Subtracting Fractions with BorrowingDate: 12/17/2002 at 17:01:46 From: Hayley Hansen Subject: Fractions When you are subtracting a fraction, do you always take one away from the whole number? 16 8/9 - 7 2/5 I don't know when to take a whole number away and when not to. Date: 12/17/2002 at 22:04:02 From: Doctor Ian Subject: Re: Fractions Hi Hayley, You only take one away if you need to. It's sort of like subtracting clock times. If you want to do this, 10:45 - 8:15 ------- you can subtract the minutes okay, 10:45 - 8:15 ------- 30 so you can just go ahead and subtract the hours, too: 10:45 - 8:15 ------- 2:30 But if you have a problem with the minutes, 10:15 - 8:45 ------- then you have to 'break' one of the hours into 60 minutes: 9:75 - 8:45 ------- and now you're okay again: 9:75 - 8:45 ------- 1:30 So if you have something like 16 8/9 - 7 2/5 -------- you have to establish whether the top fraction is already large enough. Since you're going to have to use a common denominator already, you can go ahead and change to that: 16 40/45 - 7 18/45 ---------- So it looks like you're okay: 16 40/45 - 7 18/45 ---------- 9 22/45 But if it had gone the other way, 16 18/45 - 7 40/45 ---------- you'd have to 'break' one of your ones into 45/45: 15 63/45 - 7 40/45 ---------- 8 23/45 Does that make sense? Now, just to be safe, I can go ahead and 'break a one' even if I don't need to: 16 8/9 - 7 2/5 -------- 15 17/9 - 7 2/5 => --------- 15 85/45 - 7 18/45 => ---------- 8 67/45 Then you can just 'unbreak' the one to get 8 67/45 = 9 22/45 It depends on whether you'd rather think more and work less, or think less and work more. Does that make sense? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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