Year 6 Maths reasoning (SATs): Comparing and ordering fractions
Part of the Year 6 Maths reasoning (SATs) fractions and decimals reasoning chapter. Chapter overview · whole chapter on one page
Comparing and ordering fractions
Rule
To compare fractions, write them with the same denominator. Then the fraction with the bigger numerator is bigger.
A fraction can be greater than 1, for example 7/3 = 2 1/3. For the full method, read Year 6 maths, chapter 4.
Key ideas
- Equal denominators: compare the numerators.
- A bigger denominator means smaller pieces: 1/8 is less than 1/4.
- A fraction with the top bigger than the bottom is greater than 1.
Method. Make the denominators the same, then compare the tops.
- Find a common denominator. The denominators are 6 and 9. Both divide into 18.common denominator 18
- Write both fractions with that denominator. Multiply the top and bottom of each fraction to make 18 on the bottom.5/6 = 15/18 and 7/9 = 14/18
- Compare the tops. With the same bottom number, the bigger top number is the larger fraction.15 and 14
- Write the answer. 5/6
Check. 15/18 and 14/18: the one with the bigger top is larger. ✓
Watch out. A bigger bottom number makes smaller pieces, so 1/8 is less than 1/4.
Method. Make the denominators the same, then compare the tops.
- Find a common denominator. The denominators are 4 and 3. Both divide into 12.common denominator 12
- Write both fractions with that denominator. Multiply the top and bottom of each fraction to make 12 on the bottom.9/4 = 27/12 and 7/3 = 28/12
- Compare the tops. With the same bottom number, the bigger top number is the larger fraction.27 and 28
- Write the answer. 7/3
Check. 27/12 and 28/12: the one with the bigger top is larger. ✓
Watch out. A bigger bottom number makes smaller pieces, so 1/8 is less than 1/4.
Method. Use a common denominator, then order the tops.
- Find a common denominator. Use 12, which all the denominators divide into.12
- Write each fraction with the same bottom number. Then the order depends only on the tops.3/4 = 9/12, 2/3 = 8/12, 5/6 = 10/12, 7/12 = 7/12
- Order the tops and write the fractions. Smallest top first.7/12, 2/3, 3/4, 5/6
- Write the answer. 7/12, 2/3, 3/4, 5/6
Check. Each fraction is less than the next. ✓
Watch out. Do not order by the bottom numbers alone: 1/2 is bigger than 1/3, even though 2 is less than 3.
Watch out
Watch out. 1/2 is bigger than 1/3, even though 2 is less than 3. Compare the pieces, not the bottom numbers.
Exam tip
Practice guide. Use a common denominator, then say which top number is bigger.
Exercise 2A Practice: comparing and ordering fractions
Non-calculatorMethod. Make the denominators the same, then compare the tops.
- Find a common denominator. The denominators are 3 and 8. Both divide into 24.common denominator 24
- Write both fractions with that denominator. Multiply the top and bottom of each fraction to make 24 on the bottom.2/3 = 16/24 and 5/8 = 15/24
- Compare the tops. With the same bottom number, the bigger top number is the larger fraction.16 and 15
- Write the answer. 2/3
Check. 16/24 and 15/24: the one with the bigger top is larger. ✓
Watch out. A bigger bottom number makes smaller pieces, so 1/8 is less than 1/4.
Method. Make the denominators the same, then compare the tops.
- Find a common denominator. The denominators are 9 and 7. Both divide into 63.common denominator 63
- Write both fractions with that denominator. Multiply the top and bottom of each fraction to make 63 on the bottom.4/9 = 28/63 and 3/7 = 27/63
- Compare the tops. With the same bottom number, the bigger top number is the larger fraction.28 and 27
- Write the answer. 4/9
Check. 28/63 and 27/63: the one with the bigger top is larger. ✓
Watch out. A bigger bottom number makes smaller pieces, so 1/8 is less than 1/4.
Method. Make the denominators the same, then compare the tops.
- Find a common denominator. The denominators are 10 and 4. Both divide into 20.common denominator 20
- Write both fractions with that denominator. Multiply the top and bottom of each fraction to make 20 on the bottom.7/10 = 14/20 and 3/4 = 15/20
- Compare the tops. With the same bottom number, the bigger top number is the smaller fraction.14 and 15
- Write the answer. 7/10
Check. 14/20 and 15/20: the one with the smaller top is smaller. ✓
Watch out. A bigger bottom number makes smaller pieces, so 1/8 is less than 1/4.
Method. Make the denominators the same, then compare the tops.
- Find a common denominator. The denominators are 6 and 5. Both divide into 30.common denominator 30
- Write both fractions with that denominator. Multiply the top and bottom of each fraction to make 30 on the bottom.11/6 = 55/30 and 9/5 = 54/30
- Compare the tops. With the same bottom number, the bigger top number is the larger fraction.55 and 54
- Write the answer. 11/6
Check. 55/30 and 54/30: the one with the bigger top is larger. ✓
Watch out. A bigger bottom number makes smaller pieces, so 1/8 is less than 1/4.
Method. Use a common denominator, then order the tops.
- Find a common denominator. Use 30, which all the denominators divide into.30
- Write each fraction with the same bottom number. Then the order depends only on the tops.1/2 = 15/30, 1/3 = 10/30, 2/5 = 12/30, 3/10 = 9/30
- Order the tops and write the fractions. Smallest top first.3/10, 1/3, 2/5, 1/2
- Write the answer. 3/10, 1/3, 2/5, 1/2
Check. Each fraction is less than the next. ✓
Watch out. Do not order by the bottom numbers alone: 1/2 is bigger than 1/3, even though 2 is less than 3.
Method. Use a common denominator, then order the tops.
- Find a common denominator. Use 24, which all the denominators divide into.24
- Write each fraction with the same bottom number. Then the order depends only on the tops.5/4 = 30/24, 3/2 = 36/24, 7/8 = 21/24, 2/3 = 16/24
- Order the tops and write the fractions. Smallest top first.2/3, 7/8, 5/4, 3/2
- Write the answer. 2/3, 7/8, 5/4, 3/2
Check. Each fraction is less than the next. ✓
Watch out. Do not order by the bottom numbers alone: 1/2 is bigger than 1/3, even though 2 is less than 3.
Method. Test each option.
- Check each option. Test each one against the rule or the calculation.
- Tick the true ones. Each ticked fraction is more than 1/2 (for example 5/9 is more than 4.5/9).3/5, 5/9, 7/12
- Leave the others unticked. These do not match.2/5, 4/10, 1/2 are not ticked
- Write the answer. 3/5, 5/9, 7/12
Check. Each ticked option is true. ✓
Watch out. 1/2 is equal to a half, so it is not greater than a half.
Method. Compare the two fractions with the same denominator.
- Common denominator. The denominators are 8 and 5, so use 40.5/8 = 25/40 and 3/5 = 24/40
- Compare. Ravi has 25/40 and Lena has 24/40, so Ravi ran further.25 is bigger than 24
- Write the answer. Ravi
Check. 25/40 is bigger than 24/40. ✓
Method. Halfway between two fractions is their average.
- Add the two fractions. 1/4 + 3/4 = 4/4 = 1.1
- Halve the total. 1 / 2 = 1/2.1/2
- Write the answer. 1/2
Check. 1/4 and 3/4 are equally spaced around 1/2. ✓
Method. Write both fractions with the same bottom number.
- Common denominator. 1/8 and 1/4 can be written with 8.1/8 and 2/8
- Compare. 2/8 is bigger than 1/8, so 1/4 is bigger.1/4 is bigger
- Write the answer. No, because 1/4 is 2 pieces of 1/8, so 1/4 is bigger.
Check. 1/4 = 2/8, which is bigger than 1/8. ✓
Method. Think about how many whole ones are in the fraction.
- Write as a mixed number. 7/4 = 4/4 + 3/4 = 1 3/4.1 3/4
- Compare with 1. One whole is 4/4, and 7/4 is more than 4/4.7/4 > 1
- Write the answer. Yes, because 7/4 is 1 3/4, which is more than 1 whole.
Check. 7/4 = 1 3/4, which is more than 1. ✓
Method. Make the denominators the same, then compare the tops.
- Find a common denominator. The denominators are 3 and 8. Both divide into 24.common denominator 24
- Write both fractions with that denominator. Multiply the top and bottom of each fraction to make 24 on the bottom.1/3 = 8/24 and 3/8 = 9/24
- Compare the tops. With the same bottom number, the bigger top number is the larger fraction.8 and 9
- Write the answer. 3/8
Check. 8/24 and 9/24: the one with the bigger top is larger. ✓
Watch out. A bigger bottom number makes smaller pieces, so 1/8 is less than 1/4.
Method. Make the denominators the same, then compare the tops.
- Find a common denominator. The denominators are 7 and 6. Both divide into 42.common denominator 42
- Write both fractions with that denominator. Multiply the top and bottom of each fraction to make 42 on the bottom.6/7 = 36/42 and 5/6 = 35/42
- Compare the tops. With the same bottom number, the bigger top number is the larger fraction.36 and 35
- Write the answer. 6/7
Check. 36/42 and 35/42: the one with the bigger top is larger. ✓
Watch out. A bigger bottom number makes smaller pieces, so 1/8 is less than 1/4.
Method. Use a common denominator, then order the tops.
- Find a common denominator. Use 60, which all the denominators divide into.60
- Write each fraction with the same bottom number. Then the order depends only on the tops.7/5 = 84/60, 4/3 = 80/60, 3/2 = 90/60, 5/4 = 75/60
- Order the tops and write the fractions. Smallest top first.5/4, 4/3, 7/5, 3/2
- Write the answer. 5/4, 4/3, 7/5, 3/2
Check. Each fraction is less than the next. ✓
Watch out. Do not order by the bottom numbers alone: 1/2 is bigger than 1/3, even though 2 is less than 3.
Method. Compare the fractions with a common denominator of 105.
- Common denominator. 5, 7 and 3 all divide into 105.3/5 = 63/105, 4/7 = 60/105 and 2/3 = 70/105
- Compare the tops. The smallest top is 60, which is 4/7.4/7
- Write the answer. 4/7
Check. 60 is the smallest of 63, 60 and 70. ✓