Analysis: The school has purchased a new batch of books and distributed them to the fourth, fifth and sixth grades according to 4: 5: 6. Then,

The fifth grade accounts for 5 ÷ (4+5+6) = 5/ 15.

Grade four accounts for 4 ÷ (4+5+6) = 4/ 15.

The sixth grade accounts for 6 ÷ (4+5+6) = 6/ 15.

Then: level 4 is less than level 6/15-4/15 = 2/15.

"It is known that grade four gets 40 books less than grade six", so the total number of books is: 40÷2/ 15=300 (books).

It is known above that the fifth grade accounts for 5 ÷ (4+5+6) = 5/ 15,

Then the book obtained in the fifth grade: 300×5/ 15= 100 (book).

After analysis, the formula is:

5÷(4+5+6)=5/ 15 4÷(4+5+6)=4/ 15 6÷(4+5+6)=6/ 15

40 (6/15-4/15) = 300 (Ben) 300×5/ 15= 100 (Ben)

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