Borrowing in Subtraction in Various ContextsDate: 10/25/2006 at 23:48:36 From: Evelyn Subject: 12 5/11 - 2 6/11 How can you subtract 12 5/11 - 2 6/11? You can't take 6 apples from 5! Date: 10/26/2006 at 10:09:57 From: Doctor Ian Subject: Re: 12 5/11 - 2 6/11 Hi Evelyn, You're right, but you CAN take 6 apples from 16. What do I mean by that? Well, note that 12 5/11 = 12 + 5/11 This is what we MEAN by a mixed number = 11 + 1 + 5/11 Because 12 = 11 + 1 = 11 + 11/11 + 5/11 Because 1 = 11/11 = 11 + 16/11 Add the fractions Were you able to follow that? If so, note that your subtraction can be written this way: 11 16/11 - 2 6/11 ---------- Can you do it now? Note that this is EXACTLY the same thing we do with a "normal" subtraction, like 43 - 17 ---- where we "borrow" or "regroup", trading one group of 10 for 10 "groups" of 1, so we can complete the subtraction in each column: 1 3 3 40 + 3 is the same as 30 + 13 - 1 7 ------ 2 6 |____ 13 - 7 = 6 It's just the same idea, appearing in a different situation. You can use the same idea again when dealing with times, e.g., 4:22 3:82 4 hours + 22 minutes is the - 1:40 -> - 1:40 same as 3 hours + 82 minutes. ------ ------ 2:42 or other units, 4 gallons, 2 quarts 3 gallons, 6 quarts - 1 gallon, 3 quarts -> - 1 gallon, 3 quarts --------------------- --------------------- 2 gallons, 3 quarts So this single idea turns out to be pretty useful! The trick is remembering that it IS the same idea, and not a bunch of unrelated techniques. Does that make sense? Let me know if you need more help. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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