Ordering and comparing fractions with like and unlike denominators
- 1. Ordering fractions We can order numbers fairly easily. E.g. 7 14 6 19 50
- 2. Ordering fractions becomes this 6 7 14 19 50 (if ordered smallest largest)
- 3. Ordering fractions Fractions are ordered the same way 3 7 4 1 2 9 9 9 9 9
- 4. Ordering fractions 1 2 3 4 7 9 9 9 9 9 (if ordered smallest largest) If the DENOMINATOR is the same, look at the NUMERATORS, and put the fractions in order.
- 5. 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. 3 7 4 1 2 6 8 4 3 4
- 6. Ordering fractions If the DENOMINATOR is the different, we have a problem that must be dealt with differently. 4 3 6 9 Here’s an easier example, with just 2 fractions to start us off.
- 7. Ordering fractions Look at the denominators. We must look for a COMMON MULTIPLE. 4 3 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.
- 8. 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……
- 9. 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……
- 10. 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 we’ll use this.
- 11. Ordering fractions 4 6 We need to convert these fractions so they have the same denominator. ? 18 x 3 x 3
- 12. Ordering fractions 4 6 We need to convert these fractions so they have the same denominator. 12 18 x 3 x 3
- 13. Ordering fractions 3 9 We need to convert these fractions so they have the same denominator. ? 18 x 2 x 2
- 14. Ordering fractions 3 9 We need to convert these fractions so they have the same denominator. 6 18 x 2 x 2
- 15. Ordering fractions 4 3 6 9 So these fractions: Are EQUIVALENT to these ones: 6 18 12 18
- 16. Ordering fractions 3 4 9 6 And this is the correct order Because these EQUIVALENT FRACTIONS are in order 12 18 6 18
- 17. 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 3 7 4 1 2 6 8 4 3 4
- 18. 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 12 21 24 8 12 24 24 24 24 24
- 19. Ordering fractions This tells you how large our fractions are. Check which order they go in. Convert to 24ths 12 21 24 8 12 24 24 24 24 24 2nd 4th 5th 1st 3rd
- 20. Ordering fractions This tells you how large our fractions are. Check which order they go in. Convert to 24ths 2nd 4th 5th 1st 3rd 3 7 4 1 2 6 8 4 3 4
- 21. Ordering fractions So this is the correct order 1 3 2 7 4 3 6 4 8 4
- 22. 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 7 3 3 9 12 6 4 We look for a COMMON MULTIPLE.
- 23. Ordering Fractions 2 5 7 3 3 9 12 6 4 Look at the DENOMINATORS. What are the MULTIPLES?
- 24. Ordering Fractions 2 5 7 3 3 9 12 6 4 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,…
- 25. Ordering Fractions 2 5 7 3 3 9 12 6 4 Use 36 as the COMMON DENOMINATOR.
- 26. Ordering Fractions 2 5 7 3 3 9 12 6 4 36 36 36 36
- 27. Ordering Fractions 2 5 7 3 3 9 12 6 4 36 36 36 36 x 4 x 3 x 6 x 9 Find the number that you need to multiply the DENOMINATORS by to get 36.
- 28. Ordering Fractions 2 5 7 3 3 9 12 6 4 36 36 36 36 x 4 x 3 x 6 x 9 Multiply the NUMERATORS by the same amount as you multiplied the DENOMINATORS
- 29. Ordering Fractions 2 5 7 3 3 9 12 6 4 20 21 18 27 36 36 36 36 x 4 x 3 x 6 x 9
- 30. Ordering Fractions 2 5 7 3 3 9 12 6 4 20 21 18 27 36 36 36 36 x 4 x 3 x 6 x 9 2nd 3rd 1st 4th Decide which order the fractions need to be in.
- 31. Ordering Fractions 2 5 7 3 3 9 12 6 4 20 21 18 27 36 36 36 36 x 4 x 3 x 6 x 9 2 3 1 4 18 20 21 27 36 36 36 36 putting them in order…
- 32. Ordering Fractions 2 5 7 3 3 9 12 6 4 20 21 18 27 36 36 36 36 x 4 x 3 x 6 x 9 2 3 1 4 18 20 21 27 36 36 36 36 Now convert them back… 3 5 7 3 6 9 12 4
- 33. Ordering Fractions 2 and the final answer… 5 7 3 3 9 12 6 4 20 21 18 27 36 36 36 36 x 4 x 3 x 6 x 9 2 3 1 4 18 20 21 27 36 36 36 36 3 5 7 3 6 9 12 4