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Gage
New Member

USA
1 Posts

Posted - 01/02/2012 :  19:08:45  Show Profile  Reply with Quote
1/5, -3/10, 7/6, 3/4, -1/2

Use these fractions below to make equations true.

______+_______+______=-1/12. How do I solve these type equations I have ten of them to do.
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the_hill1962
Advanced Member

USA
1468 Posts

Posted - 01/04/2012 :  11:18:03  Show Profile  Reply with Quote
Do you know about needing a common denominator in order to add fractions? If not, I think there is a lesson on this site about it.
Once you know about common denominators, think about how you would get -1/12 for an answer. The common denominator would have had to be 12 (or it could have been a multiple of 12 like 24, 36, 48... because -2/24 is -1/12 or -3/36 is -1/12...)
Multiples of 12 are 12, 24, 36, 48, 60, 72, 84...
Now, looking at 1/5------it would need to be changed to the above condition. That would be 12/60 (60 is the smallest multiple of 12 that 5 can be made into).
Looking at -3/10, that would be made into -18/60
7/6 is 14/12
3/4 is 9/12
-1/2 is -6/12
So, your choices 1/5, -3/10, 7/6, 3/4, -1/2
are easier to "see" as
12/60, -18/60, 14/12, 9/12, -6/12
Even better is to convert everything to denominator 60 because many people can easily see reducing 60ths into 12ths when possible. That means the simplest way of looking at your problem would be:

12/60, -18/60, 70/60, 45/60, -30/60
Use these fractins to make
___+___+___=-5/60 true

See that this is just the same problem as:

Use 12, -18, 70, 45, -30 in ___+___+___=-5

What three of the numbers would add up to make -5 ?
Remember that a positive and negative actually 'subtract' when you add them together.

Edited by - the_hill1962 on 01/04/2012 11:21:11
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the_hill1962
Advanced Member

USA
1468 Posts

Posted - 01/04/2012 :  11:41:30  Show Profile  Reply with Quote
There is no way to take a combination of three of the numbers
12, -18, 70, 45, -30
to add to be -5. Therefore, the problem can't be done unless I have done something wrong in my previous post OR you are allowed to use more than just 3 of the numbers in the sum.
I do find that 12*4 + (-30)*2 + 70*4 + (-18)*16 + 45*1 + (-30)*1 = -5
This means that adding the following should be -1/12:
Four of the 1/5
Two of the -1/2
Four of the 7/6
Sixteen of the -3/10
One of the 3/4
One of the -1/2

You may be wondering how I figured out
12*4 + (-30)*2 + 70*4 + (-18)*16 + 45*1 + (-30)*1 = -5

If so, I just first saw that 45-30=15 so if I could find a combination that summed to -20, it would be 15+(-20)=-5.
I saw that 12+12-30=-6 and then experimented with the combination of 70 and -18. I eventually thought 140 minus several 18s would get -4.
(that is 140-18*8=-4) and thus combining that -4 with the -6 gives -10. TWO of those would make -20 (as was needed for 15+(-20)=-5.

I hope this helps.
If anyone sees a better way to do this problem, please post!

Edited by - the_hill1962 on 01/04/2012 12:05:39
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