Transcript Fractions - Mr. Norr

FRACTIONS
Fractions have numerators and denominators
Fractions represent the division of the numerator by the
denominator or it’s the same as 4 divided by 5
numerator
4/5
denominator
The numerator is the top number or tells us how many such
pieces are being considered.
The denominator is the bottom number or tells us how many
congruent (equal) pieces the whole is divided into.
What is a fraction?
Fractions are one or more parts of a whole that is divided into equal
parts. Fractions can represent numbers less than 1, equal to 1, or
greater than 1. The whole can be broken up into regions, sets, or
segments.
How does the denominator control a fraction?
If you share a cake evenly among two
people, you will get 1
2
If you share a cake evenly among three
people, you will get 1
3
If you share a cake evenly among four
people, you will get
1
4
Conclusion:
The larger the
denominator the
smaller the pieces,
and if the numerator
is kept fixed, the
larger the
denominator the
smaller the fraction!!!
Equivalent fractions: are fractions that represent the same
amount but they have different numerators and
denominators. You can multiply or divide the numerator and
denominator by the same number to get an equivalent fraction.
1
2
2
= 4
X
2
2
In the following picture we
have ½ of a cake because the
whole cake is divided into two
equal parts and we have only one
of those parts.
Find the Equivalent Fraction
•
Multiply the numerator and the denominator
by the same number.
1 x3 =3
3 3
9
• or you can also divide the numerator and the
denominator by the same number.
1
4
4
=
÷
12
4
3
Equivalent Fractions
• What number was multiplied by the
numerator and the dominator to get the new
equivalent fraction?
1
2
1 = 2
2
4
1
4
1
4
Make An Equivalent Fraction
Find the Missing Numerator!
x4
x4
Given the new
denominator, can you
find the missing
numerator?
Make An Equivalent Fraction
Find the Missing Numerator!
x9
x9
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 Equivalent Fractions
Find the Missing Numerators!
44
12
55
42
45
28
54
63
Find a new Equivalent fraction by
multiplying the numerator and
dominator by the same number
• 1/3 =
2/7=
• 5/6=
5/10=
• 9/18=
12/24=
• 30/40
3/8 =
Putting Fractions in Simplest Form
A fraction is in its lowest terms is reduced or simplified if we cannot
find a whole number that can divide into both its numerator and
denominator. Reducing a fraction in lowest terms gives you its
equivalent fraction with the lowest possible numerator and
denominator.
Steps to Reducing Fractions or putting fractions into Simplest Forms:
1. Find the GCF of the numerator and the denominator.
2. Divide the GCF into both the numerator and the denominator to
get the fraction in simplest form.
6
10
6= 1, 2, 3, 6
10= 1, 2, 5, 10
=3
5
2 is the GCF so divide 2 into the numerator and
the dominator to get the fraction in simplest forms.
Simplify Fractions
• Divide both numerator and denominator by
the Greatest Common Factor
28
72
Factors are 1, 2, 4, 7, 14, 28
Factors are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 48, 72
Greatest Common Factor is 4
28 ÷ 4 = 7
72 ÷ 4 = 18
28
7
So
=
72
18
Fractions in Simplest Forms: Remember to first find the
GCF, then divide.
10

60
35

40
11

23
10= 1, 2, 5, 10
60= 1, 2, 3, 4, 6,10, 30, 60
10 is the GCF and can be divided into both
10 and 60.
35= 1, 5, 7, 35
40= 1,2, 4,10, 20, 40
5 is the GCF and divides into both 35 and
40.
11= 1,11
23= 1, 23
1 is the GCF and so this fraction is already in
simplest form.
Simplification - Let’s Try It!
3
1
=
9
3
7
1
=
21
3
18
2
=
63
7
24
2
=
84
7
6
2
=
15
5
78
13
=
114 19
Simplify/Reduce the Fractions
• 8/32 =
• 7/56 =
• 24/36
• 32/48 =
Comparing Fractions with Like
Denominators
Comparing fractions with like denominators is a lot like
comparing whole numbers
5
7
EXAMPLE: George walks 10 mile to school. Susan walks 10
mile. Who walks the greater distance?
When fractions have the same denominator, compare the
numerator.
7>5
so
Susan walks a greater
distance
7
10 >
5
10
That makes sense
because 7 of
something is more than
5 of something
Fractions with Like Denominators
1
4
3
4
1
3
and
have the same denominator.
4
4
Fractions with the same denominators are like fractions.
The fractions
Compare. Write <, >, or =.
4
__
_5_
6
6
4
__
6
<
5
__
6
4
__
5
__
From the model, 6 < 6 .
Compare. Write <, >, or =.
6
__
4
__
7
7
6
__
7
>
4
__
7
6
__
4
__
From the model, 7 > 7 .
Sometimes you can compare fractions just
by looking at them
1
2
1
4
>
I’ll take
1
2