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Ordering fractions We can order numbers fairly easily. E.g. 71461950

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Ordering fractions becomes this 67141950 (if ordered smallest largest)

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Ordering fractions Fractions are ordered the same way 3741237412 9999999999

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Ordering fractions 1234712347 9999999999 (if ordered smallest largest) If the DENOMINATOR is the same, look at the NUMERATORS, and put the fractions in order.

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Ordering fractions We need to convert our fractions to EQUIVALENT fractions of the same DENOMINATOR. We will come back to this example. If the DENOMINATOR is the different, we have a problem that must be dealt with differently. 3741237412 6843468434

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Ordering fractions If the DENOMINATOR is the different, we have a problem that must be dealt with differently. 4343 6969 Heres an easier example, with just 2 fractions to start us off.

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Ordering fractions Look at the denominators. We must look for a COMMON MULTIPLE. 4343 6969 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. 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: Multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60…… Multiples of 9 are 9, 18, 27, 36, 45, 54……

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Ordering fractions COMMON MULTIPLES are: 18, 36 and 54. 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.

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Ordering fractions 4 6 We need to convert these fractions so they have the same denominator. ? 18 x 3

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Ordering fractions 4 6 We need to convert these fractions so they have the same denominator. 12 18 x 3

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Ordering fractions 3 9 We need to convert these fractions so they have the same denominator. ? 18 x 2

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Ordering fractions 3 9 We need to convert these fractions so they have the same denominator. 6 18 x 2

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Ordering fractions 4343 6969 So these fractions: Are EQUIVALENT to these ones: 6 18 12 18

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Ordering fractions 3434 9696 And this is the correct order Because these EQUIVALENT FRACTIONS are in order 12 18 6

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Ordering fractions 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. Remember our example 3741237412 6843468434

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Ordering fractions 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. Convert to 24ths 122124812 2424242424

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Ordering fractions This tells you how large our fractions are. Check which order they go in. Convert to 24ths 122124812 2424242424 2 nd 4 th 5 th 1 st 3 rd

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Ordering fractions This tells you how large our fractions are. Check which order they go in. Convert to 24ths 2 nd 4 th 5 th 1 st 3 rd 3741237412 6843468434

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Ordering fractions So this is the correct order 1327413274 3648436484

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Ordering Fractions 2 If we want to order fractions, we need to make sure our working out is clear. For every question, please use the following method. 5 733 91264 We look for a COMMON MULTIPLE.

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Ordering Fractions 2 5 733 91264 Look at the DENOMINATORS. What are the MULTIPLES?

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Ordering Fractions 2 5 733 91264 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,…

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Ordering Fractions 2 5 733 91264 Use 36 as the COMMON DENOMINATOR.

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Ordering Fractions 2 5 733 91264 3636 36 36

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Ordering Fractions 2 5 733 91264 3636 36 36 x 4x 3x 6x 9 Find the number that you need to multiply the DENOMINATORS by to get 36.

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Ordering Fractions 2 5 733 91264 3636 36 36 x 4x 3x 6x 9 Multiply the NUMERATORS by the same amount as you multiplied the DENOMINATORS

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Ordering Fractions 2 5 733 91264 202118 27 3636 36 36 x 4x 3x 6x 9

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Ordering Fractions 2 5 733 91264 202118 27 3636 36 36 x 4x 3x 6x 9 2nd 3rd 1st 4th Decide which order the fractions need to be in.

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Ordering Fractions 2 5 733 91264 202118 27 3636 36 36 x 4x 3x 6x 9 2 3 1 4 182021 27 3636 36 36 putting them in order…

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Ordering Fractions 2 5 733 91264 202118 27 3636 36 36 x 4x 3x 6x 9 2 3 1 4 182021 27 3636 36 36 Now convert them back… 3 5 73 6 9124

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Ordering Fractions 2 and the final answer… 5 733 91264 202118 27 3636 36 36 x 4x 3x 6x 9 2 3 1 4 182021 27 3636 36 36 3 5 73 6 9124

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