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

Sixers Guide to Ordering Fractions
You have 30 seconds to do the following:
 Write the title “Ordering Fractions” with today’s date  Do “Belly Taps, Belly Rubs” when finished

Ordering fractions

We can order numbers fairly easily.

For example:
7 14 6 19 50

Ordering fractions

This becomes:

6

<

7

<

14

<

19

<

50

(if ordered smallest to largest)

Ordering fractions

Fractions are ordered the same way. For example- Order these fractions from smallest to greatest 3 8 5 8 4 8 1 8 2 8

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
becomes

8

8

1 8

<

2 8

<

3 8

<

4 8

<

5 8

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?

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

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

Ordering fractions
Therefore, 3/4 (75 cents) is greater than 3/5 (60 cents)

3
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4

>

3 5
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Therefore, Mr. Meldrum has more money!

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

Ordering fractions
How else can we compare 3/4 to 3/5?

3

3

4

5

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.

Ordering fractions
Look at the denominators. We must look for a COMMON MULTIPLE.

3

3

4
Multiples of 4 are

5

4, 8, 12, 16, 20, 24, 28, 32, 36, 40…… Multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50……

Ordering fractions
COMMON MULTIPLES are:

3

3

4
Multiples of 4 are

5

4, 8, 12, 16, 20, 24, 28, 32, 36, 40…… Multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50……

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 we’ll use this.
* This is called the Lowest Common Denominator or LCD

Ordering fractions
We need to convert these fractions so they have the same denominator.
3 3

4
3 4 x5 x5 ? 20

5

Ordering fractions
We need to convert these fractions so they have the same denominator.
3 3

4
3 4 x5 x5 15 20

5

Ordering fractions
We need to convert these fractions so they have the same denominator.
3 3

4
3 4 x5 x5 15 20

5
3 5 x4 x4 ? 20

Ordering fractions
We need to convert these fractions so they have the same denominator.
3 3

4
3 4 x5 x5 15 20

5
3 5 x4 x4 12 20

Ordering fractions
So these fractions: 3
4

3
5

Are EQUIVALENT to these ones: 15 20 12 20

Ordering fractions
So this is the correct answer: 3
4 Because: 15 20

>
>

3
5

12 20

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.

Ordering fractions
Try this one…
4 7

6

9

Which fraction is bigger? (Explain your thinking to a neighbour in 30 seconds or less)

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.

Ordering fractions

Look at the denominators. We must look for a COMMON MULTIPLE.

4

7

6
Multiples of 6 are

9

6, 12, 18, 24, 30, 36, 42, 48, 54, 60…… Multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72, 81, 90……

Ordering fractions

COMMON MULTIPLES are:

4

7

6
Multiples of 6 are

9

6, 12, 18, 24, 30, 36, 42, 48, 54, 60…… Multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72, 81, 90……

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 we’ll use this.
* This is called the Lowest Common Denominator or LCD

Ordering fractions

We need to convert these fractions so they have the same denominator.
4 7

6
4 6 x3 x3 ? 18

9

Ordering fractions

We need to convert these fractions so they have the same denominator.
4 7

6
4 6 x3 x3 12 18

9

Ordering fractions

We need to convert these fractions so they have the same denominator.
4 7

6
4 6 x3 x3 12 18

9
7 9 x2 x2 ? 18

Ordering fractions

We need to convert these fractions so they have the same denominator.
4 7

6
4 6 x3 x3 12 18

9
7 9 x2 x2 14 18

Ordering fractions

So these fractions: 4
6

7
9

Are EQUIVALENT to these ones: 12 18 14 18

Ordering fractions

So this is the correct answer: 4
6 Because: 12 18

<
<

7
9

14 18

Ordering fractions Your homework: Which fraction is bigger? Use < or > 1. 5 7 3 4

2.

2
3

6
8

3.

4
5

7
9

Ordering fractions

Here’s one for you to try: 4 3

5

4

Which fraction is bigger?

Ordering fractions

Here’s one for you to try:

4

5 4 1) Find the Lowest Common Denominator 20 2) Rewrite the fractions with 20 as the denominator 16

>

3

20

>

15

20

Ordering fractions

If the DENOMINATOR is the different, we have a problem that must be dealt with differently.

3 6

7 8

4 4

1 3

2 4

We need to convert our fractions to EQUIVALENT fractions of the same DENOMINATOR. We will come back to this example.

Ordering fractions

Remember our example

3 6

7 8

4 4

1 3

2 4

1) Find the Lowest Common Denominator of 6, 8, 4 & 3 24

Ordering fractions Convert to 24ths 3 7 4 1 2

6
12 24

8
21 24

4
24 24

3
8 24

4
12 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.

Ordering fractions Convert to 24ths 3 7 4 1 2

6
2nd 12 24

8
4th 21 24

4
5th 24 24

3
1st 8 24

4
3rd 12 24

Now put the fractions in order from smallest to largest.

Ordering fractions Convert to 24ths 3 7 4 1 2

6
2nd 12

8
4th 21

4
5th 24

3
1st 8

4
3rd 12

24 24 24 24 24 Now put the fractions in order from smallest to largest. 1 3 3 6 2 4 7 8 4 4

Ordering fractions Now it’s 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

Ordering fractions

5
9

7
12

3
6

3
4

Look at the DENOMINATORS. What are the MULTIPLES?

Ordering fractions

5
9

7
12

3
6

3
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,…

Ordering fractions

5
9

7
12

3
6

3
4

Use 36 as the COMMON DENOMINATOR.

Ordering fractions 5 9 7 12 3 6 3 4

36

36

36

36

Ordering fractions

5
9
x 4

7
12
x 3

3
6
x 6

3
4
x 9

Find the number that you need to multiply the DENOMINATORS by to get 36.

36

36

36

36

Ordering fractions

5
9
x 4

7
12
x 3

3
6
x 6

3
4
x 9

Multiply the NUMERATORS by the same amount as you multiplied the DENOMINATORS

36

36

36

36

Ordering fractions

5
9
x 4

7
12
x 3

3
6
x 6

3
4
x 9

20 36

21 36

18 36

27 36

Ordering fractions

5
9
x 4

7
12
x 3

3
6
x 6

3
4
x 9

Decide which order the fractions need to be in.

20 36 2nd

21 36 3rd

18 36 1st

27 36 4th

Ordering fractions

5
9
x 4

7
12
x 3

3
6
x 6

3
4
x 9

putting them in order…

20 36 2

21 36 3

18 36 1

27 36 4

18 36

20 36

21 36

27 36

Ordering fractions

5
9
x 4

7
12
x 3

3
6
x 6

3
4
x 9

Now convert them back…

20 36 2

21 36 3

18 36 1

27 36 4

18 36

20 36

21 36

27 36

3

5

7

3

6

9

12

4

Ordering fractions

5
9
x 4

7
12
x 3

3
6
x 6

3
4
x 9

20 36 2

21 36 3

18 36 1

27 36 4

18 36

20 36

21 36

27 36

3

5

7

3

6

9

12

4

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