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### Subtracting Fractions with Borrowing

```Date: 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

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/
```
Associated Topics:
Elementary Fractions
Elementary Subtraction

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