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How does the concept of fraction in the primary school mathematics textbook published by People's Education Press present two specific meanings of fraction?
You can give some examples to illustrate:

Such as 3/5 meters.

It means that 1 m is regarded as the unit 1, and three of them are divided into five parts, that is, three fifths of 1 m;

That is, divide the three meters into five parts on average, and take one of them, which is one fifth of the three meters.

These are two different meanings of a fraction.