Math CentralQuandaries & Queries


Question from Nathalie:

I'm in 4th grade and two weeks ago my class learned how to use compatible numbers.
I was REALLY confused but I didn't want to say I didn't understand because I just wanted to go home.
Tomorrow we have the Topic 7 Test and I'm stuck on a problem that requires using compatible numbers.
My mom apparently hasn't heard of compatible numbers and she can't really help me too much.
Here's the problem : The local library places new books in a section with 31 shelves. Each shelf
fits 18 books. Use compatible numbers to estimate the number of books that the library can fit on
the shelves.

Hi Nathalie,

"Compatible numbers" are used to estimate a calculation. If there are 31 shelves and each shelf holds 18 books then there are $31 \times 18$ books. Since this is a multiplication problem I want to increase one of the numbers slightly, decrease the other number slightly to arrive at two numbers that allow me to do the arithmetic in my head. One way to do this is to decrease 31 to 30 and increase 18 to 20 since I can multiply 30 and 20 without having to write it down. 3 times 2 is 6 so 30 times 20 is 600 and thus $31 \times 18$ is approximately $30 \times 20 = 600.$

The one thing to remember is that if you are using compatible numbers to approximation a MULTIPLICATION and you increase on of the numbers you should decrease the other. If you are using compatible numbers to estimate a DIVISION and you increase one of the numbers you should increase the other and if you decrease on of the numbers you should also decrease the other.

Good luck on the test,

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