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 two plus four is the same as four plus two. But, what about multiplication and division? Is three multiplication two the same as two multiplication three? Is four division two the same as two division four? 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, three multiplication two is the same as two multiplication three. 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 equation left hand side three multiplication two equals right hand side two multiplication three.

You can also check it by using the idea that multiplication is repeated addition. Remember that equation sequence three multiplication two equals three plus three equals six, and equation sequence two multiplication three equals sum with, 3 , summands two plus two plus two equals six. 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: four division two is not the same as two division four. 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.

3.3.6 Multiplication and Division Strategies

3.3.8 More Division Strategies