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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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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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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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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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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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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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• 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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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 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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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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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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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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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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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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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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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