Division QuotientDate: 11/06/2002 at 22:19:12 From: Lillian Subject: Division quotient In a division sentence, when will the quotient be odd? When will it be even? I've confirmed that if both numbers are even, the answer will be even, and if both numbers are odd, the answer will be odd. But when one number is even and the other odd, the answer could be either. Help. Date: 11/07/2002 at 09:32:52 From: Doctor Peterson Subject: Re: Division quotient Hi, Lillian. I assume you are talking about a division sentence in which all the numbers are whole, like 6/3 = 2. This will be equivalent to a multiplication, like 6 = 3*2. You can make a table for multiplication: * | even | odd examples ----+------+----- even| even | even 4*6=24 4*5=20 odd | even | odd 5*4=20 3*5=15 When we turn this inside out to make the corresponding table for division, we find that some spaces are empty: some divisions will not give a whole number, so the quotient will be neither odd nor even. Moreover, there are some cases where the quotient can be either even or odd. This is perfectly valid. Here is my result: / | even | odd examples ----+------+----- even| ? | even 24/4=6, 20/4=5 20/5=4 odd | - | odd (5/2=2.5) 15/3=5 Note that you are wrong in saying that even divided by even is even, and also that the result is indeterminate if the numbers have different parity. Can you explain how you determined this? So what is the answer to the question "when will the quotient be odd"? It CAN be odd when both numbers are even or both are odd; in the case where both are even, you need to look for something beyond the evenness of the numbers. I suggest thinking about the prime factorizations of the numbers. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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