Subtracting Decimals with BorrowingDate: 10/09/2001 at 20:18:08 From: Mario Subject: Subtraction with six numbers I just don't understand how to borrow when there are five or six numbers. Example: 536.30 - 488.354 --------- Please help. Date: 10/10/2001 at 15:21:05 From: Doctor Ian Subject: Re: Subtraction with six numbers Hi Mario, The first thing you need to know is that you can always add zeros after the decimal point without changing anything: 1.3 = 1.30 = 1.300 = 1.3000 = ... So you can add zeros to get both numbers to the same number of decimal places: 536.300 - 488.354 ---------- Okay, so now you can't subtract 4 from 0, so you have to 'borrow'. Borrowing is sort of like converting dollars to dimes, or dimes to pennies. For example, if you have 4 dollars and 2 dimes, that's the same as having 3 dollars and 12 dimes: 4 dollars + 2 dimes = 3 dollars + 12 dimes Make sure you understand why this is true. If you don't, nothing else about borrowing is going to make any sense at all. So if you have something like 35 - 18 ---- This is really the same as 2 15 - 1 8 -------- 1 7 ^ ^ | | dimes | | pennies Sometimes you have to do it more than once: Exchange Exchange one $100 one $10 for ten $10's for ten $1's _____________ _____________ / \ / \ 3 0 4 2 10 4 2 9 14 - 2 9 -> - 2 9 -> - 2 9 ------ ----------- ---------- 2 7 5 But all this is kind of a drag to do, and it's easy to make mistakes. Fortunately, there is a simpler way to do subtraction - by doing addition instead! Think about what it _means_ to subtract 18 from 35. It means there is some number that you can add to 18 to get 35. You can try to do that the standard way (lining up numbers and borrowing). But you can also try to do it by building up the missing amount. For example, adding 2 to 18 gets you to 20: 18 + 2 = 20 Adding 10 to 20 gets you to 30: 18 + 2 + 10 = 30 Adding 5 more gets you to 35: 18 + 2 + 10 + 5 = 35 \________/ This must be equal to 35 - 18 35 - 18 = 2 + 10 + 5 = 17 Let's try the second example: 304 - 29 add 1 to get to 30 ---- add 70 to get to 100 add 200 to get to 300 add 4 to get to 304 --- 275 <-- Add the differences to get the total difference. You can even do it with your problem: 536.300 - 488.354 add .006 to get to 488.360 ---------- add .04 to get to 488.40 add .6 to get to 489 add 1 to get to 490 add 10 to get to 500 add 36.3 to get to 536.3 ------- 47.946 <--- This is how much you have to add to 488.354 to get to 536.300 There are teachers who would say that this is like counting on your fingers to solve a problem. I say: Apart from the fact that it's slow, there is nothing wrong with conting on your fingers! I would rather come up with a 'dumb' solution that I _know_ is right than follow a bunch of instructions that I don't understand to come up with an answer that I _hope_ is correct. At some point, when you're familiar enough with the 'dumb' method, you'll actually begin to see why the 'standard' method makes sense, at which point things like borrowing will seem perfectly obvious, rather than mysterious. Does this help? Write back if you'd like to talk about this some more, or if you have any other questions. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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