Year 6: Comparing and ordering fractions
Part of the Year 6 fractions chapter. Chapter overview · whole chapter on one page
Comparing and ordering fractions
To compare two fractions, make their bottom numbers the same. Then the bigger top number is the bigger fraction. Fractions can be greater than 1 too. On the number line below, 32 is one and a half, and 74 is one and three quarters, so 74 is the bigger one.
A mixed number such as 1 1/2 and an improper fraction such as 3/2 can be the same amount. Changing the mixed number to an improper fraction makes it easier to compare.
Key ideas
- Compare fractions by writing them with the same bottom number, then compare the top numbers.
- When the bottoms are the same, the bigger top number is the bigger fraction.
- A fraction bigger than 1 has a top number bigger than its bottom number. A mixed number like 2 1/3 is bigger than 2.
- To order fractions, put them all over the same bottom number first.
Key words. A common denominator is a bottom number that two or more fractions share. The lowest common denominator is the lowest common multiple (LCM) of the bottom numbers.
Method. Write both fractions with the same bottom number, then compare the top numbers.
- Find the lowest common denominator. Use the LCM of the two bottom numbers.LCM of 8 and 12 = 24
- Write both with the same bottom number. Multiply the top and bottom of each fraction by the same number.58 = 1524
712 = 1424 - Compare the top numbers. When the bottoms are the same, the bigger top number is the bigger fraction.15 and 14: the bigger top number is 15
- Say which fraction is bigger. Write the smaller one, then the bigger one.712 < 58
Check. 1524 is the bigger value of the two, so 58 is the bigger fraction. ✓
Watch out. Do not just compare the bottom numbers. A bigger bottom number means smaller pieces.
Key words. A common denominator is a bottom number that two or more fractions share. The lowest common denominator is the lowest common multiple (LCM) of the bottom numbers.
Method. Make the bottom numbers the same, then compare the top numbers.
- Write them all with the same bottom number, 30. The lowest common denominator of the bottoms is 30. Change each fraction so that its bottom number is 30.23 = 2030
710 = 2130
56 = 2530
35 = 1830 - Compare the top numbers. The bigger top number is the bigger fraction. Put them smallest first.18, 20, 21, 25 (out of 30)
- Write the fractions in order, using the fractions from the question. 35, 23, 710, 56
Check. 35 is the smallest and 56 is the largest. ✓
Watch out. A bigger bottom number means smaller pieces. Compare the top numbers only after the bottoms are the same.
Key words. A common denominator is a bottom number that two or more fractions share. The lowest common denominator is the lowest common multiple (LCM) of the bottom numbers.
Method. Make the bottom numbers the same, then compare the top numbers.
- Write them all with the same bottom number, 8. The lowest common denominator of the bottoms is 8. Change each fraction so that its bottom number is 8.114 = 228
52 = 208
138 = 138
32 = 128 - Compare the top numbers. The bigger top number is the bigger fraction. Put them smallest first.12, 13, 20, 22 (out of 8)
- Write the fractions in order, using the fractions from the question. 32, 138, 52, 114
Check. 32 is the smallest and 114 is the largest. ✓
Watch out. A bigger bottom number means smaller pieces. Compare the top numbers only after the bottoms are the same.
Key words. A common denominator is a bottom number that two or more fractions share. The lowest common denominator is the lowest common multiple (LCM) of the bottom numbers.
Method. Write both fractions with the same bottom number, then compare the top numbers.
- Write any mixed number as an improper fraction. Multiply the whole number by the bottom, then add the top.225: 2 × 5 + 2 = 12, so 125
212: 2 × 2 + 1 = 5, so 52 - Find the lowest common denominator. Use the LCM of the two bottom numbers.LCM of 5 and 2 = 10
- Write both with the same bottom number. Multiply the top and bottom of each fraction by the same number.125 = 2410
52 = 2510 - Compare the top numbers. When the bottoms are the same, the bigger top number is the bigger fraction.24 and 25: the bigger top number is 25
- Say which fraction is bigger. Write the smaller one, then the bigger one.225 < 212
Check. 2510 is the bigger value of the two, so 212 is the bigger fraction. ✓
Watch out. Do not just compare the bottom numbers. A bigger bottom number means smaller pieces.
Watch out
A bigger bottom number means smaller pieces, not a bigger fraction. 13 is bigger than 15, because thirds are bigger than fifths. Also, do not compare the top numbers before you make the bottoms the same.Exercise 4C Comparing and ordering fractions
Non-calculatorKey words. A common denominator is a bottom number that two or more fractions share. The lowest common denominator is the lowest common multiple (LCM) of the bottom numbers.
Method. Write both fractions with the same bottom number, then compare the top numbers.
- Find the lowest common denominator. Use the LCM of the two bottom numbers.LCM of 3 and 5 = 15
- Write both with the same bottom number. Multiply the top and bottom of each fraction by the same number.23 = 1015
35 = 915 - Compare the top numbers. When the bottoms are the same, the bigger top number is the bigger fraction.10 and 9: the bigger top number is 10
- Say which fraction is bigger. Write the smaller one, then the bigger one.35 < 23
Check. 1015 is the bigger value of the two, so 23 is the bigger fraction. ✓
Watch out. Do not just compare the bottom numbers. A bigger bottom number means smaller pieces.
Key words. A common denominator is a bottom number that two or more fractions share. The lowest common denominator is the lowest common multiple (LCM) of the bottom numbers.
Method. Write both fractions with the same bottom number, then compare the top numbers.
- Find the lowest common denominator. Use the LCM of the two bottom numbers.LCM of 8 and 2 = 8
- Write both with the same bottom number. Multiply the top and bottom of each fraction by the same number.58 = 58
12 = 48 - Compare the top numbers. When the bottoms are the same, the bigger top number is the bigger fraction.5 and 4: the bigger top number is 5
- Say which fraction is bigger. Write the smaller one, then the bigger one.12 < 58
Check. 58 is the bigger value of the two, so 58 is the bigger fraction. ✓
Watch out. Do not just compare the bottom numbers. A bigger bottom number means smaller pieces.
Key words. A common denominator is a bottom number that two or more fractions share. The lowest common denominator is the lowest common multiple (LCM) of the bottom numbers.
Method. Write both fractions with the same bottom number, then compare the top numbers.
- Find the lowest common denominator. Use the LCM of the two bottom numbers.LCM of 10 and 4 = 20
- Write both with the same bottom number. Multiply the top and bottom of each fraction by the same number.710 = 1420
34 = 1520 - Compare the top numbers. When the bottoms are the same, the bigger top number is the bigger fraction.14 and 15: the bigger top number is 15
- Say which fraction is bigger. Write the smaller one, then the bigger one.710 < 34
Check. 1520 is the bigger value of the two, so 34 is the bigger fraction. ✓
Watch out. Do not just compare the bottom numbers. A bigger bottom number means smaller pieces.
Key words. A common denominator is a bottom number that two or more fractions share. The lowest common denominator is the lowest common multiple (LCM) of the bottom numbers.
Method. Write both fractions with the same bottom number, then compare the top numbers.
- Find the lowest common denominator. Use the LCM of the two bottom numbers.LCM of 9 and 12 = 36
- Write both with the same bottom number. Multiply the top and bottom of each fraction by the same number.49 = 1636
512 = 1536 - Compare the top numbers. When the bottoms are the same, the bigger top number is the bigger fraction.16 and 15: the bigger top number is 16
- Say which fraction is bigger. Write the smaller one, then the bigger one.512 < 49
Check. 1636 is the bigger value of the two, so 49 is the bigger fraction. ✓
Watch out. Do not just compare the bottom numbers. A bigger bottom number means smaller pieces.
Key words. A common denominator is a bottom number that two or more fractions share. The lowest common denominator is the lowest common multiple (LCM) of the bottom numbers.
Method. Make the bottom numbers the same, then compare the top numbers.
- Write them all with the same bottom number, 12. The lowest common denominator of the bottoms is 12. Change each fraction so that its bottom number is 12.34 = 912
56 = 1012
23 = 812 - Compare the top numbers. The bigger top number is the bigger fraction. Put them smallest first.8, 9, 10 (out of 12)
- Write the fractions in order, using the fractions from the question. 23, 34, 56
Check. 23 is the smallest and 56 is the largest. ✓
Watch out. A bigger bottom number means smaller pieces. Compare the top numbers only after the bottoms are the same.
Key words. A common denominator is a bottom number that two or more fractions share. The lowest common denominator is the lowest common multiple (LCM) of the bottom numbers.
Method. Make the bottom numbers the same, then compare the top numbers.
- Write them all with the same bottom number, 24. The lowest common denominator of the bottoms is 24. Change each fraction so that its bottom number is 24.12 = 1224
712 = 1424
58 = 1524 - Compare the top numbers. The bigger top number is the bigger fraction. Put them smallest first.12, 14, 15 (out of 24)
- Write the fractions in order, using the fractions from the question. 12, 712, 58
Check. 12 is the smallest and 58 is the largest. ✓
Watch out. A bigger bottom number means smaller pieces. Compare the top numbers only after the bottoms are the same.
Key words. A common denominator is a bottom number that two or more fractions share. The lowest common denominator is the lowest common multiple (LCM) of the bottom numbers.
Method. Make the bottom numbers the same, then compare the top numbers.
- Write them all with the same bottom number, 20. The lowest common denominator of the bottoms is 20. Change each fraction so that its bottom number is 20.45 = 1620
34 = 1520
710 = 1420 - Compare the top numbers. The bigger top number is the bigger fraction. Put them smallest first.14, 15, 16 (out of 20)
- Write the fractions in order, using the fractions from the question. 710, 34, 45
Check. 710 is the smallest and 45 is the largest. ✓
Watch out. A bigger bottom number means smaller pieces. Compare the top numbers only after the bottoms are the same.
Key words. A mixed number has a whole part and a fraction part, such as 2 1/3. An improper fraction has a top number that is bigger than its bottom number, such as 7/3. The two forms are the same amount.
Method. Change both to improper fractions. If the values match, the two numbers are equal.
- Write both as improper fractions. Multiply the whole number by the bottom, then add the top.214: 2 × 4 + 1 = 9, so 94
- Compare them. Both have the same value, so their top numbers are the same when the bottoms match.94 and 94 both have the value 214
- Say what you found. The two fractions have the same value.They are equal
Check. 94 and 94 are both 214. ✓
Watch out. Two numbers can look different but still be equal. Mixed numbers and improper fractions can be the same amount.
Key words. A common denominator is a bottom number that two or more fractions share. The lowest common denominator is the lowest common multiple (LCM) of the bottom numbers.
Method. Write both fractions with the same bottom number, then compare the top numbers.
- Write any mixed number as an improper fraction. Multiply the whole number by the bottom, then add the top.134: 1 × 4 + 3 = 7, so 74
- Find the lowest common denominator. Use the LCM of the two bottom numbers.LCM of 4 and 3 = 12
- Write both with the same bottom number. Multiply the top and bottom of each fraction by the same number.74 = 2112
53 = 2012 - Compare the top numbers. When the bottoms are the same, the bigger top number is the bigger fraction.21 and 20: the bigger top number is 21
- Say which fraction is bigger. Write the smaller one, then the bigger one.53 < 134
Check. 2112 is the bigger value of the two, so 134 is the bigger fraction. ✓
Watch out. Do not just compare the bottom numbers. A bigger bottom number means smaller pieces.
Key words. A common denominator is a bottom number that two or more fractions share. The lowest common denominator is the lowest common multiple (LCM) of the bottom numbers.
Method. Write both fractions with the same bottom number, then compare the top numbers.
- Write any mixed number as an improper fraction. Multiply the whole number by the bottom, then add the top.123: 1 × 3 + 2 = 5, so 53
- Find the lowest common denominator. Use the LCM of the two bottom numbers.LCM of 4 and 3 = 12
- Write both with the same bottom number. Multiply the top and bottom of each fraction by the same number.74 = 2112
53 = 2012 - Compare the top numbers. When the bottoms are the same, the bigger top number is the bigger fraction.21 and 20: the bigger top number is 21
- Say which fraction is bigger. Write the smaller one, then the bigger one.123 < 74
Check. 2112 is the bigger value of the two, so 74 is the bigger fraction. ✓
Watch out. Do not just compare the bottom numbers. A bigger bottom number means smaller pieces.
Key words. A common denominator is a bottom number that two or more fractions share. The lowest common denominator is the lowest common multiple (LCM) of the bottom numbers.
Method. Write both fractions with the same bottom number, then compare the top numbers.
- Find the lowest common denominator. Use the LCM of the two bottom numbers.LCM of 6 and 8 = 24
- Write both with the same bottom number. Multiply the top and bottom of each fraction by the same number.56 = 2024
78 = 2124 - Compare the top numbers. When the bottoms are the same, the bigger top number is the bigger fraction.20 and 21: the bigger top number is 21
- Say which fraction is bigger. Write the smaller one, then the bigger one.56 < 78
Check. 2124 is the bigger value of the two, so 78 is the bigger fraction. ✓
Watch out. Do not just compare the bottom numbers. A bigger bottom number means smaller pieces.
Key words. A common denominator is a bottom number that two or more fractions share. The lowest common denominator is the lowest common multiple (LCM) of the bottom numbers.
Method. Write both fractions with the same bottom number, then compare the top numbers.
- Find the lowest common denominator. Use the LCM of the two bottom numbers.LCM of 6 and 8 = 24
- Write both with the same bottom number. Multiply the top and bottom of each fraction by the same number.56 = 2024
78 = 2124 - Compare the top numbers. When the bottoms are the same, the bigger top number is the bigger fraction.20 and 21: the bigger top number is 21
- Say which fraction is bigger. Write the smaller one, then the bigger one.56 < 78
Check. 2124 is the bigger value of the two, so 78 is the bigger fraction. ✓
Watch out. Do not just compare the bottom numbers. A bigger bottom number means smaller pieces.
Key words. A common denominator is a bottom number that two or more fractions share. The lowest common denominator is the lowest common multiple (LCM) of the bottom numbers.
Method. Test some examples. The top numbers are the same, so compare how big each part is.
- Try some pairs with the same top number. The bottom number shows how many parts the whole is cut into.34 is bigger than 35, because the parts are bigger
27 is bigger than 29, because the parts are bigger
56 is bigger than 58, because the parts are bigger - Look at the size of the parts. A smaller bottom number means each part is bigger. So the fraction with the smaller bottom number has bigger parts.Smaller bottom number = bigger parts = bigger fraction
- Decide. The rule works for every positive top number, so it is always true.Always
Check. Both checks agree: 34 is bigger than 35, and 27 is bigger than 29. ✓
Watch out. One example is not a proof. Give a reason that works for every fraction of this kind.
Key words. A common denominator is a bottom number that two or more fractions share. The lowest common denominator is the lowest common multiple (LCM) of the bottom numbers.
Method. Change both boundaries to twelfths, then find the twelfths in between.
- Write 12 with a bottom number of 12. 12 ÷ 2 = 6, so multiply the top and bottom by 6.12 = 612
- Write 34 with a bottom number of 12. 12 ÷ 4 = 3, so multiply the top and bottom by 3.34 = 912
- List the twelfths between them. The top numbers must be bigger than 6 and smaller than 9.712 and 812
Check. 712 is bigger than 612 and smaller than 912. ✓
Watch out. Do not include the end values. The fractions must be strictly between them.
Key words. A common denominator is a bottom number that two or more fractions share. The lowest common denominator is the lowest common multiple (LCM) of the bottom numbers.
Method. Make the bottom numbers the same, then compare the top numbers.
- Write them all with the same bottom number, 84. The lowest common denominator of the bottoms is 84. Change each fraction so that its bottom number is 84.23 = 5684
34 = 6384
57 = 6084 - Compare the top numbers. The bigger top number is the bigger fraction. Put them largest first.63, 60, 56 (out of 84)
- Write the fractions in order, using the fractions from the question. 34, 57, 23
Check. 23 is the largest and 34 is the smallest. ✓
Watch out. A bigger bottom number means smaller pieces. Compare the top numbers only after the bottoms are the same.