8.2 Communicative Law
What is the sum if you add the following two numbers? Use your calculator if you are unsure.
A) 3 + 7 = ?
B) 7 + 3 = ?
Hopefully you have figured out that the answer becomes the same, 10.
We can therefore write: 3 + 7
= 7 + 3 |
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Addition
Because if works no matter which number you choose, we can write a rule: |
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Multiplication
We can try to see what applies when multiplying. What does the product become if you multiply:
A) 3 · 7 = ?
B) 7 · 3 = ?
Hopefully, you noted that you received the same product, 21.
We can therefore write: 3 · 7 = 7 · 3
Even this expression should apply for all numbers. We can therefore write it with variables instead: |
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If you haven’t done calculations with variables earlier, you might think that it looks odd to calculate with letters. You can learn more about this in the section Algebra. |
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Have you ever thought that it might be easier sometimes to multiply two factors if you change their place?
Which of the following calculations is the easiest?
7 · 8 =
56 or 8 · 7 = 56?
It is different depending on how you think. If you are practicing your multiplication tables, you can cross out have the table because the communicative law applies. |
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Practice and check that you know your multiplication tables – you will have greater use of this. |
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Here, you have learned that the communicative law applies concerning addition and multiplication. Does this work even with subtraction and division? We will show you with an example:
Subtraction
A. 5 - 2 = 3
B. 2 - 5 is not 3, and it cannot be expressed with natural numbers.
Division
A. 36 ÷ 9 = 4
B.
9 ÷ 36 is not 4 and it cannot be expressed with natural numbers. |
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