Date: 09/10/2011 at 19:16:26 From: Annie Subject: Using % (Modulus) in Python/order of operations OK, so I started learning Python for this Intro to AI course they're teaching online via Stanford this fall. And I was buzzing along breezily until we got to this: 100 - 25 * 3 % 4 I interpreted the problem as 100 - [(25 *3)%4] In other words: multiply 25 times 3, divide the result (75) by 4 and get the remainder, then subtract that remainder from 100. But both in the text and via running the actual program, the answer was given as "97." If the order of operations is the standard one (i.e., multiplication/division, left to right, followed by addition/subtraction, left to right), and if I understand modulus correctly (the remainder left over when you divide the left number by the right number), then I don't get how "97" is the right answer. So maybe I don't understand that "%" (the modulus symbol in Python) as well as I think I do? What, exactly, is modulus telling me to do? Find the remainder of 3 divided by 4? Seventy-five divided by 4? Either way, when I run the problem according to standard operation order, I get something very different than 97! Or maybe it's the order I'm getting wrong?
Date: 09/10/2011 at 20:31:38 From: Doctor Peterson Subject: Re: Using % (Modulus) in Python/order of operations Hi, Annie. Most of what you say is correct -- especially the order; but you haven't told me what answer you got, so I can't tell what went wrong. The "order of operations" (operator precedence) for any computer language is defined by that language, not necessarily by human mathematical standards; but if you look that up for Python, you'll find that it does agree. Multiplication, division, and remainder are done with the same precedence, from left to right. And if you do that, just the way you said, you should get the right answer: 100 - 25 * 3 % 4 100 - [(25 * 3) % 4] \______/ 100 - [ 75 % 4] \____________/ 100 - 3 \____________/ 97 To see that 75%4 = 3, you can either do a long division ... __18_r_3 4 ) 75 4 - 35 32 -- 3 ... or divide, multiply, and subtract ... 75 / 4 = 18.75, quotient = 18 18 * 4 = 72 75 - 72 = 3 ... or divide, take the fraction part, and multiply: 75 / 4 = 18.75, fraction part = .75 .75 * 4 = 3 The calculator accessory in Windows has a MOD button that will do this for you. To check a remainder, you can make sure that quotient * divisor + remainder = dividend 18 * 4 + 3 = 75 If this isn't enough to clarify what you did wrong, write back and show me what you actually did and what answer you got, and I can probably figure it out. My best guess is that you may have done what some people do when they write to us about remainders, and took 18.75 to mean the remainder is 75. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
Date: 09/10/2011 at 21:13:48 From: Annie Subject: Thank you (Using % (Modulus) in Python/order of operations) YES! That's exactly what I did, and got 18.75. Thank you so much! Very clear. I just needed to take it one step further. You rock!
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