Year 6: Common multiples and the same denominator
Part of the Year 6 fractions chapter. Chapter overview · whole chapter on one page
Common multiples and the same denominator
To add, subtract or compare fractions, the bottom numbers (the denominators) must be the same. We say the fractions are in the same denomination. Look at the bars below. 14 and 56 are cut into different-sized parts, so it is hard to compare them. Cut both bars into twelfths, and the fractions are easy to see: 312 and 1012.
The new bottom number must be a common multiple of the bottoms: 12 is in the 4 times table and in the 6 times table. The lowest common denominator is the lowest common multiple (LCM), so it gives the smallest numbers to work with.
Key ideas
- A common denominator is a bottom number that two or more fractions share.
- The lowest common denominator is the LCM of the bottom numbers.
- To change a fraction, multiply its top and bottom by the same number. The value stays the same.
- Work out what the bottom must be multiplied by: 14 needs × 3 to make 12.
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. Find the lowest common denominator, then change each fraction to it.
- Find the lowest common denominator. It is the LCM of the bottom numbers.LCM of 4, 6 = 12
- Make every bottom number 12. Multiply the top and the bottom of each fraction by the same number.14 = 312 (top and bottom × 3)
56 = 1012 (top and bottom × 2) - Write the answer. All the fractions now have the same bottom number.312 and 1012
Check. Each new fraction still has the same value as the old one. ✓
Watch out. The lowest common denominator is the smallest common multiple of the bottoms, so the numbers stay as small as possible.
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. Find the lowest common denominator, then change each fraction to it.
- Find the lowest common denominator. It is the LCM of the bottom numbers.LCM of 3, 5 = 15
- Make every bottom number 15. Multiply the top and the bottom of each fraction by the same number.23 = 1015 (top and bottom × 5)
35 = 915 (top and bottom × 3) - Write the answer. All the fractions now have the same bottom number.1015 and 915
Check. Each new fraction still has the same value as the old one. ✓
Watch out. The lowest common denominator is the smallest common multiple of the bottoms, so the numbers stay as small as possible.
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. Find the lowest common denominator, then change each fraction to it.
- Find the lowest common denominator. It is the LCM of the bottom numbers.LCM of 8, 12 = 24
- Make every bottom number 24. Multiply the top and the bottom of each fraction by the same number.58 = 1524 (top and bottom × 3)
712 = 1424 (top and bottom × 2) - Write the answer. All the fractions now have the same bottom number.1524 and 1424
Check. Each new fraction still has the same value as the old one. ✓
Watch out. The lowest common denominator is the smallest common multiple of the bottoms, so the numbers stay as small as possible.
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. Find the lowest common denominator, then change each fraction to it.
- Find the lowest common denominator. It is the LCM of the bottom numbers.LCM of 2, 3, 4 = 12
- Make every bottom number 12. Multiply the top and the bottom of each fraction by the same number.12 = 612 (top and bottom × 6)
23 = 812 (top and bottom × 4)
34 = 912 (top and bottom × 3) - Write the answer. All the fractions now have the same bottom number.612, 812 and 912
Check. Each new fraction still has the same value as the old one. ✓
Watch out. The lowest common denominator is the smallest common multiple of the bottoms, so the numbers stay as small as possible.
Watch out
Any common multiple works as a common denominator, but the lowest one gives the smallest numbers. 4 and 6 share 12 and 24, but 12 is quicker. Do not just multiply the two bottoms together (4 × 6 = 24) unless you have to.Exercise 4B Common multiples and common denominators
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. The common multiples are the multiples of the LCM. Count up in steps of the LCM.
- Find the lowest common multiple (LCM). Every common multiple is a multiple of the LCM, so start there.LCM of 3 and 4 = 12
- Count up in steps of 12. Each answer is in both times tables.12, 24, 36, 48
- Check the first one. 12 is in the 3 times table and the 4 times table.12 ÷ 3 = 4, 12 ÷ 4 = 3
Check. 48 ÷ 3 = 16 and 48 ÷ 4 = 12. ✓
Watch out. Start from the LCM, not from 0 or from 1.
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. Find the lowest common denominator, then change each fraction to it.
- Find the lowest common denominator. It is the LCM of the bottom numbers.LCM of 2, 3 = 6
- Make every bottom number 6. Multiply the top and the bottom of each fraction by the same number.12 = 36 (top and bottom × 3)
13 = 26 (top and bottom × 2) - Write the answer. All the fractions now have the same bottom number.36 and 26
Check. Each new fraction still has the same value as the old one. ✓
Watch out. The lowest common denominator is the smallest common multiple of the bottoms, so the numbers stay as small as possible.
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. Find the lowest common denominator, then change each fraction to it.
- Find the lowest common denominator. It is the LCM of the bottom numbers.LCM of 4, 6 = 12
- Make every bottom number 12. Multiply the top and the bottom of each fraction by the same number.34 = 912 (top and bottom × 3)
16 = 212 (top and bottom × 2) - Write the answer. All the fractions now have the same bottom number.912 and 212
Check. Each new fraction still has the same value as the old one. ✓
Watch out. The lowest common denominator is the smallest common multiple of the bottoms, so the numbers stay as small as possible.
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. Find the lowest common denominator, then change each fraction to it.
- Find the lowest common denominator. It is the LCM of the bottom numbers.LCM of 5, 10 = 10
- Make every bottom number 10. Multiply the top and the bottom of each fraction by the same number.25 = 410 (top and bottom × 2)
310 = 310 (top and bottom × 1) - Write the answer. All the fractions now have the same bottom number.410 and 310
Check. Each new fraction still has the same value as the old one. ✓
Watch out. The lowest common denominator is the smallest common multiple of the bottoms, so the numbers stay as small as possible.
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. Find the lowest common denominator, then change each fraction to it.
- Find the lowest common denominator. It is the LCM of the bottom numbers.LCM of 6, 8 = 24
- Make every bottom number 24. Multiply the top and the bottom of each fraction by the same number.56 = 2024 (top and bottom × 4)
38 = 924 (top and bottom × 3) - Write the answer. All the fractions now have the same bottom number.2024 and 924
Check. Each new fraction still has the same value as the old one. ✓
Watch out. The lowest common denominator is the smallest common multiple of the bottoms, so the numbers stay as small as possible.
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 number 20 by multiplying the top and the bottom by 4.
- Find what the bottom number 5 must be multiplied by to make 20. 20 ÷ 5 = 4.20 ÷ 5 = 4
- Multiply the top and the bottom by the same number. Doing the same to both numbers keeps the fraction equal.35 × 4/4 = 1220
Check. 12 ÷ 4 = 3 and 20 ÷ 4 = 5. ✓
Watch out. Multiply the top as well as the bottom. Changing only the bottom changes the value.
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 number 24 by multiplying the top and the bottom by 3.
- Find what the bottom number 8 must be multiplied by to make 24. 24 ÷ 8 = 3.24 ÷ 8 = 3
- Multiply the top and the bottom by the same number. Doing the same to both numbers keeps the fraction equal.78 × 3/3 = 2124
Check. 21 ÷ 3 = 7 and 24 ÷ 3 = 8. ✓
Watch out. Multiply the top as well as the bottom. Changing only the bottom changes the value.
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 number 18 by multiplying the top and the bottom by 3.
- Find what the bottom number 6 must be multiplied by to make 18. 18 ÷ 6 = 3.18 ÷ 6 = 3
- Multiply the top and the bottom by the same number. Doing the same to both numbers keeps the fraction equal.56 × 3/3 = 1518
Check. 15 ÷ 3 = 5 and 18 ÷ 3 = 6. ✓
Watch out. Multiply the top as well as the bottom. Changing only the bottom changes the value.
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. List the multiples of each number until they meet. The first number in both lists is the LCM.
- Write the multiples of 4. Count up in steps of 4 until you reach a number that is also in the list for 6.4, 8, 12
- Write the multiples of 6. Stop at the first number that is in both lists.6, 12
- Find the lowest common multiple (LCM). It is the first number that appears in both lists.LCM = 12
Check. 12 ÷ 4 = 3 and 12 ÷ 6 = 2. ✓
Watch out. The LCM can be one of the numbers, such as the LCM of 4 and 8 being 8.
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. List the multiples of each number until they meet. The first number in both lists is the LCM.
- Write the multiples of 5. Count up in steps of 5 until you reach a number that is also in the list for 8.5, 10, 15, 20, 25, 30, 35, 40
- Write the multiples of 8. Stop at the first number that is in both lists.8, 16, 24, 32, 40
- Find the lowest common multiple (LCM). It is the first number that appears in both lists.LCM = 40
Check. 40 ÷ 5 = 8 and 40 ÷ 8 = 5. ✓
Watch out. The LCM can be one of the numbers, such as the LCM of 4 and 8 being 8.
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. List the multiples of each number until they meet. The first number in both lists is the LCM.
- Write the multiples of 3. Count up in steps of 3 until you reach a number that is also in the list for 10.3, 6, 9, 12, 15, 18, 21, 24, 27, 30
- Write the multiples of 10. Stop at the first number that is in both lists.10, 20, 30
- Find the lowest common multiple (LCM). It is the first number that appears in both lists.LCM = 30
Check. 30 ÷ 3 = 10 and 30 ÷ 10 = 3. ✓
Watch out. The LCM can be one of the numbers, such as the LCM of 4 and 8 being 8.
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. List the multiples of each number until they meet. The first number in both lists is the LCM.
- Write the multiples of 9. Count up in steps of 9 until you reach a number that is also in the list for 12.9, 18, 27, 36
- Write the multiples of 12. Stop at the first number that is in both lists.12, 24, 36
- Find the lowest common multiple (LCM). It is the first number that appears in both lists.LCM = 36
Check. 36 ÷ 9 = 4 and 36 ÷ 12 = 3. ✓
Watch out. The LCM can be one of the numbers, such as the LCM of 4 and 8 being 8.
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. Find the lowest common denominator, then change each fraction to it.
- Find the lowest common denominator. It is the LCM of the bottom numbers.LCM of 4, 6 = 12
- Make every bottom number 12. Multiply the top and the bottom of each fraction by the same number.34 = 912 (top and bottom × 3)
56 = 1012 (top and bottom × 2) - Write the answer. All the fractions now have the same bottom number.912 and 1012
Check. Each new fraction still has the same value as the old one. ✓
Watch out. The lowest common denominator is the smallest common multiple of the bottoms, so the numbers stay as small as possible.
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. Find the lowest common denominator, then change each fraction to it.
- Find the lowest common denominator. It is the LCM of the bottom numbers.LCM of 4, 3 = 12
- Make every bottom number 12. Multiply the top and the bottom of each fraction by the same number.14 = 312 (top and bottom × 3)
23 = 812 (top and bottom × 4) - Write the answer. All the fractions now have the same bottom number.312 and 812
Check. Each new fraction still has the same value as the old one. ✓
Watch out. The lowest common denominator is the smallest common multiple of the bottoms, so the numbers stay as small as possible.
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. Find the lowest common denominator, then change each fraction to it.
- Find the lowest common denominator. It is the LCM of the bottom numbers.LCM of 8, 12 = 24
- Make every bottom number 24. Multiply the top and the bottom of each fraction by the same number.58 = 1524 (top and bottom × 3)
712 = 1424 (top and bottom × 2) - Write the answer. All the fractions now have the same bottom number.1524 and 1424
Check. Each new fraction still has the same value as the old one. ✓
Watch out. The lowest common denominator is the smallest common multiple of the bottoms, so the numbers stay as small as possible.
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. Use common multiples of the two bottom numbers, 3 and 5. Try 15 first, then 30.
- Write the fractions with a denominator of 15. Multiply the top and bottom of each fraction so the bottom becomes 15 and 30.13 = 515 and 15 = 315
- Write them with a denominator of 30. Lily uses 30, which is also a common multiple of 3 and 5.13 = 1030 and 15 = 630
- Decide who is right. Both 15 and 30 work, because both are common multiples. But 15 is the lowest, so it is the lowest common denominator.Both are right, and 15 is the lowest common denominator
Check. 515 = 13 and 1030 = 13. ✓
Watch out. Any common multiple works, but the lowest one is the easiest.
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. Find the lowest common denominator, then change each fraction to it.
- Find the lowest common denominator. It is the LCM of the bottom numbers.LCM of 4, 8 = 8
- Make every bottom number 8. Multiply the top and the bottom of each fraction by the same number.14 = 28 (top and bottom × 2)
38 = 38 (top and bottom × 1) - Write the answer. All the fractions now have the same bottom number.28 and 38
Check. Each new fraction still has the same value as the old one. ✓
Watch out. The lowest common denominator is the smallest common multiple of the bottoms, so the numbers stay as small as possible.
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. Find the lowest common denominator, then change each fraction to it.
- Find the lowest common denominator. It is the LCM of the bottom numbers.LCM of 12, 18 = 36
- Make every bottom number 36. Multiply the top and the bottom of each fraction by the same number.512 = 1536 (top and bottom × 3)
718 = 1436 (top and bottom × 2) - Write the answer. All the fractions now have the same bottom number.1536 and 1436
Check. Each new fraction still has the same value as the old one. ✓
Watch out. The lowest common denominator is the smallest common multiple of the bottoms, so the numbers stay as small as possible.