Year 6 Arithmetic (SATs): Comparing and ordering fractions
Part of the Year 6 Arithmetic (SATs) fractions chapter. Chapter overview · whole chapter on one page
Comparing and ordering fractions
Rule
To compare fractions, write them with the same denominator. The fraction with the bigger top number is bigger, when the bottoms are the same.
Fractions greater than 1 work the same way: 7/4 is bigger than 5/3 once both are written with 12 as the denominator.
Key ideas
- Write the fractions with a common denominator, then compare the tops.
- The bigger the top for the same bottom, the bigger the fraction.
- Fractions greater than 1 can be compared the same way.
Method. Write both fractions with the same denominator, then compare.
- Find a common denominator. 4 and 8 both divide into 8.8
- Write both fractions with that denominator. Multiply each top and bottom by the same number.3/4 = 6/8 and 5/8 = 5/8
- Compare the top numbers. 6 and 5 tell us which fraction is bigger.6 > 5, so 3/4 > 5/8
- Write the answer. >
Check. 3/4 = 6/8, which is bigger than 5/8. ✓
Watch out. Compare the tops only after the bottoms are equal.
Method. Use the common denominator 12 for both.
- Find a common denominator. 4 and 3 both divide into 12.12
- Write both fractions with that denominator. Multiply each top and bottom by the same number.7/4 = 21/12 and 5/3 = 20/12
- Compare the top numbers. 21 and 20 tell us which fraction is bigger.21 > 20, so 7/4 > 5/3
- Write the answer. >
Check. 7/4 = 1 3/4 and 5/3 = 1 2/3, and 1 3/4 is bigger. ✓
Method. Write each fraction with the denominator 12, then order the tops.
- Write with denominator 12. 5/6 = 10/12, 2/3 = 8/12 and 7/12 stays the same.10/12, 8/12, 7/12
- Order the tops from smallest. 7 is smallest, then 8, then 10.7/12 < 8/12 < 10/12
- Write the original fractions. Put back the original fractions in the same order.7/12, 2/3, 5/6
- Write the answer. 7/12, 2/3, 5/6
Check. The order is 7/12 (0.58), 2/3 (0.67), 5/6 (0.83). ✓
Exercise 3B Practice: comparing and ordering
Non-calculatorMethod. Write both with the same denominator.
- Find a common denominator. 4 and 8 both divide into 8.8
- Write both fractions with that denominator. Multiply each top and bottom by the same number.3/4 = 6/8 and 5/8 = 5/8
- Compare the top numbers. 6 and 5 tell us which fraction is bigger.6 > 5, so 3/4 > 5/8
- Write the answer. >
Check. The bigger fraction has the bigger top after this step. ✓
Method. Write both with the same denominator.
- Find a common denominator. 3 and 5 both divide into 15.15
- Write both fractions with that denominator. Multiply each top and bottom by the same number.2/3 = 10/15 and 3/5 = 9/15
- Compare the top numbers. 10 and 9 tell us which fraction is bigger.10 > 9, so 2/3 > 3/5
- Write the answer. >
Check. The bigger fraction has the bigger top after this step. ✓
Method. Write both with the same denominator.
- Find a common denominator. 10 and 4 both divide into 20.20
- Write both fractions with that denominator. Multiply each top and bottom by the same number.7/10 = 14/20 and 3/4 = 15/20
- Compare the top numbers. 14 and 15 tell us which fraction is bigger.14 < 15, so 7/10 < 3/4
- Write the answer. <
Check. The bigger fraction has the bigger top after this step. ✓
Method. Write both with the same denominator.
- Find a common denominator. 6 and 9 both divide into 18.18
- Write both fractions with that denominator. Multiply each top and bottom by the same number.5/6 = 15/18 and 7/9 = 14/18
- Compare the top numbers. 15 and 14 tell us which fraction is bigger.15 > 14, so 5/6 > 7/9
- Write the answer. >
Check. The bigger fraction has the bigger top after this step. ✓
Method. Write both with the same denominator.
- Find a common denominator. 5 and 11 both divide into 55.55
- Write both fractions with that denominator. Multiply each top and bottom by the same number.4/5 = 44/55 and 9/11 = 45/55
- Compare the top numbers. 44 and 45 tell us which fraction is bigger.44 < 45, so 4/5 < 9/11
- Write the answer. <
Check. The bigger fraction has the bigger top after this step. ✓
Method. Write both with the same denominator.
- Find a common denominator. 2 and 9 both divide into 18.18
- Write both fractions with that denominator. Multiply each top and bottom by the same number.1/2 = 9/18 and 4/9 = 8/18
- Compare the top numbers. 9 and 8 tell us which fraction is bigger.9 > 8, so 1/2 > 4/9
- Write the answer. >
Check. The bigger fraction has the bigger top after this step. ✓
Method. Both fractions are greater than 1; use the denominator 12.
- Find a common denominator. 4 and 3 both divide into 12.12
- Write both fractions with that denominator. Multiply each top and bottom by the same number.7/4 = 21/12 and 5/3 = 20/12
- Compare the top numbers. 21 and 20 tell us which fraction is bigger.21 > 20, so 7/4 > 5/3
- Write the answer. >
Check. 7/4 = 1 3/4 and 5/3 = 1 2/3. ✓
Method. Write each fraction with the denominator 8.
- Write with denominator 8. 3/4 = 6/8, 5/8 stays, 1/2 = 4/8.6/8, 5/8, 4/8
- Order the tops from largest. 6 is biggest, then 5, then 4.6/8 > 5/8 > 4/8
- Write the answer. 3/4, 5/8, 1/2
Check. 3/4 is 0.75, 5/8 is 0.625 and 1/2 is 0.5. ✓
Method. Use the common denominator 24.
- Write with denominator 24. 7/8 = 21/24 and 11/12 = 22/24.21/24 and 22/24
- Compare. 22 is bigger than 21.11/12 > 7/8
- Write the answer. 11/12
Check. 7/8 = 0.875 and 11/12 = 0.917. ✓
Method. Use the denominator 12 for both.
- Find a common denominator. 4 and 3 both divide into 12.12
- Write both fractions with that denominator. Multiply each top and bottom by the same number.9/4 = 27/12 and 7/3 = 28/12
- Compare the top numbers. 27 and 28 tell us which fraction is bigger.27 < 28, so 9/4 < 7/3
- Write the answer. <
Check. 9/4 = 2 1/4 and 7/3 = 2 1/3. ✓
Method. Look at the size of each piece, not the number of pieces.
- Write both with denominator 6. 1/3 = 2/6 and 1/2 = 3/6.2/6 and 3/6
- Compare. 3/6 is bigger than 2/6, so 1/2 is bigger.1/2 > 1/3
- Write the answer. No, 1/2 is greater, because a bigger bottom means smaller pieces.
Check. 0.5 is greater than 0.33. ✓