8 and 5/6
. How many rational numbers lie between 7/8 and 5/6 ?
Try This: Find three fractions between 1/4 and 1/3.
Class work Fraction Circle Worksheet
Homework Math XL section 5.1 and problems from the
book page 310313 # 1,4, 6, 7, 8, 10, 12, 20, 35