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Fractions
Index
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What is a fraction?
Equivalent Fractions
Making Equivalent Fractions by multiplying
Making Equivalent Fractions by dividing
Simplest Form
Uses of Fractions
Fractions Written as a Whole
Improper Fraction
Mixed Number
How to change from Improper Fraction to Mixed Number
How to change from Mixed Number to Improper Fraction
Comparing Fractions
Ordering Fractions
Ordering Fractions with Number Line
Adding Fractions
What is a Fraction?
A fraction is formed by dividing a whole into a
number of parts
I’m the
NUMERATOR. I tell
you the number of
equal parts you are
looking at or have.
2
3
I’m the
DENOMINATOR. I tell
you the number of
equal parts into
which the whole is
divided.
Uses of Fractions
• A fraction may represent division.
• Fractions can express probability.
• Fractions are used to compare two
quantities as a ratio.
Student Reference Book p. 57-58
Equivalent Fractions
Equivalent fraction: fractions that have the same value
1 WHOLE
1
632

2
12
64
6

12 1 WHOLE
To Make Equivalent Fractions
• Multiply the numerator and
denominator by the same number.
• You will get a new fraction with the
same value as the original fraction.
• We are not changing the value of the
fraction, because we are simply
multiplying by a fraction that is
equivalent to ONE.
What do you get when you multiply
a fraction by 1?
You get
AN EQUIVALENT FRACTION
that makes
adding & subtracting fractions
possible.
Make An Equivalent Fraction
Find the Missing Numerator!
x3
x3
Given the new
denominator, can you
find the missing
numerator?
Make An Equivalent Fraction
Find the Missing Numerator!
x4
x4
Given the new
denominator, can you
find the missing
numerator?
Make An Equivalent Fraction
If you have larger numbers, you can make equivalent
fractions using division. Divide by a common factor.
In this example,
we can divide both
28
35
÷7
÷7
4
5
numbers by 7.
Fractions in Simplest Form
Fractions are in simplest form when the numerator and
denominator do not have any common factors besides 1.
Examples of fractions that are in simplest form:
4
5
2
11
3
8
Writing Fractions in
Simplest Form
• Find the greatest common factor (GCF) of
the numerator and denominator.
• Divide both numbers by the GCF.
Example:
20 ÷ 4 =
28 ÷ 4
20
28
5
7
20: 1, 2, 4, 5, 10, 20
28: 1, 2, 4, 7, 14, 28
1 x 20
1 x 28
Common Factors: 1, 2, 4
2 x 10
2 x 14
GCF: 4
4x5
4x7
We will divide by 4.
Simplest
Form
Fractions Written as a Whole
23
11 
23
If a hexagon is worth 1, what are 5
trapezoids worth?
Trapezoid
1 Whole
1 Whole
Trapezoid
2 Trapezoids = 1 Hexagon
1 Whole
Trapezoid
Trapezoid
½
Trapezoid
We can report
this as 2 ½ or 5/2
Trapezoid
Improper Fraction
fractions that are equal to or greater than 1
5/2
is read as – five halves
Mixed Number
a whole number and a fraction written
together
2½
is read as - two and one half
If a triangle is 1/3,
what shape is ONE whole?
1/3
Trapezoid
11/3
Whole
1/3
1/3 + 1/3 + 1/3 = 3/3 or 1 Whole
How
many
more
do
Remember:
What
shape
cantriangles
we make?
Numerator
youahave1.
you
need tois what
make
whole?
Denominator is how many pieces your whole
is cut into - 3.
If the triangle is 1/3,
what is the rhombus?
If Ifthe
thetriangle
rhombus
is ½,
is 1/3,
whatwhat
is the
shapetrapezoid?
is the WHOLE?
If the rhombus is 1/3, what is
the triangle?
Turn to MJ p. 124
If the triangle is ½, what shape
is the WHOLE?
Mixed Number
• A mixed number has a part that
is a whole number and a part
that is a fraction.
3
= 1 4
What is the mixed number?
3
= 3
4
What is the mixed number?
3
= 4
4
What is the mixed number?
1
= 5
2
Improper Fraction
• A fraction in which the
numerator is greater than the
denominator.
=
8
4
What is the improper fraction?
=
15
4
What is the improper fraction?
=
19
4
What is the improper fraction?
=
11
2
How is the mixed number below
related to the
improper fraction?
1
= 52
11
= 2
How to change an improper fraction
to a mixed number
 Divide the numerator by the
denominator.
 Put your remainder over the
denominator.
=
5
2
How to change an improper fraction
to a mixed number
2) 5
numerator
denominator
=
5
2
How to change an improper fraction
to a mixed number
2r1
numerator
2) 5
denominator
=
5
2
How to change an improper fraction
to a mixed number
2
2) 5
denominator
1
2
numerator
Put your remainder over the
Denominator.
=
5
2
Change this improper fraction to a
mixed number.
7
3
2 r1
= 3) 7
1
Put your remainder over= 2
3
the denominator.
Change this improper fraction to a
mixed number.
8
3
2 r2
= 3) 8
2
Put your remainder over= 2
3
the denominator.
Change this improper fraction to a
mixed number.
9
2
4 r1
= 2) 9
1
Put your remainder over= 4
2
the denominator.
Change this improper fraction to a
mixed number.
2
r
1
11
= 5 ) 11
5
1
Put your remainder over= 2
5
the denominator.
Change this improper fraction to a
mixed number.
2
10 =
5 ) 10
5
If there is no remainder
your answer is a whole
number.
= 2
Change this improper fraction to a
mixed number.
4
16 =
4 ) 16
4
If there is no remainder
your answer is a whole
number.
= 4
How to change a mixed number to an
improper fraction
• Multiply the whole
number times the
denominator.
• Add your answer to the
numerator.
• Put your new number
over the denominator.
+1
4x =
2
9
2
Change this mixed number to an
improper fraction
• Multiply the whole
number times the
denominator.
• Add your answer to the
numerator.
• Put your new number
over the denominator.
+2 20
6x =
3 3
Change this mixed number to an
improper fraction
• Multiply the whole
number times the
denominator.
• Add your answer to the
numerator.
• Put your new number
over the denominator.
+2 17
3x =
5 5
Change this mixed number to an
improper fraction
• Multiply the whole
number times the
denominator.
• Add your answer to the
numerator.
• Put your new number
over the denominator.
+3 19
4x =
4 4
Change this mixed number to an
improper fraction
• Multiply the whole
number times the
denominator.
• Add your answer to the
numerator.
• Put your new number
over the denominator.
+2 20
6x =
3 3
Change this mixed number to an
improper fraction
• Multiply the whole
number times the
denominator.
• Add your answer to the
numerator.
• Put your new number
over the denominator.
+3 43
8x =
5 5
Comparing Fractions
Cross Multiply or “Butterfly Method”
Use >, <, or =.
9
<
10
3
5
<
2
3
Cross Multiply or “Butterfly Method”
Use >, <, or =.
12
3
10
>
>
10
1
4
Ordering Fractions
To order fractions you
can draw a picture or
use the Least Common
Denominator (LCD).
One way to compare or
order fractions is to
express them with the
same denominator.
Any common denominator
could be used. But the
Least Common
Denominator (LCD)
makes the computation
easier.
Use LCD
List the fractions in order
from greatest to least.
1 7 5 2
, , ,
6 12 9 3
Use LCD
Step 1: Find a common
denominator
1 7 5 2
, , ,
6 12 9 3
Find the LCD:
the36,
largest
first and
12,Put
24,
48, denominator
60 …
write down the first 5 multiples
9, 18, 27, 36 …
Then
continue
with
the36
next
6, 12,
18, 24,
30,
….
denominator until you find a common
3, 6, 9, 12, 15, 18, 21, 24, 27, 30,
digit…
33, 36 …
LCD = 36
Step 2: Write
equivalent
fractions. x 6
1 6

6 x 636
5 x 4 20

9 x 4 36
7 x 3 21

12 x 3 36
2x 1224

3x 1236
Step 3: Compare the numerators
7 21 5 20
1 6
2 24




6 36 12 36 9 36
3 36
In order from
greatest to least:
2 7 5 1
, , ,
3 12 9 6
PRACTICE: Use LCD
In order from
greatest to least:
2 7 5 1
, , ,
3 12 9 6
Finding Fractions on a Number Line
• We can use number
lines to help us order
fractions.
Finding Fractions on a Number Line
• This number line breaks one whole into
fourths.
• Where would ¼ be on the number line?
• What about 4/4?
1
4
4
4
Finding Fractions on a Number Line
• How many sections does this number line
break one whole into?
• Can you locate where 1/8 would be?
• Name a fraction in eighths that is between
½ and ¾.
1
8
1
4
2
4
3
4
Finding Fractions on a Number Line
• What does this number line show?
• Where would 7/9 be?
• What fraction is between 1/9 and 2/9?
Finding Fractions on a Number Line
• How would you explain this number line
using words?
• Can you find 3/5?
• Can you mark a fraction larger than 4/5 on
the number line?
Finding Fractions on a Number Line
• What type of number line is this?
• Can you order 5/8, 1/4, 2/3, and 3/16 on
this number line?
Adding Fractions with common
denominators
3 4
7


8
8 8
Add these fractions
4
3 +1
=
5 5
5
1/5
1/5
1/5
1/5
1/5
Add these fractions
1/4
3
2 + 1
=
4
4
4
1/4
1/4
Adding Fractions with different
denominators
Problem:
You can’t add fractions with different denominators
without getting them ready first. They will be ready to
add when they have common denominators
Solution:
Turn fractions into equivalent fractions with a
common denominator
that is find the Lowest
Common Multiple (LCM) of the two denominators
1
2
3
7
We need a common
denominator to add
these fractions.
2, 4, 6, 8, 10, 12, 14, 16, 18, 20
7, 14, 21, 28, 35…
2, 4, 6, 8, 10, 12, 14, 16, 18, 20
7, 14, 21, 28, 35…
REMEMBER the first number IN COMMON
that appears on both lists
becomes the common denominator
1
2
x7
3
7
x2
X7
x2
7
14
6
14
13
14
7 + 6 = 13
3
7
1
5
We need a common
denominator to add
these fractions.
7, 14, 21, 28, 35, 42, 49, 56, 63
5, 10, 15, 20, 25, 30, 35, 40, 45
3
7
x5
1
5
x7
X5
x7
15
35
7
35
22
35
15 + 7 = 22
Try These
A
D
B
E
C
F
Answers On Next Slide
• Each click on the next slide
reveals an answer.
• Check your papers.
• If you discover an incorrect
answer, be able to explain
your mistake.
Try These
17
27
D
10
9
B
13
12
E
41
28
C
19
20
F
26
21
A