Question P4–P5–P6 Gap and difference
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In a library, books were arranged on shelves with exactly 8 books on each shelf. The librarian brought 4 more books into the library and rearranged all the books. There are now exactly 6 books on each shelf and 10 more shelves than before. How many books are there in the library now?
Answer
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Share the same things two ways. One way leaves too many, the other too few.
In this one. The 10 extra shelves need 60 books, but only 4 books are new, so the other 56 books must be the 2 books freed from each old shelf.
Objects are grouped two different ways with a leftover in one arrangement and a shortage in the other, using words like 'left over' and 'short of'.
Children combine the leftover and the shortfall in the wrong direction. The gap must then be divided by the difference in group size, not by either group size.
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