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For example, the product of 2, 5 and 7 is. While the product obtained by multiplying specific numbers together is always the same, products are not unique. The product of 6 and 4 is always 24, but so is the product of 2 and 12, or 8 and 3. No matter which numbers you multiply to obtain a product, the multiplication operation has four properties that distinguish it from other basic arithmetic operations, Addition, subtraction and division share some of these properties, but each has a unique combination.
Commutation means that the terms of an operation can be switched around, and the sequence of the numbers makes no difference to the answer. When you obtain a product by multiplication, the order in which you multiply the numbers does not matter. The same is true of addition. Subtraction and division don't have the property of commutation.
If you change the order of the numbers, you'll get a different answer. For example,. Distribution in math means that multiplying a sum by a multiplier gives the same answer as multiplying the individual numbers of the sum by the multiplier and then adding. Adding before multiplying gives the same answer as distributing the multiplier over the numbers to be added and then multiplying before adding. The associative property means that if you are performing an arithmetic operation on more than two numbers, you can associate or put brackets around two of the numbers without affecting the answer.
Products and sums have the associative property while differences and quotients do not. For example, if an arithmetical operation is performed on the numbers 12, 4 and 2, the sum can be calculated as. If you perform an arithmetic operation on a number and an operational identity, the number remains unchanged. All four basic arithmetic operations have identities, but they are not the same. So 12 is the product of 3 and 4, 20 is the product of 4 and 5 and so on.
Children need to become familiar with this concept in Key Stage 2 as questions such as the following often come up in mental maths test and written tests: What is the product of 10 and 3? If children are not aware of the definition of this word, it is very easy for them to think the above question requires addition of 10 and 3 13 instead of multiplication of 10 and 3 Multiplication vocabulary in KS2 In Years 3, 4, 5 and 6 children are expected to be familiar with a range of mathematical vocabulary.
Vocabulary related to multiplication includes: product times multiplied 'lots' of often represented visually as arrays. Children may be given puzzles or investigations which include vocabulary that they need to be confident with, for example: Which two even numbers below twenty give a product of ?
For this, children need to be aware of the meaning of the words 'even' and 'product'. Their next task is to think about how to work out the answer. A good way to do this would be to list all the even numbers below twenty and then practise multiplying different pairs together.
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