Multiplication can be done in either order
2 x 5 and 5 x 2 both make 10.
2 groups of 5 make 10.
5 groups of 2 also make 10.
The groups are arranged differently, but the total stays the same.
Year 2
Show that multiplication of two numbers can be done in any order and division of one number by another cannot
See that multiplication can be swapped without changing the total, but division changes when the order changes.
Lesson overview
Number - multiplication and division
Multiplication is commutative. This means we can swap the two numbers and the total stays the same. Division is different. The number we start with matters, so swapping the numbers does not keep the same answer. Looking at equal groups and paired number sentences helps us notice this clearly.
Division changes when the order changes
10 ÷ 2 is not the same as 2 ÷ 10.
Division depends on the starting number, so changing the order changes the answer.
Another multiplication pair
3 x 10 and 10 x 3 both make 30.
Swapping the factors changes the order, but not the product.
Worked example
Compare 2 x 4 with 4 x 2, then compare 8 ÷ 2 with 2 ÷ 8.
2 groups of 4 make 8.
4 groups of 2 also make 8.
- Read the first multiplication sentence: 2 x 4 = 8.
- Swap the numbers: 4 x 2 still equals 8.
- Now look at division: 8 ÷ 2 = 4.
- Swap the numbers: 2 ÷ 8 does not give the same answer.
- So multiplication can be done in any order, but division cannot.
Try it
Look at the pair of number sentences, then choose the answer that fits.
Question 1
Question 2
Question 3
Question 4
Question 5
Common mistakes
These are the slips to watch for when comparing the two operations.
- Thinking division works like multiplication when the numbers are swapped.
- Looking only at the numbers and not at which number comes first.
- Assuming every operation keeps the same answer when the order changes.
Related topics
These ideas support checking and comparing multiplication and division facts.
- Recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers.
- Calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication, division and equals signs.
- Solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts.