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1. To understand fractions
2. To reduce fractions
3. To compare fractions
4. To find fractions between two given


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}


Classify each of the expressions above as rational numbers,
fractions or both?

Any integer x is view as


N: Natural Numbers
W: Whole Numbers
I: Integers
Q: Rational Numbers
R: Real Numbers


Assign page 297 Preliminary Problem


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

Draw a number line and include the following points.

4. Fraction Strip Model page A-29 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 fraction-A 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

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,

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.


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

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

Let’s use method 3 to explain our next Property.
When are equivalent?

therefore thus

if and only if ad = bc.

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

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 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 310-313 # 1,4, 6, 7, 8, 10, 12, 20, 35

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