Year 4: Comparing and ordering fractions
Part of the Year 4 fractions chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Comparing and ordering fractions
To compare two fractions means to say which one is bigger. We use the signs < (less than) and > (greater than), and = (equal to).
Same bottom number. The pieces are the same size, so the fraction with more pieces is bigger. Compare the top numbers. 5/8 is bigger than 3/8, because 5 pieces are more than 3 pieces.
Unit fractions with different bottom numbers. Cut a whole into 4 equal parts, and another whole into 8 equal parts. The more parts you cut, the smaller each part is. So 1/8 is smaller than 1/4. A fraction wall shows this well.
Different bottom numbers, harder fractions. Make the bottom numbers the same using equivalent fractions (Section 5.3). To compare 3/4 and 5/8, change 3/4 into eighths: 3/4 = 6/8. Now compare 6/8 and 5/8. 6 is more than 5, so 3/4 is more than 5/8.
Ordering means putting fractions in a list from smallest to biggest (or biggest to smallest). Give them all the same bottom number, then order the top numbers. A handy trick is to compare with one half. Half of 12 is 6, so 7/12 is more than a half and 5/12 is less than a half.
Key words. To compare is to say which is bigger. To order is to put things in a list from smallest to biggest, or the other way round.
Key ideas
- Same bottom number: the bigger top number is the bigger fraction.
- Unit fractions: the bigger the bottom number, the SMALLER the fraction. (1/8 < 1/4)
- Different bottom numbers: change one fraction into an equivalent fraction so the bottom numbers match.
- A fraction wall shows the sizes: a longer brick is a bigger fraction.
- Compare with 1/2: half of the bottom number is the top number of a half.
- < means less than. > means greater than.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. When the bottom numbers are the same, the pieces are the same size. The fraction with the bigger top number is bigger.
- Look at the bottom numbers. They are both 8, so the pieces are the same size.
3 8 5 8 - Compare the top numbers. The same size pieces: more pieces means a bigger fraction.3 < 5
- Write the answer.
3 8 5 8
Check. Think of bars or a fraction wall: the longer shaded bar is the bigger fraction. ✓
Watch out. Only compare the top numbers when the bottom numbers are the same.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. For unit fractions (1 on the top), the bigger the bottom number, the smaller the piece. Use a fraction wall to see it.
- Look at the bottom numbers. They are different: 5 and 8. The pieces are not the same size.
1 5 1 8 - Think about the size of the pieces. When you cut a whole into MORE equal parts, each part is SMALLER.5 parts: each part is bigger. 8 parts: each part is smaller.
- Write the answer. The fraction with the bigger bottom number is the smaller fraction (for unit fractions).
1 5 1 8
Check. Think of bars or a fraction wall: the longer shaded bar is the bigger fraction. ✓
Watch out. 1/8 is smaller than 1/4. A bigger bottom number does not mean a bigger fraction!
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. The bottom numbers are the same, so put the fractions in order using their top numbers, smallest first.
- Look at the bottom numbers. They are all 9, so the pieces are the same size and we can order the fractions by their top numbers.
7 9 2 9 4 9 1 9 - Put the top numbers in order. The bottom numbers are the same, so the bigger top number is the bigger fraction. We want smallest first.1, 2, 4, 7
- Write the ORIGINAL fractions in that order. The question uses the original fractions.
1 9 2 9 4 9 7 9
Check. Look at the picture: the bars get longer from left to right in the list. ✓
Watch out. Write the original fractions in your answer, not the rewritten ones.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Change one fraction so both have the same bottom number. Then compare the top numbers.
- Look at the bottom numbers. They are different. But 8 is in the 4 times table, so we can change
3 4 4 × 2 = 8 - Rewrite
3 4 3 4 6 8 - Compare the top numbers. Now the bottom numbers are the same (8).6 and 5: 6 > 5
- Write the answer.
3 4 5 8
Check. Think of bars or a fraction wall: the longer shaded bar is the bigger fraction. ✓
Watch out. Do not compare the bottom numbers or the top numbers on their own. Make the bottom numbers the same first.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. For unit fractions, the bigger the bottom number, the smaller the piece. Use a fraction wall to see it.
- Look at the bottom numbers. These are all unit fractions (1 on the top). The bottom number tells us how many equal parts the whole is cut into.2, 6, 3, 10
- Think about the size of the pieces. More parts means smaller pieces. So the bigger the bottom number, the smaller the fraction.Biggest bottom number 10: smallest piece.
Smallest bottom number 2: biggest piece. - Put them smallest first.
1 10 1 6 1 3 1 2
Check. On the wall the shaded bricks get shorter as we read down. ✓
Watch out. 5 is bigger than 3, but 1/5 is smaller than 1/3.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Half of the bottom number is the top number of a half. Compare the top number with it.
- Find half of the bottom number. The whole is 12 parts. Half of the whole is half of 12 parts.12 ÷ 2 = 6, so
6 12 1 2 - Compare the top number 5 with 6. If we have more than 6 parts we have more than a half.5 < 6
- Write the answer.
5 12 1 2
Check.
Watch out. Compare the top number with HALF of the bottom number, not with the bottom number itself.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Give the fractions the same bottom number. Then put the top numbers in order, smallest first.
- Find a bottom number that all the bottom numbers go into. The biggest bottom number is 8. The other bottom numbers (2, 4) all go into 8.Use eighths.
- Rewrite every fraction as eighths. Multiply the top and the bottom by the same number each time.
1 2 4 8 3 8 3 8 3 4 6 8 - Put the top numbers in order. The bottom numbers are the same, so the bigger top number is the bigger fraction. We want smallest first.3, 4, 6
- Write the ORIGINAL fractions in that order. The question uses the original fractions.
3 8 1 2 3 4
Check. Look at the picture: the bars get longer from left to right in the list. ✓
Watch out. Write the original fractions in your answer, not the rewritten ones.
Watch out
A bigger bottom number does not mean a bigger fraction. 1/8 is smaller than 1/4, even though 8 is bigger than 4. The bottom number says how many parts the whole is cut into. More parts means smaller parts. Also, only compare the top numbers when the bottom numbers are the same.Exercise 5E Comparing and ordering fractions
Non-calculatorKey words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. When the bottom numbers are the same, the pieces are the same size. The fraction with the bigger top number is bigger.
- Look at the bottom numbers. They are both 8, so the pieces are the same size.
3 8 5 8 - Compare the top numbers. The same size pieces: more pieces means a bigger fraction.3 < 5
- Write the answer.
3 8 5 8
Check. Think of bars or a fraction wall: the longer shaded bar is the bigger fraction. ✓
Watch out. Only compare the top numbers when the bottom numbers are the same.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. When the bottom numbers are the same, the pieces are the same size. The fraction with the bigger top number is bigger.
- Look at the bottom numbers. They are both 10, so the pieces are the same size.
7 10 4 10 - Compare the top numbers. The same size pieces: more pieces means a bigger fraction.7 > 4
- Write the answer.
7 10 4 10
Check. Think of bars or a fraction wall: the longer shaded bar is the bigger fraction. ✓
Watch out. Only compare the top numbers when the bottom numbers are the same.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. When the bottom numbers are the same, the pieces are the same size. The fraction with the bigger top number is bigger.
- Look at the bottom numbers. They are both 5, so the pieces are the same size.
2 5 1 5 - Compare the top numbers. The same size pieces: more pieces means a bigger fraction.2 > 1
- Write the answer.
2 5 1 5
Check. Think of bars or a fraction wall: the longer shaded bar is the bigger fraction. ✓
Watch out. Only compare the top numbers when the bottom numbers are the same.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. When the bottom numbers are the same, the pieces are the same size. The fraction with the bigger top number is bigger.
- Look at the bottom numbers. They are both 5, so the pieces are the same size.
2 5 4 5 - Compare the top numbers. The same size pieces: more pieces means a bigger fraction.2 < 4
- Write the answer.
2 5 4 5
Check. Think of bars or a fraction wall: the longer shaded bar is the bigger fraction. ✓
Watch out. Only compare the top numbers when the bottom numbers are the same.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. When the bottom numbers are the same, the pieces are the same size. The fraction with the bigger top number is bigger.
- Look at the bottom numbers. They are both 8, so the pieces are the same size.
7 8 3 8 - Compare the top numbers. The same size pieces: more pieces means a bigger fraction.7 > 3
- Write the answer.
7 8 3 8
Check. Think of bars or a fraction wall: the longer shaded bar is the bigger fraction. ✓
Watch out. Only compare the top numbers when the bottom numbers are the same.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. When the bottom numbers are the same, the pieces are the same size. The fraction with the bigger top number is bigger.
- Look at the bottom numbers. They are both 9, so the pieces are the same size.
5 9 5 9 - Compare the top numbers. The same size pieces: more pieces means a bigger fraction.5 = 5
- Write the answer.
5 9 5 9
Check. Think of bars or a fraction wall: the longer shaded bar is the bigger fraction. ✓
Watch out. Only compare the top numbers when the bottom numbers are the same.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. When the bottom numbers are the same, the pieces are the same size. The fraction with the bigger top number is bigger.
- Look at the bottom numbers. They are both 6, so the pieces are the same size.
1 6 5 6 - Compare the top numbers. The same size pieces: more pieces means a bigger fraction.1 < 5
- Write the answer.
1 6 5 6
Check. Think of bars or a fraction wall: the longer shaded bar is the bigger fraction. ✓
Watch out. Only compare the top numbers when the bottom numbers are the same.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. When the bottom numbers are the same, the pieces are the same size. The fraction with the bigger top number is bigger.
- Look at the bottom numbers. They are both 10, so the pieces are the same size.
9 10 7 10 - Compare the top numbers. The same size pieces: more pieces means a bigger fraction.9 > 7
- Write the answer.
9 10 7 10
Check. Think of bars or a fraction wall: the longer shaded bar is the bigger fraction. ✓
Watch out. Only compare the top numbers when the bottom numbers are the same.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. When the bottom numbers are the same, the pieces are the same size. The fraction with the bigger top number is bigger.
- Look at the bottom numbers. They are both 12, so the pieces are the same size.
4 12 11 12 - Compare the top numbers. The same size pieces: more pieces means a bigger fraction.4 < 11
- Write the answer.
4 12 11 12
Check. Think of bars or a fraction wall: the longer shaded bar is the bigger fraction. ✓
Watch out. Only compare the top numbers when the bottom numbers are the same.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. For unit fractions (1 on the top), the bigger the bottom number, the smaller the piece. Use a fraction wall to see it.
- Look at the bottom numbers. They are different: 4 and 6. The pieces are not the same size.
1 4 1 6 - Think about the size of the pieces. When you cut a whole into MORE equal parts, each part is SMALLER.4 parts: each part is bigger. 6 parts: each part is smaller.
- Write the answer. The fraction with the bigger bottom number is the smaller fraction (for unit fractions).
1 4 1 6
Check. Think of bars or a fraction wall: the longer shaded bar is the bigger fraction. ✓
Watch out. 1/8 is smaller than 1/4. A bigger bottom number does not mean a bigger fraction!
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. For unit fractions (1 on the top), the bigger the bottom number, the smaller the piece. Use a fraction wall to see it.
- Look at the bottom numbers. They are different: 3 and 2. The pieces are not the same size.
1 3 1 2 - Think about the size of the pieces. When you cut a whole into MORE equal parts, each part is SMALLER.3 parts: each part is smaller. 2 parts: each part is bigger.
- Write the answer. The fraction with the bigger bottom number is the smaller fraction (for unit fractions).
1 3 1 2
Check. Think of bars or a fraction wall: the longer shaded bar is the bigger fraction. ✓
Watch out. 1/8 is smaller than 1/4. A bigger bottom number does not mean a bigger fraction!
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. For unit fractions (1 on the top), the bigger the bottom number, the smaller the piece. Use a fraction wall to see it.
- Look at the bottom numbers. They are different: 10 and 5. The pieces are not the same size.
1 10 1 5 - Think about the size of the pieces. When you cut a whole into MORE equal parts, each part is SMALLER.10 parts: each part is smaller. 5 parts: each part is bigger.
- Write the answer. The fraction with the bigger bottom number is the smaller fraction (for unit fractions).
1 10 1 5
Check. Think of bars or a fraction wall: the longer shaded bar is the bigger fraction. ✓
Watch out. 1/8 is smaller than 1/4. A bigger bottom number does not mean a bigger fraction!
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. For unit fractions (1 on the top), the bigger the bottom number, the smaller the piece. Use a fraction wall to see it.
- Look at the bottom numbers. They are different: 8 and 12. The pieces are not the same size.
1 8 1 12 - Think about the size of the pieces. When you cut a whole into MORE equal parts, each part is SMALLER.8 parts: each part is bigger. 12 parts: each part is smaller.
- Write the answer. The fraction with the bigger bottom number is the smaller fraction (for unit fractions).
1 8 1 12
Check. Think of bars or a fraction wall: the longer shaded bar is the bigger fraction. ✓
Watch out. 1/8 is smaller than 1/4. A bigger bottom number does not mean a bigger fraction!
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. For unit fractions (1 on the top), the bigger the bottom number, the smaller the piece. Use a fraction wall to see it.
- Look at the bottom numbers. They are different: 2 and 9. The pieces are not the same size.
1 2 1 9 - Think about the size of the pieces. When you cut a whole into MORE equal parts, each part is SMALLER.2 parts: each part is bigger. 9 parts: each part is smaller.
- Write the answer. The fraction with the bigger bottom number is the smaller fraction (for unit fractions).
1 2 1 9
Check. Think of bars or a fraction wall: the longer shaded bar is the bigger fraction. ✓
Watch out. 1/8 is smaller than 1/4. A bigger bottom number does not mean a bigger fraction!
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. For unit fractions (1 on the top), the bigger the bottom number, the smaller the piece. Use a fraction wall to see it.
- Look at the bottom numbers. They are different: 7 and 4. The pieces are not the same size.
1 7 1 4 - Think about the size of the pieces. When you cut a whole into MORE equal parts, each part is SMALLER.7 parts: each part is smaller. 4 parts: each part is bigger.
- Write the answer. The fraction with the bigger bottom number is the smaller fraction (for unit fractions).
1 7 1 4
Check. Think of bars or a fraction wall: the longer shaded bar is the bigger fraction. ✓
Watch out. 1/8 is smaller than 1/4. A bigger bottom number does not mean a bigger fraction!
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. The bottom numbers are the same, so put the fractions in order using their top numbers, smallest first.
- Look at the bottom numbers. They are all 7, so the pieces are the same size and we can order the fractions by their top numbers.
3 7 6 7 1 7 5 7 - Put the top numbers in order. The bottom numbers are the same, so the bigger top number is the bigger fraction. We want smallest first.1, 3, 5, 6
- Write the ORIGINAL fractions in that order. The question uses the original fractions.
1 7 3 7 5 7 6 7
Check. Look at the picture: the bars get longer from left to right in the list. ✓
Watch out. Write the original fractions in your answer, not the rewritten ones.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. The bottom numbers are the same, so put the fractions in order using their top numbers, smallest first.
- Look at the bottom numbers. They are all 6, so the pieces are the same size and we can order the fractions by their top numbers.
5 6 2 6 4 6 - Put the top numbers in order. The bottom numbers are the same, so the bigger top number is the bigger fraction. We want smallest first.2, 4, 5
- Write the ORIGINAL fractions in that order. The question uses the original fractions.
2 6 4 6 5 6
Check. Look at the picture: the bars get longer from left to right in the list. ✓
Watch out. Write the original fractions in your answer, not the rewritten ones.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. The bottom numbers are the same, so put the fractions in order using their top numbers, smallest first.
- Look at the bottom numbers. They are all 10, so the pieces are the same size and we can order the fractions by their top numbers.
8 10 3 10 9 10 1 10 - Put the top numbers in order. The bottom numbers are the same, so the bigger top number is the bigger fraction. We want smallest first.1, 3, 8, 9
- Write the ORIGINAL fractions in that order. The question uses the original fractions.
1 10 3 10 8 10 9 10
Check. Look at the picture: the bars get longer from left to right in the list. ✓
Watch out. Write the original fractions in your answer, not the rewritten ones.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. For unit fractions, the bigger the bottom number, the smaller the piece. Use a fraction wall to see it.
- Look at the bottom numbers. These are all unit fractions (1 on the top). The bottom number tells us how many equal parts the whole is cut into.3, 8, 5
- Think about the size of the pieces. More parts means smaller pieces. So the bigger the bottom number, the smaller the fraction.Biggest bottom number 8: smallest piece.
Smallest bottom number 3: biggest piece. - Put them biggest first.
1 3 1 5 1 8
Check. On the wall the shaded bricks get longer as we read up. ✓
Watch out. 5 is bigger than 3, but 1/5 is smaller than 1/3.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. For unit fractions, the bigger the bottom number, the smaller the piece. Use a fraction wall to see it.
- Look at the bottom numbers. These are all unit fractions (1 on the top). The bottom number tells us how many equal parts the whole is cut into.10, 2, 4, 5
- Think about the size of the pieces. More parts means smaller pieces. So the bigger the bottom number, the smaller the fraction.Biggest bottom number 10: smallest piece.
Smallest bottom number 2: biggest piece. - Put them biggest first.
1 2 1 4 1 5 1 10
Check. On the wall the shaded bricks get longer as we read up. ✓
Watch out. 5 is bigger than 3, but 1/5 is smaller than 1/3.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. For unit fractions, the bigger the bottom number, the smaller the piece. Use a fraction wall to see it.
- Look at the bottom numbers. These are all unit fractions (1 on the top). The bottom number tells us how many equal parts the whole is cut into.12, 6, 3
- Think about the size of the pieces. More parts means smaller pieces. So the bigger the bottom number, the smaller the fraction.Biggest bottom number 12: smallest piece.
Smallest bottom number 3: biggest piece. - Put them biggest first.
1 3 1 6 1 12
Check. On the wall the shaded bricks get longer as we read up. ✓
Watch out. 5 is bigger than 3, but 1/5 is smaller than 1/3.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Change one fraction so both have the same bottom number. Then compare the top numbers.
- Look at the bottom numbers. They are different. But 8 is in the 2 times table, so we can change
1 2 2 × 4 = 8 - Rewrite
1 2 1 2 4 8 - Compare the top numbers. Now the bottom numbers are the same (8).4 and 3: 4 > 3
- Write the answer.
1 2 3 8
Check. Think of bars or a fraction wall: the longer shaded bar is the bigger fraction. ✓
Watch out. Do not compare the bottom numbers or the top numbers on their own. Make the bottom numbers the same first.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Change one fraction so both have the same bottom number. Then compare the top numbers.
- Look at the bottom numbers. They are different. But 8 is in the 4 times table, so we can change
3 4 4 × 2 = 8 - Rewrite
3 4 3 4 6 8 - Compare the top numbers. Now the bottom numbers are the same (8).6 and 5: 6 > 5
- Write the answer.
3 4 5 8
Check. Think of bars or a fraction wall: the longer shaded bar is the bigger fraction. ✓
Watch out. Do not compare the bottom numbers or the top numbers on their own. Make the bottom numbers the same first.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Change one fraction so both have the same bottom number. Then compare the top numbers.
- Look at the bottom numbers. They are different. But 6 is in the 3 times table, so we can change
2 3 3 × 2 = 6 - Rewrite
2 3 2 3 4 6 - Compare the top numbers. Now the bottom numbers are the same (6).4 and 5: 4 < 5
- Write the answer.
2 3 5 6
Check. Think of bars or a fraction wall: the longer shaded bar is the bigger fraction. ✓
Watch out. Do not compare the bottom numbers or the top numbers on their own. Make the bottom numbers the same first.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Change one fraction so both have the same bottom number. Then compare the top numbers.
- Look at the bottom numbers. They are different. But 8 is in the 4 times table, so we can change
1 4 4 × 2 = 8 - Rewrite
1 4 1 4 2 8 - Compare the top numbers. Now the bottom numbers are the same (8).2 and 3: 2 < 3
- Write the answer.
1 4 3 8
Check. Think of bars or a fraction wall: the longer shaded bar is the bigger fraction. ✓
Watch out. Do not compare the bottom numbers or the top numbers on their own. Make the bottom numbers the same first.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Change one fraction so both have the same bottom number. Then compare the top numbers.
- Look at the bottom numbers. They are different. But 10 is in the 5 times table, so we can change
2 5 5 × 2 = 10 - Rewrite
2 5 2 5 4 10 - Compare the top numbers. Now the bottom numbers are the same (10).4 and 7: 4 < 7
- Write the answer.
2 5 7 10
Check. Think of bars or a fraction wall: the longer shaded bar is the bigger fraction. ✓
Watch out. Do not compare the bottom numbers or the top numbers on their own. Make the bottom numbers the same first.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Half of the bottom number is the top number of a half. Compare the top number with it.
- Find half of the bottom number. The whole is 8 parts. Half of the whole is half of 8 parts.8 ÷ 2 = 4, so
4 8 1 2 - Compare the top number 3 with 4. If we have more than 4 parts we have more than a half.3 < 4
- Write the answer.
3 8 1 2
Check.
Watch out. Compare the top number with HALF of the bottom number, not with the bottom number itself.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Half of the bottom number is the top number of a half. Compare the top number with it.
- Find half of the bottom number. The whole is 12 parts. Half of the whole is half of 12 parts.12 ÷ 2 = 6, so
6 12 1 2 - Compare the top number 7 with 6. If we have more than 6 parts we have more than a half.7 > 6
- Write the answer.
7 12 1 2
Check.
Watch out. Compare the top number with HALF of the bottom number, not with the bottom number itself.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Half of the bottom number is the top number of a half. Compare the top number with it.
- Find half of the bottom number. The whole is 10 parts. Half of the whole is half of 10 parts.10 ÷ 2 = 5, so
5 10 1 2 - Compare the top number 5 with 5. If we have more than 5 parts we have more than a half.5 = 5
- Write the answer.
5 10 1 2
Check.
Watch out. Compare the top number with HALF of the bottom number, not with the bottom number itself.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Half of the bottom number is the top number of a half. Compare the top number with it.
- Find half of the bottom number. The whole is 6 parts. Half of the whole is half of 6 parts.6 ÷ 2 = 3, so
3 6 1 2 - Compare the top number 4 with 3. If we have more than 3 parts we have more than a half.4 > 3
- Write the answer.
4 6 1 2
Check.
Watch out. Compare the top number with HALF of the bottom number, not with the bottom number itself.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Half of the bottom number is the top number of a half. Compare the top number with it.
- Find half of the bottom number. The whole is 10 parts. Half of the whole is half of 10 parts.10 ÷ 2 = 5, so
5 10 1 2 - Compare the top number 3 with 5. If we have more than 5 parts we have more than a half.3 < 5
- Write the answer.
3 10 1 2
Check.
Watch out. Compare the top number with HALF of the bottom number, not with the bottom number itself.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Half of the bottom number is the top number of a half. Compare the top number with it.
- Find half of the bottom number. The whole is 12 parts. Half of the whole is half of 12 parts.12 ÷ 2 = 6, so
6 12 1 2 - Compare the top number 6 with 6. If we have more than 6 parts we have more than a half.6 = 6
- Write the answer.
6 12 1 2
Check.
Watch out. Compare the top number with HALF of the bottom number, not with the bottom number itself.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Give the fractions the same bottom number. Then put the top numbers in order, smallest first.
- Find a bottom number that all the bottom numbers go into. The biggest bottom number is 8. The other bottom numbers (2, 4) all go into 8.Use eighths.
- Rewrite every fraction as eighths. Multiply the top and the bottom by the same number each time.
1 2 4 8 5 8 5 8 3 4 6 8 - Put the top numbers in order. The bottom numbers are the same, so the bigger top number is the bigger fraction. We want smallest first.4, 5, 6
- Write the ORIGINAL fractions in that order. The question uses the original fractions.
1 2 5 8 3 4
Check. Look at the picture: the bars get longer from left to right in the list. ✓
Watch out. Write the original fractions in your answer, not the rewritten ones.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Give the fractions the same bottom number. Then put the top numbers in order, biggest first.
- Find a bottom number that all the bottom numbers go into. The biggest bottom number is 6. The other bottom numbers (2, 3) all go into 6.Use sixths.
- Rewrite every fraction as sixths. Multiply the top and the bottom by the same number each time.
5 6 5 6 2 3 4 6 1 2 3 6 1 6 1 6 - Put the top numbers in order. The bottom numbers are the same, so the bigger top number is the bigger fraction. We want biggest first.5, 4, 3, 1
- Write the ORIGINAL fractions in that order. The question uses the original fractions.
5 6 2 3 1 2 1 6
Check. Look at the picture: the bars get shorter from left to right in the list. ✓
Watch out. Write the original fractions in your answer, not the rewritten ones.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Change one fraction so both have the same bottom number. Then compare the top numbers.
- Look at the bottom numbers. They are different. But 10 is in the 5 times table, so we can change
3 5 5 × 2 = 10 - Rewrite
3 5 3 5 6 10 - Compare the top numbers. Now the bottom numbers are the same (10).6 and 7: 6 < 7
- Write the answer.
3 5 7 10 - Answer the question. Jack has the bigger fraction (
7 10
Check. Think of bars or a fraction wall: the longer shaded bar is the bigger fraction. ✓
Watch out. Do not compare the bottom numbers or the top numbers on their own. Make the bottom numbers the same first.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Give the fractions the same bottom number. Then put the top numbers in order, biggest first.
- Find a bottom number that all the bottom numbers go into. The biggest bottom number is 8. The other bottom numbers (2) all go into 8.Use eighths.
- Rewrite every fraction as eighths. Multiply the top and the bottom by the same number each time.
5 8 5 8 1 2 4 8 3 8 3 8 - Put the top numbers in order. The bottom numbers are the same, so the bigger top number is the bigger fraction. We want biggest first.5, 4, 3
- Write the ORIGINAL fractions in that order. The question uses the original fractions.
5 8 1 2 3 8
Check. Look at the picture: the bars get shorter from left to right in the list. ✓
Watch out. Write the original fractions in your answer, not the rewritten ones.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Draw or look at a fraction wall. The bigger the bottom number, the smaller each piece.
- Look at what Tom said. Tom said
1 8 1 4 8 > 4 - Check with a picture. Cut one whole into 8 equal parts and another whole into 4 equal parts.
- Find the mistake. More parts means each part is smaller. A piece of size
1 8 1 4 1 8 1 4 - Answer. No.
1 4 1 8
Check. 4 equal parts are bigger parts than 8 equal parts. ✓
Watch out. The bottom number says how many parts the whole is cut into, not how big the fraction is.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. A fraction is more than a half when the top number is more than half of the bottom number. Check each one.
- Find half of each bottom number. This is the top number of a half with that bottom number.
5 8 4 6 3 10 7 12 - Compare the top number with it. More than a half means more pieces than half of them.
5 8 4 6 3 10 7 12 - Find the odd one out. Three fractions are more than a half. One is less.
3 10
Check. Half of 10 is 5, and 3 is less than 5. ✓
Watch out. Compare with half of the bottom number.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Try some pairs of fractions. Find a pair where the bigger bottom number gives the smaller fraction, and a pair where it does not.
- Try unit fractions. Cut the whole into more parts.
1 8 1 4 - Try fractions with different top numbers. Change the top numbers.
7 8 1 4 - Decide. One example works and one does not.Sometimes
Check.
Watch out. This rule works for unit fractions only.
Key words. To compare is to say which is bigger. < means “is less than” and > means “is greater than”.
Method. Write 1/4 as eighths, then list the eighths that are in between.
- Write
1 4 1 4 2 8 - Find the eighths in between. They must have a top number bigger than 2 and smaller than 5.The top numbers are 3 and 4:
3 8 4 8 - Count them. 2 fractions
Check.
Watch out. “Between” does not include the two fractions at the ends.