Sixers Guide to Ordering Fractions

1
Sixers Guide to Ordering Fractions
I love ordering fractions!
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Sixers Guide to Ordering Fractions

• You have 30 seconds to do the following
• Write the title Ordering Fractions with
  todays date
• Do Belly Taps, Belly Rubs when finished

3
Ordering fractions
We can order numbers fairly easily. For example
7 14 6 19 50
4
Ordering fractions
This becomes
lt
lt
lt
lt
6 7 14 19 50
(if ordered smallest to largest)
5
Ordering fractions
Fractions are ordered the same way.
For example- Order these fractions from smallest
to greatest
3 5 4 1 2
8 8 8 8 8
6
Ordering fractions
If the DENOMINATOR is the same, look at the
NUMERATORS, and put the fractions in order.
Remember DENOMINATOR the BOTTOM
number NUMERATOR the TOP number
3 5 4 1 2
8 8 8 8 8
becomes
1 2 3 4 5
lt
lt
lt
lt
8 8 8 8 8
7
But what if the denominators are different?
For example
Mr. Meldrum has 3/4 of a dollar.
Mr. Slater has 3/5 of a dollar.
Who has more money?
8
Ordering fractions
Mr. Meldrum has 3/4 of a dollar.

• How much is 3/4 of a dollar?
• One quarter is 25 cents
• Therefore, 3 quarters is 75 cents
• Mr. Meldrum has 75 cents

9
Ordering fractions
Mr. Slater has 3/5 of a dollar.

• How much is 3/5 of a dollar?
• 1 dollar 100 cents
• To find one fifth of a dollar, divide 100 by 5
• 100 divided by 5 20
• 20 cents is 1/5 of a dollar
• Therefore, 3/5 of a dollar 20 x 3
• Mr. Slater has 60 cents

10
Ordering fractions
Therefore, 3/4 (75 cents) is greater than 3/5 (60
cents)
3 3
gt
4 5
Therefore, Mr. Meldrum has more money!
11
Ordering fractions
How else can we compare 3/4 to 3/5?

• Both fractions have the same numerator
• Fourths are bigger than fifths
• So, three-quarters are bigger than three-fifths

If the numerators are the same, the fraction
with the smallest denominator is greater
12
Ordering fractions
How else can we compare 3/4 to 3/5?
3 3
4 5
13
Ordering fractions
Look at the denominators. We must look for a
COMMON MULTIPLE.
3 3
4 5
This means that we check to see which numbers are
in the 4 times table, and the 5 times table. We
need a number that appears in both lists.
14
Ordering fractions
Look at the denominators. We must look for a
COMMON MULTIPLE.
3 3
4 5
Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32,
36, 40
Multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40,
45, 50
15
Ordering fractions
COMMON MULTIPLES are
3 3
4 5
Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32,
36, 40
Multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40,
45, 50
16
Ordering fractions
COMMON MULTIPLES of 4 and 5 are 20 and 40
3 3
4 5
There are others that are higher, but we only
look at smaller numbers. Remember Smaller
numbers are SIMPLER. 20 is the smallest number
that is common, so well use this.
This is called the Lowest Common Denominator or
LCD
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Ordering fractions
We need to convert these fractions so they have
the same denominator.
3 3
4 5
3
?
x 5
x 5
4
20
18
Ordering fractions
We need to convert these fractions so they have
the same denominator.
3 3
4 5
3
15
x 5
x 5
4
20
19
Ordering fractions
We need to convert these fractions so they have
the same denominator.
3 3
4 5
3
?
x 4
3
15
x 5
x 5
5
20
x 4
4
20
20
Ordering fractions
We need to convert these fractions so they have
the same denominator.
3 3
4 5
12
3
x 4
3
15
x 5
x 5
5
20
x 4
4
20
21
Ordering fractions
So these fractions
3 3
4 5
Are EQUIVALENT to these ones
12
15
20
20
22
Ordering fractions
So this is the correct answer
3 3
gt
4 5
Because
12
15
gt
20
20
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Ordering fractions
Keys to putting fractions in order

• If the denominators are the same, the fraction
  with the bigger numerator is greater
• If numerators are the same, the fraction smaller
  denominator is greater.
• If neither the numerator or denominator are the
  same, you must change both fractions into
  equivalent fractions with a common denominator.

24
Ordering fractions
Try this one
4 7
6 9
Which fraction is bigger?
(Explain your thinking to a neighbour in 30
seconds or less)
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Ordering fractions
Look at the denominators. We must look for a
COMMON MULTIPLE.
4 7
6 9
This means that we check to see which numbers are
in the 6 times table, and the 9 times table. We
need a number that appears in both lists.
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Ordering fractions
Look at the denominators. We must look for a
COMMON MULTIPLE.
4 7
6 9
Multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48,
54, 60
Multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72,
81, 90
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Ordering fractions
COMMON MULTIPLES are
4 7
6 9
Multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48,
54, 60
Multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72,
81, 90
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Ordering fractions
COMMON MULTIPLES of 6 and 9 are 18, 36 and 54
4 7
6 9
There are others that are higher, but we only
look at smaller numbers. Remember Smaller
numbers are SIMPLER. 18 is the smallest number
that is common, so well use this.
This is called the Lowest Common Denominator or
LCD
29
Ordering fractions
We need to convert these fractions so they have
the same denominator.
4 7
6 9
4
?
x 3
x 3
6
18
30
Ordering fractions
We need to convert these fractions so they have
the same denominator.
4 7
6 9
4
12
x 3
x 3
6
18
31
Ordering fractions
We need to convert these fractions so they have
the same denominator.
4 7
6 9
7
?
x 2
4
x 3
12
x 3
9
18
x 2
6
18
32
Ordering fractions
We need to convert these fractions so they have
the same denominator.
4 7
6 9
7
14
x 2
4
x 3
12
x 3
9
18
x 2
6
18
33
Ordering fractions
So these fractions
4 7
6 9
Are EQUIVALENT to these ones
14
12
18
18
34
Ordering fractions
So this is the correct answer
4 7
lt
6 9
Because
14
12
lt
18
18
35
Ordering fractions
Your homework Which fraction is bigger? Use lt or
gt
5 3
1.
7 4
6
2
2.
8
3
7
4
3.
9
5
36
Ordering fractions
Heres one for you to try
4 3
5 4
Which fraction is bigger?
37
Ordering fractions
Heres one for you to try
gt
4 3
5 4
1) Find the Lowest Common Denominator
20
2) Rewrite the fractions with 20 as the
denominator
16
15
gt
20 20
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Ordering fractions
If the DENOMINATOR is the different, we have a
problem that must be dealt with differently.
3 7 4 1 2
6 8 4 3 4
We need to convert our fractions to EQUIVALENT
fractions of the same DENOMINATOR. We will come
back to this example.
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Ordering fractions
Remember our example
3 7 4 1 2
6 8 4 3 4
1) Find the Lowest Common Denominator of 6, 8, 4
3
24
40
Ordering fractions
Convert to 24ths
3 7 4 1 2
6 8 4 3 4
12
21
24
8
12
24 24 24 24 24
The LOWEST COMMON DENOMINATOR is 24 check for
all the multiples of the DENOMINATORS. 24 is the
first number to appear in all the lists.
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Ordering fractions
Convert to 24ths
3 7 4 1 2
6 8 4 3 4
2nd 4th 5th 1st 3rd
12
21
24
8
12
24 24 24 24 24
Now put the fractions in order from smallest to
largest.
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Ordering fractions
Convert to 24ths
3 7 4 1 2
6 8 4 3 4
2nd 4th 5th 1st 3rd
12
21
24
8
12
24 24 24 24 24
Now put the fractions in order from smallest to
largest.
1 3 2 7 4
3 6 4 8 4
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Ordering fractions
Now its your turn
Put the following fractions in order from
smallest to largest
5 7 3 3 9 12 6 4
REMEMBER THE FOLLOWING STEPS
1) We look for a COMMON DENOMINATOR.
2) Rewrite the fractions as equivalent fractions
using the LCD
3) Order the fractions from smallest to largest
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Ordering fractions
5 7 3 3 9 12 6 4
Look at the DENOMINATORS. What are the MULTIPLES?
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Ordering fractions
5 7 3 3 9 12 6 4
Look at the DENOMINATORS. What are the MULTIPLES?
9 9, 18, 27, 36, 45, 54, 12 12, 24, 36, 48,
60, 6 6, 12, 18, 24, 30, 36, 48, 4 4, 8,
12, 16, 20, 24, 28, 32, 36,
46
Ordering fractions
5 7 3 3 9 12 6 4
Use 36 as the COMMON DENOMINATOR.
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Ordering fractions
5 7 3 3 9 12 6 4
36 36 36 36
48
Ordering fractions
5 7 3 3 9 12 6 4
Find the number that you need to multiply the
DENOMINATORS by to get 36.
x 4
x 3
x 6
x 9
36 36 36 36
49
Ordering fractions
5 7 3 3 9 12 6 4
Multiply the NUMERATORS by the same amount as you
multiplied the DENOMINATORS
x 4
x 3
x 6
x 9
36 36 36 36
50
Ordering fractions
5 7 3 3 9 12 6 4
x 4
x 3
x 6
x 9
20 21 18 27 36 36 36 36
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Ordering fractions
5 7 3 3 9 12 6 4
Decide which order the fractions need to be in.
x 4
x 3
x 6
x 9
20 21 18 27 36 36 36 36
2nd
3rd
1st
4th
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Ordering fractions
5 7 3 3 9 12 6 4
putting them in order
x 4
x 3
x 6
x 9
20 21 18 27 36 36 36 36
18 20 21 27 36 36 36 36
2
3
1
4
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Ordering fractions
Now convert them back
5 7 3 3 9 12 6 4
x 4
x 3
x 6
x 9
20 21 18 27 36 36 36 36
18 20 21 27 36 36 36 36
2
3
1
4
3 5 7 3 6 9 12 4
54
Ordering fractions
and the final answer
5 7 3 3 9 12 6 4
x 4
x 3
x 6
x 9
20 21 18 27 36 36 36 36
18 20 21 27 36 36 36 36
2
3
1
4
3 5 7 3 6 9 12 4