The document provides information about fractions, including: - Definitions of factors, greatest common divisors (GCD), and least common multiples (LCM) as they relate to fractions - Examples of equivalent, simple, improper and mixed fractions - Methods for comparing fractions, writing fractions as decimals or percentages, and performing fraction operations like addition and subtraction - Properties of fraction operations like commutativity and associativity The overall purpose is to review fraction concepts and provide examples and explanations of how to work with different fraction types and operations.

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FRACTION
SITI NURAINI
NUR ENDAH P.
ICHWANU T
AFFILIATIS S. R.

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INTRODUCTION

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Do you still remember about the definition of
factor?
factor of a number is natural number that can
divide a number till nothing remainder
Do you still remember about the definition of
GCD?
Greatest Common Divisor / Greatest Common
Factor is the greatest factor that satisfied for two
or more than two numbers.

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• Do you still remember about the definition of
LCM?
Least Common Multiple (LCM) is the least
multiple that satisfied for two or more than two
numbers.
• How about if natural number can’t divide a
number till nothing remainder?
Who am I??

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Learning Objective: Students are able to:
• Simplify fraction.
• Change a mixed number into fractions and its
inverse.
• Compare fractions and order the fractions.
• Write a fraction in a decimal or a percent form,
• Operate fractions and apply it in everyday life.
• Explain properties of the operations and its
application in everyday life

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• Fraction numbers is numbers that
can be stated as , with p and q
are integers number and q are not
equal to zero and q is not the factor
of p
• p is called numerator and q is called
denominator.
Numerator
Denominator

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The cake is divided into
4 equal parts. So, a
part shows part of
cake.
The circle is divided
into 4 equal parts.
So, a part shows
part of circle.

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EQUIVALENT FRACTION

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 The region of circle is divided
into some equal parts. The
shaded area are shown by
numbers beside each figure.
 Because the shaded area are
equal, so those three fractions
are “Equivalent Fraction”

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Look at the relations of fractions below !
From the examples beside,
we can conclude that “The
Equivalent Fraction” can be
obtained if numerator and
denominator from a fraction
are multiplied by the same
number

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Look at the relations of fractions below !
From the examples beside,
we can conclude that “The
Equivalent Fraction” can be
obtained if numerator and
denominator from a fraction
are divided by the same
number

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Conclusion
To determine “The Equivalent Fraction” with
is used the following characteristics :
OR

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Look at the bars on the
left.
• How many parts are in each
bar?
• How many parts are
shadowed?

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Simple Fractions
Fractions 1/2, 2/4, and
3/6 have equal values ( you
can look from the picture ).
Of these fractions, ½ is
the simplest form.
A fraction is called the
simplest form (simple
fraction) if the Greatest
Common Factor (GCF) of the
numerator and the
denominator is 1.

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Write in the simplest form !
The GCF of 28 = 1, 2, 3, 4, 7, 14, 28
The GCF of 56 = 1, 2, 3, 4, 7, 8, 14, 28, 56

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CHANGE A MIXED fraction INTO
FRACTIONS AND ITS INVERSE

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What is mixed fraction?
Mixed Fraction is fractions whose
numerator greater than denominator and
the denominator is not the factor of
numerator , for example
Those fractions can be changed into
number consist of integer number and
fraction named “mixed fraction”.

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Changing improper Fraction into Mixed
Fraction
• First Method
• Second Method
Denominator

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conclusion

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Changing Mixed Fraction into improper
Fraction
1 2 3 4 5 6 7 8
1

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Changing Mixed Fraction into improper
Fraction
1. Multiple the integer with the
denominator
2. Add the product of step 1 with
the numerator
3. Write the fraction as
1.
2.
3.

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We can conclude that....

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exercise
• Change this fraction into mixed fraction and
converesly

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Comparing Two Fractions
It can be stated that is
“Less Than” or written
as
It also can be stated
that is “Greater Than”
or written as
4
2
4
3
4
2
4
3
4
3
4
2
4
3
4
2
4
2
4
3

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Therefore, suppose we have
two fractions with equal
denominator, to state that one
is greater than or less than the
other, we only need to compare
the numerators.

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From the pictures, we
know that:
is “Greater Than” .
Or, written as
is “Less Than” . Or,
written as
8
5
4
3
4
3
8
5
8
5
4
3
8
5
4
3
8
5

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Looking for the Greater and the Less
1. Determine the LCM
of both
denominators.
2. Express the fractions
in equal fraction that
we get similar
denominators.
3. Compare the
numerator
1. 4=4, 8, 12, …
8=8, 16, 24, …
The LCM is 8
2.
3. So,
So,
8
6
4
3
8
5
8
5
65 8
6
8
5
56
8
5
8
6

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Example
Arrange these fraction from the least to the
greatest
5=5, 10, 15, 20, 25, 30, 35, 40, 45, …
4=4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, …
8=8, 16, 24, 32, 40, 48, …
LCM of denominators is 40. So, we have the equal
fractioon:
8
5
,
4
3
,
5
2
40
25
8
5
40
30
4
3
40
16
5
2
By comparing the numerator, we get the
arrangement from the least to the
greatest is
4
3
,
8
5
,
5
2

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WRITE A FRACTION IN A DECIMAL
OR A PERCENT FORM

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• How about decimal?
• Have you ever known about
decimal?

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• A fraction can also be expressed as decimal.
• Similarly, a decimal can be expressed as a fraction.
How can it be?

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How to change fractional into
decimal forms? Conversely,
How to convert decimal into
fractional forms?

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To convert Fractional into Decimal Forms
• Fractions can be changed into decimal by changing its
denominator into 10, 100, 1000, etc.
example:
Such a number as
0.4 is called
decimal and read
“zero point four”.

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Changing Decimal into Fractional Forms
• By reversing order of process in abovementioned
problems, fraction of any decimal form can be obtained
Example:

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• How about the denominator is difficult to change into 10,
100, 1000, etc?
Example:
Therefore, to change the fraction into
decimal form, common division is made.
Beside that, you can get the calculator to
get decimal value .

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Exercise:
Change the following fractions into decimal form and
change the following decimals into fraction form

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PERCENTAGE

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Look at the article on the left
In this article, it is
written 18% and 60-
70%. Do you know
what percentage is? If
you compare a
number to 100, then
you will have a
percentage.

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How to change fractional into
percent forms? Conversely,
How to change percent into
fractional forms?

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Forming Fractions into Percentage
%75
4
3
%25
4
1
%50
2
1
How
Could
It be?

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How to change fraction into percentage?
1. Change the fraction into
decimal form
2. Multiple the product with
100%
75,0
4
3
%75%10075,0
Now, we have known
that %75
4
3

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How to Change Percentage into Fraction?
1. Divide the percentage
with 100% to get
decimal form
2. Change the decimal
form into fraction
1.
2.
Factor of 5 are 5 and 1
Factor of 10 are 1, 2, 5, and
10
So, the GCD of 5 and 10 is 5
10
5
5,0
2
1
510
55
10
5
We Get
2
1
%50
5,0
%100
%50
%100%50

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Fractional Addition by Fraction
Example 1:
Solution:
1. Drawing of circle
2. Drawing of circle

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From those picture, we can conclude that,
the result of fraction addition that has same
denominator can be gotten by adding the
numerator, while the denominator is same.
For every fractions and with b ≠ 0, so

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By using number line
So, 0

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Example 2:
Solution:
1. Find the LCM of 2 and 3
2= 2, 4, 6, 8,…
3= 3, 6, 9, 12,…
2. Express the fractions in equal fraction that we get similar
denominator
,
3. Add the numerator and get the result

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If the fractions that will be added
has different denominator, firstly we
must make it same by using
LCM(Least Common Multiplication)
from its denominator

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Adding Mixed Fraction
1. Change the denominator
of the fractions
2. Express the fractions in
equal fraction that we
get similar
denominators.
3. Add the numerator and
get the result
1.
2.The multiple of 4 are 4
4, 8, 12, …
8 8, 16, 24, …
The LCM is 8
3.

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EXERCISES
Find the addition of fractions below:
1.
2.
3.
4.

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The Properties of Addition in
Fractions

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Commutative
For example:
So, =

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For any fraction and with b≠0 and q≠0,
applies
it is called commutative in addition

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• Example:

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Associative Properties
For any fractions , , and with b, d, f ≠ 0 applies:

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Ani found parts of a cake on the table. Then she
ate part of the cake. What part of the cake
remained?

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For any fractions and with b≠ 0, so

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Subtracting Unlike Fractions
Solve
Solution:
1. Find the LCM of 2 and 3
2= 2, 4, 6, 8, …
3= 3, 6, 9, 12,…
the LCM is 6
2. Express the fractions in equal
fraction that we get similar
denominators
,
3. Find the result

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From that example, we can conclude
that subtract unlike fractions, you have to
convert the fractions to like fractions first by
using the Least Common Multiple (LCM) of
the denominators.

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Subtracting Mixed Numbers
Calculate
Solution:
1. Convert the mixed
fractions into common
fractions
2. Find the LCM of 3 and 5
3= 3, 6, 9, 12, 15,…
5= 5, 10, 15, 20,…
3. Express the fractions into
equivalent fractions, so we
get same denominator
4. Find the result
1.
2. The LCM is 15
3. ,
4.

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Exercises
Find the result of fractions subtraction

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Multiplication of Fraction

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Multiplying a Whole Number by a Fraction
Example:
Student A, B, and C will make handicraft. Each of
them needs of ribbon. How many meter of
ribbon that are need?
Solution:
A B C
SO, it can be written as:

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From the example, we can conclude that a
whole number multiply by a fraction is a
whole number multiply with the numerator
and the denominator is exist or can be
denoted:

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Multiplying a Fraction by a Whole Number
Example:
Ani has 5 meters of ribbon. m of ribbon will be
make a flower. How many meter of ribbon that is
needed to make a flower?
Solution:
1m 1m 1m 1m 1m
Based on the picture m of 5 m is 1 m or

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Multiplying a Fraction by a Fraction
Example:
My mother has parts of chocolate, then my mother want to present
its of chocolate. How many part of chocolate that my mother
present?
Solution:
fold the shaded area that
represent
Based on the picture there are 1 little fold from 2 flod.
So

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Based on the example, to multiply a fraction with a
fraction, multiply the numerator and then multiply the
denominator or can be written as where b
≠ 0 and d≠0.

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Multiplying a whole number and a fraction
1
11
1

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Multiplication of Fractions
{ {
{

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Draw a quadrilateral with a length of cm and a width of
cm as shown in the following figure.
1 1
1
11

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Exercises

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The properties of Multiplication in Fractions

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Commutative Properties
For example:
so, =
so, =

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For any fractions and whereb≠0 and q≠ 0 applies

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Associative Property
For any fraction , , and with b, d, f ≠ 0 can be
stated

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Distributive Property
For any fraction , , and with b, d, f ≠ 0 can be
stated:

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Division Fractions
How to solve 8 : 2
Solution:
Suppose there 8 marbles
Suppose the 6 chocolates are given to your friends. Each of them will get 1
chocolate. How many people will get the chocolates?
Answer:
written as 6: 1 = 6

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Suppose the 3 piece of papers are divided so that each of
your friends gets piece of paper. How many people will
get the piece of paper?
Answer:
It means that
So there are 6 people who get a half piece of paper.

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From the example, we can conclude that
natural number divided by a fraction can be
denoted as:

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proof
3: =
Solution:
3: can be written as a fraction, where 3 as numerator and
as denominator.

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my mother has three-fourth of sugar. It will be made a cake.
If one recipe needs a half of sugar. How many recipe can
be made?
Solution:
Draw a bar that represent three-fourth.
kg can be made
recipe
kg can be made 1
recipe recipe
So

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For any fractions and where b, c, d ≠ 0,
÷ = × applies.

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Dividing mixed numbers
Calculate
Solution:
Change the mixed numbers.
find the product

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exercises
1.
2.
3.
4.

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APPLICATION IN DAILY LIFE

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Examples
1. Nindya went to his office by
car. His office is 10 km from
his house. the time needed to
be arrived is 2 hours.
if velocity (v) is stated as
distance (s) per time (t),
What is the velocity of her
car?
1.
So, the velocity is 50km/h
50
2
100
v
v
t
s
v

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2. Feni’s mother has a
cake. She divide it into
two equal parts and she
give one part for Feni.
But, feni has three
friends.
2. Feni’s mother has a cake
and it divided into two.
And one part for feni. So,
Feni’s is
Feni has three friends. So, each
friend get:
2
1
6
1
3
1
2
1
3
2
1

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