3.3.7 Commutative Property
Remember we said in Unit 2 that when you add two numbers together, the order does not matter—the same as saying that addition is commutative; so is the same as . But, what about multiplication and division? Is the same as ? Is the same as ? What do you think and how can you convince yourself that your answers are right? When you have given this some thought see below!
When you multiply two numbers together, the order does not matter. So, is the same as . Look at the diagram above, which shows on the left three rows of two dots (3 x 2). Turn this around so that it shows two rows of three dots (2 x 3). The number of dots in both arrangements is the same, 6, and hence you can see that .
You can also check it by using the idea that multiplication is repeated addition. Remember that , and . This means you can carry out the calculation in whichever order you find easier. Multiplication, like addition, is therefore commutative.
However, the order you carry out division does matter: is not the same as . For example, if we divide $4 between two people, each person gets $2. If instead we need to divide $2 among 4 people, each person only gets $0.50. So division is not commutative.