123× 456 ÷ 789 ÷ 456× 789 ÷123 According to the nature of division,? ÷(? ×? )=? ÷? ÷?
We can rewrite the formula as:123× 456 ÷ (789× 456) × (789 ÷123).
According to the nature of multiplication and division, ×? ÷? =? ÷? ×? We can further simplify the formula as follows:
123÷ 123×(456÷456)×789÷789
Next, we can calculate:
123÷ 123×(456÷456)×789÷789= 1
So the result of 1 23× 456 ÷ 789 ÷ 456× 789 ÷123 is:1.
The key to understand this problem is to understand the operation rules and order of multiplication and division.
In the mixed operation of multiplication and division, generally speaking, we calculate from left to right. But sometimes in order to simplify the calculation, we can use the nature of multiplication and division to adjust the operation order.
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The first question you mentioned is about adjusting the operation order. In the mixed operation of multiplication and division, if you want to adjust the operation order, you need to follow the rules of multiplication and division. Specifically, multiplication and division satisfy the law of association, that is, no matter how you change the operation order, the result is the same. For example, a × b ÷ c ÷ d = (a× b) ÷ (c× d) = a ÷ c × b ÷ d. That's why you can adjust 123÷ 123×456 to.
Then there is the second question you mentioned, which involves how to deal with persistent division. The key here is to understand the nature of division. In mathematics, division satisfies the associative law, that is, a÷b÷c=(a÷b)÷c=a÷(b×c). This is why you can convert 456÷789÷456 into 456÷(789÷456), and then convert it into 456÷456×789 according to the nature of division.
To sum up, adjusting the operation order of multiplication and division will not change the result, but it should be noted that the adjustment of operation order must follow the nature and operation law of multiplication and division. I hope this answer will help you understand this question. If you have any other questions, please feel free to ask them.