Step-by-step Maths Level 4: Division is the inverse of multiplication
Part of the Step-by-step Maths Level 4 division as sharing and grouping chapter. Chapter overview · whole chapter on one page
Division is the inverse of multiplication
Multiplication and division are opposites. If 6 × 9 = 54, then 54 ÷ 6 = 9 and 54 ÷ 9 = 6.
Use the times table you know to find the division. Check by multiplying back.
Key ideas
- A multiplication fact gives two divisions.
- Division is the inverse of multiplication.
- Check with multiplication: groups × size = total.
Method. Division is the inverse of multiplication. Use the times table fact to find the division.
- Write the fact: 6 × 9 = 54. This is the multiplication we know.6 × 9 = 54
- Turn it round to division. Division undoes multiplication, so the total is shared into groups of 6.54 ÷ 6 = 9
- Write the answer. The number of groups is the answer.9
Check. Check: 9 × 6 = 54, so 54 ÷ 6 = 9.
Watch out. The same three numbers make the division.
Method. Sharing: put the same number into each group. Divide the total by the number of groups.
- Count the friends. Each friend gets the same number.4 friends
- Share the sweets one at a time. Put one in each group, then start again until none are left.24 shared into 4 groups
- Count the sweets in one group. Each group has the same number.24 ÷ 4 = 6
- Write the answer. This is how many each friend gets.6
Check. Check: 6 × 4 = 24.
Watch out. The number of friends is the number of groups.
Method. Grouping: count how many groups of the size you are given can be made from the total.
- Count in fours until you reach 20. Each bag takes 4. Count one bag at a time.4, 8, 12, 16, 20
- Count the bags. Each count is one full bag of 4.5 bags
- Write the answer. This is the number of bags.5
Check. Check: 5 × 4 = 20.
Watch out. In grouping, you are given the size of each group.
Watch out
Watch out. 54 ÷ 6 is 9, because 6 × 9 = 54. Do not divide 6 by 54.
Exam tip
Grown-up tip. Ask: “Which times table fact helps you here?” before the child works out the division.
Exercise 6D Practice: division and multiplication together
Non-calculatorMethod. Division is the inverse of multiplication. Use the times table fact to find the division.
- Write the fact: 2 × 11 = 22. This is the multiplication we know.2 × 11 = 22
- Turn it round to division. Division undoes multiplication, so the total is shared into groups of the same size.22 ÷ 2 = 11
- Write the answer. The number of groups is the answer.11
Check. Check: 11 × 2 = 22, so 22 ÷ 2 = 11.
Watch out. Use the multiplication you know. The same three numbers make the division.
Method. Division is the inverse of multiplication. Use the times table fact to find the division.
- Write the fact: 6 × 3 = 18. This is the multiplication we know.6 × 3 = 18
- Turn it round to division. Division undoes multiplication, so the total is shared into groups of the same size.18 ÷ 6 = 3
- Write the answer. The number of groups is the answer.3
Check. Check: 3 × 6 = 18, so 18 ÷ 6 = 3.
Watch out. Use the multiplication you know. The same three numbers make the division.
Method. Division is the inverse of multiplication. Use the times table fact to find the division.
- Write the fact: 2 × 5 = 10. This is the multiplication we know.2 × 5 = 10
- Turn it round to division. Division undoes multiplication, so the total is shared into groups of the same size.10 ÷ 2 = 5
- Write the answer. The number of groups is the answer.5
Check. Check: 5 × 2 = 10, so 10 ÷ 2 = 5.
Watch out. Use the multiplication you know. The same three numbers make the division.
Method. Division is the inverse of multiplication. Use the times table fact to find the division.
- Write the fact: 8 × 11 = 88. This is the multiplication we know.8 × 11 = 88
- Turn it round to division. Division undoes multiplication, so the total is shared into groups of the same size.88 ÷ 8 = 11
- Write the answer. The number of groups is the answer.11
Check. Check: 11 × 8 = 88, so 88 ÷ 8 = 11.
Watch out. Use the multiplication you know. The same three numbers make the division.
Method. Division is the inverse of multiplication. Use the times table fact to find the division.
- Write the fact: 10 × 2 = 20. This is the multiplication we know.10 × 2 = 20
- Turn it round to division. Division undoes multiplication, so the total is shared into groups of the same size.20 ÷ 10 = 2
- Write the answer. The number of groups is the answer.2
Check. Check: 2 × 10 = 20, so 20 ÷ 10 = 2.
Watch out. Use the multiplication you know. The same three numbers make the division.
Method. Division is the inverse of multiplication. Use the times table fact to find the division.
- Write the fact: 10 × 12 = 120. This is the multiplication we know.10 × 12 = 120
- Turn it round to division. Division undoes multiplication, so the total is shared into groups of the same size.120 ÷ 10 = 12
- Write the answer. The number of groups is the answer.12
Check. Check: 12 × 10 = 120, so 120 ÷ 10 = 12.
Watch out. Use the multiplication you know. The same three numbers make the division.
Method. Division is the inverse of multiplication. Use the times table fact to find the division.
- Write the fact: 8 × 6 = 48. This is the multiplication we know.8 × 6 = 48
- Turn it round to division. Division undoes multiplication, so the total is shared into groups of the same size.48 ÷ 8 = 6
- Write the answer. The number of groups is the answer.6
Check. Check: 6 × 8 = 48, so 48 ÷ 8 = 6.
Watch out. Use the multiplication you know. The same three numbers make the division.
Method. Division is the inverse of multiplication. Use the times table fact to find the division.
- Write the fact: 9 × 6 = 54. This is the multiplication we know.9 × 6 = 54
- Turn it round to division. Division undoes multiplication, so the total is shared into groups of the same size.54 ÷ 9 = 6
- Write the answer. The number of groups is the answer.6
Check. Check: 6 × 9 = 54, so 54 ÷ 9 = 6.
Watch out. Use the multiplication you know. The same three numbers make the division.
Method. Division is the inverse of multiplication. Use the times table fact to find the division.
- Write the fact: 8 × 5 = 40. This is the multiplication we know.8 × 5 = 40
- Turn it round to division. Division undoes multiplication, so the total is shared into groups of the same size.40 ÷ 8 = 5
- Write the answer. The number of groups is the answer.5
Check. Check: 5 × 8 = 40, so 40 ÷ 8 = 5.
Watch out. Use the multiplication you know. The same three numbers make the division.
Method. Division is the inverse of multiplication. Use the times table fact to find the division.
- Write the fact: 2 × 6 = 12. This is the multiplication we know.2 × 6 = 12
- Turn it round to division. Division undoes multiplication, so the total is shared into groups of the same size.12 ÷ 2 = 6
- Write the answer. The number of groups is the answer.6
Check. Check: 6 × 2 = 12, so 12 ÷ 2 = 6.
Watch out. Use the multiplication you know. The same three numbers make the division.
Method. Division is the inverse of multiplication. Use the times table fact to find the division.
- Write the fact: 8 × 3 = 24. This is the multiplication we know.8 × 3 = 24
- Turn it round to division. Division undoes multiplication, so the total is shared into groups of the same size.24 ÷ 8 = 3
- Write the answer. The number of groups is the answer.3
Check. Check: 3 × 8 = 24, so 24 ÷ 8 = 3.
Watch out. Use the multiplication you know. The same three numbers make the division.
Method. Division is the inverse of multiplication. Use the times table fact to find the division.
- Write the fact: 5 × 10 = 50. This is the multiplication we know.5 × 10 = 50
- Turn it round to division. Division undoes multiplication, so the total is shared into groups of the same size.50 ÷ 5 = 10
- Write the answer. The number of groups is the answer.10
Check. Check: 10 × 5 = 50, so 50 ÷ 5 = 10.
Watch out. Use the multiplication you know. The same three numbers make the division.
Method. Division is the inverse of multiplication. Use the times table fact to find the division.
- Write the fact: 9 × 2 = 18. This is the multiplication we know.9 × 2 = 18
- Turn it round to division. Division undoes multiplication, so the total is shared into groups of the same size.18 ÷ 9 = 2
- Write the answer. The number of groups is the answer.2
Check. Check: 2 × 9 = 18, so 18 ÷ 9 = 2.
Watch out. Use the multiplication you know. The same three numbers make the division.
Method. Division is the inverse of multiplication. Use the times table fact to find the division.
- Write the fact: 3 × 11 = 33. This is the multiplication we know.3 × 11 = 33
- Turn it round to division. Division undoes multiplication, so the total is shared into groups of the same size.33 ÷ 3 = 11
- Write the answer. The number of groups is the answer.11
Check. Check: 11 × 3 = 33, so 33 ÷ 3 = 11.
Watch out. Use the multiplication you know. The same three numbers make the division.
Method. Division is the inverse of multiplication. Use the times table fact to find the division.
- Write the fact: 6 × 8 = 48. This is the multiplication we know.6 × 8 = 48
- Turn it round to division. Division undoes multiplication, so the total is shared into groups of the same size.48 ÷ 6 = 8
- Write the answer. The number of groups is the answer.8
Check. Check: 8 × 6 = 48, so 48 ÷ 6 = 8.
Watch out. Use the multiplication you know. The same three numbers make the division.
Method. Division is the inverse of multiplication. Use the times table fact to find the division.
- Write the fact: 4 × 4 = 16. This is the multiplication we know.4 × 4 = 16
- Turn it round to division. Division undoes multiplication, so the total is shared into groups of the same size.16 ÷ 4 = 4
- Write the answer. The number of groups is the answer.4
Check. Check: 4 × 4 = 16, so 16 ÷ 4 = 4.
Watch out. Use the multiplication you know. The same three numbers make the division.