4-6 Comparing and Ordering Fractions
Learn to use pictures and number lines to
compare and order fractions.
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4-6 Comparing and Ordering Fractions
Vocabulary
like fractions
unlike fractions
common denominator
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4-6 Comparing and Ordering Fractions
When you are comparing fractions, first
check their denominators. When
fractions have the same denominator,
they are called like fractions. For
example,
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6
___
7
and
4
___
7
are like fractions.
4-6 Comparing and Ordering Fractions
Additional Example 1A: Comparing Like
Fractions
Compare. Write <, >, or =.
6
A. __
4
__
7
7
6
__
7
>
4
__
7
6
__
4
__
From the model, 7 > 7 .
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4-6 Comparing and Ordering Fractions
Additional Example 1B: Comparing Like
Fractions
Compare. Write <, >, or =.
1
B. __
5
__
9
9
1
__
9
<
5
__
9
1
__
5
__
From the model, 9 < 9 .
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4-6 Comparing and Ordering Fractions
Try This: Example 1A
Compare. Write <, >, or =.
4
A. __
_5_
6
6
4
__
6
<
5
__
6
4
__
5
__
From the model, 6 < 6 .
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4-6 Comparing and Ordering Fractions
Try This: Example 1B
Compare. Write <, >, or =.
3
B. __
2
__
9
9
3
__
9
>
2
__
9
3
__
2
__
From the model, 9 > 9 .
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4-6 Comparing and Ordering Fractions
When two fractions have different
denominators, they are called unlike
fractions. To compare unlike fractions,
first rename the fractions so they have
the same denominator. This is called
finding a common denominator.
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4-6 Comparing and Ordering Fractions
Additional Example 2: Cooking Application
Ray has
2
__
3
cup of nuts. He needs
3
__
4
cup to
make cookies. Does he have enough nuts
for the recipe?
Compare
2
__
3
and
3
__
4
.
Find a common denominator by multiplying the
denominators.
3 • 4 = 12
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4-6 Comparing and Ordering Fractions
Additional Example 2 Continued
Find equivalent fractions with 12 as the
denominator.
2
__
3
__
= __
3
12
2•4
______
3•4
2
__
=
8
= __
12
3
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= __
4
12
8
__
12
3•3
______
9
= __
4•3
12
3
__
4
=
9
__
12
4-6 Comparing and Ordering Fractions
Additional Example 2 Continued
Compare the like fractions.
8
__
12
<
9
__
12
, so
2
__
3
<
3
__
4
.
3
2
Since __
cup is less than __ cup, he does not
3
have enough.
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4
4-6 Comparing and Ordering Fractions
Try This: Example 2
Trevor has
1
__
3
1 cup to
cup of soil. He needs __
4
fill a small planter. Does he have enough
soil to fill the planter?
Compare
1
__
3
and
1
__
4
.
Find a common denominator by multiplying the
denominators.
3 • 4 = 12
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4-6 Comparing and Ordering Fractions
Try This: Example 2 Continued
Find equivalent fractions with 12 as the
denominator.
1
__
= __
3
12
1
__
1•4
______
4
= __
3•4
12
1•3
______
1
__
1
__
4
= __
12
3
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= __
4
12
3
= __
4•3
12
4
=
3
__
12
4-6 Comparing and Ordering Fractions
Try This: Example 2 Continued
Compare the like fractions.
4
__
3
__
12 > 12 , so
1
__
3 >
1
__
4 .
1
1 cup, he does have
Since __
cup is more than __
3
enough.
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4
4-6 Comparing and Ordering Fractions
Additional Example 3: Ordering Fractions
4
__
1
__
2
__
Order 5 , 3 , and 3 from least to greatest.
2• 5
_______
10
= __
3• 5
15
4• 3
_______
12
= __
5• 3
15
0
1• 5
_______
5
= __
3• 5
15
5
15
10
15
12
15
1
3
2
3
4
5
Rename with like
denominators.
1
The fractions in order from least to greatest
2 , __
4 .
1 , __
are __
3
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3
5
4-6 Comparing and Ordering Fractions
Remember!
Numbers increase in value as you move from left to right
on a number line.
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4-6 Comparing and Ordering Fractions
Try This: Example 3
1
4 , __
3 , and __
Order __
from least to greatest.
7
3• 7
_______
1• 7
_______
21
= __
4• 7
28
4• 4
_______
16
= __
7• 4
28
0
4
4
7
= __
4• 7
28
7
28
16
28
21
28
1
4
4
7
3
4
Rename with like
denominators.
1
The fractions in order from least to greatest
1
__
4
__
3
__
are 4 , 7 , 4 .
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4-6 Comparing
Insert Lesson
andTitle
Ordering
Here Fractions
Lesson Quiz
Compare. Write <, >, or =.
3
1. __
4
__
6
8
5
2. __
=
9
__
16
8
>
3. You drilled three holes in a piece of wood. The
3
1 , __
3 , and __
diameters of the holes are __
8 8
3 16
__
inches. Which hole is the largest?
8
Order the fractions from least to greatest.
7 , __
5 , __
2
4. __
8
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8
3
5 , __
2 , __
7
__
8
3 8
3 , __
5 , __
5
5. __
4
8
6
5 , __
3 , __
5
__
8
4
6