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When operating(adding, subtracting, multiplying, or dividing) on whole numbers, when might we end up with decimal answers?

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2 Answers

I have to say that John's answer is not entirely true.  He stated at the end that "if any one of the original numbers you use in those operations is a decimal you will get a decimal answer."  ("Those operations" referring to addition, subtraction, multiplication, and division)  However, 1.25 * 4 = 5.  1.25 is a decimal, whereas 5 is not. 


The answer to the original question is simply that when working with whole numbers, only division can result in a decimal answer. 

The addition of two or more whole numbers can only result in a whole number.
  (the logic of this is purely intuitional: to end up with a decimal, one must at some point add the decimal portion in, but this would not be a whole number so it is impossible)

Likewise, the subtraction of one or more whole numbers can only produce an integer (not necessarily a whole number, as it could come out negative as in the case 4 - 5, but still cannot produce a decimal answer for the same intuitive reason stated under addition)

Since the addition of two or more whole numbers cannot produce a decimal, neither can the multiplication of two or more whole numbers... This is because multiplication is basically a way of representing repeated addition.  For example: 5 * 4 is, 5 + 5 + 5 + 5 = 20  OR 4 + 4 + 4 + 4 + 4 = 20.  Another way of thinking of it is that 5 * 4 is 5, four times, or 4, five times. 


Division, however, is, contrary to what most people think, not exactly an opposite to multiplication, since division is not repeated subtraction.  Rather, division produces fractions.  For example 4 divided by 5 is 4/5 (four fifths).  And 4/5 = .8, which is a decimal.

If I understand your question correctly you are asking if decimal answers occur because of the "operation" type. It is true that division can produce a decimal answer if the problem is set up that way, with a decimal point, otherwise division will produce a "remainder" usually expressed as a whole number (or fraction). If you add, subtract or multiply non-decimal numbers you get non-decimal answers. If any one of the original numbers you use in those operations is a decimal you will get a decimal answer. I hope this helps.