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March 6th, 2014, 07:44 AM   #1
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Fractions?

Hi guys,

So I have this question that I'm trying to work out and was just wondering if someone could take a look and see how I'm doing?
"Calculate 7/8 ? 1/6 + 2/3, leaving your answer as a fraction in its
simplest form, showing all your working."

So I need to change the fraction into equivalent fractions by writing them with a common denominator. So I think 24 is the common denominator so the fractions are 7/8 = 21/24. 1/6 = 4/24 and 2/3 = 12/24. So the calculation is now
21/24 - 4/24 + 12/24
4/24 + 12/24 = 20/24
21/24 - 20/24 = 1/24
So the answer is 1/24 in its simplest form.

How does that look?
Thanks,
Robert.
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March 6th, 2014, 12:09 PM   #2
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Re: Fractions?

Quote:
Originally Posted by Rob158
2/3 = 12/24
2/3 = 16/24.

Quote:
Originally Posted by Rob158
So the calculation is now
21/24 - 4/24 + 12/24
4/24 + 12/24 = 20/24
21/24 - 20/24 = 1/24
You found 21/24 - (4/24 + 12/24) (note also that 4 + 12 = 16 and not 20), while the problem asks to find (21/24 - 4/24) + 16/24.
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March 6th, 2014, 01:56 PM   #3
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Re: Fractions?

My appologies, I have misplaced 16 with 12 in error.
So my calculation would be
21/24 - 4/24 + 12/24
4/24 + 16/24 = 20/24
21/24 - 20/24 = 1/24.

or 21/24 - (4/24 + 16/24) = 1/24.

Are you saying the calculation needs to be done (21/24 - 4/24) + 16/24?
The question does not have brackets around it, how do you know the calculation needs to be done like this?
I do not understand maths very well.

I have followed the BIDMAS rule to work it out, so have calculated the addition first. What is it I am missing?

Brackets
Indicies
Division
Multiplication
Addition
Subtraction

Thanks.
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March 6th, 2014, 02:14 PM   #4
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Re: Fractions?

BIDMAS does not mean that you do each of brackets, indices, division etc. before the next type of operation. There are four levels: (1) brackets, (2) indices, or exponentiation, (3) division and multiplication, and (4) addition and subtraction. Note that division and multiplication, as well as addition and subtraction, belong to the same level. Each level has to be done before the next one; however, within each level operations have to be done left to right. Thus, x - y + z is interpreted as (x - y) + z and not as x - (y + z). So the correct answer to the problem is 33/24, or 11/8.

Another approach, which is actually used in higher mathematics and leads to the same result, is described in Wikipedia:

"It is helpful to treat division as multiplication by the reciprocal (multiplicative inverse) and subtraction as addition of the opposite (additive inverse)... With this understanding, we can think of 1 ? 3 + 7 as the sum of 1, negative 3, and 7, and add in any order: (1 ? 3) + 7 = ?2 + 7 = 5 and in reverse order (7 ? 3) + 1 = 4 + 1 = 5. The important thing is to keep the negative sign with the 3."

For further explanation and examples concerning the order of operations, read your textbook or search the web for BIDMAS.
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March 6th, 2014, 09:20 PM   #5
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Re: Fractions?

Quote:
Originally Posted by Rob158
Are you saying the calculation needs to be done (21/24 - 4/24) + 16/24?
The question does not have brackets around it, how do you know the calculation needs to be done like this?
No reason for those brackets except perhaps clarity...remove them:
21/24 - 4/24 + 16/24

Forget about the denominator 24 for now: just do 21 - 4 + 16 = 33 : OK?

Now put the denominator back: 33/24 : OK?

Now simplify: 33/24 = 11/8 : OK?
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March 8th, 2014, 06:25 PM   #6
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Re: Fractions?

I agree with Denis. And I think you just mistaken the concept of BIDMAS. Thats all
If there's no bracket(s) and the question just ask to subtract and addition (subtract and addition is on the same level), so all you need to do is solve the question from left to right. In your case, the answer is 33/24. You also can write it in simplest form (if it can be simplest), 11/8.. If the fraction is inequality, you can write it in mixed rational number. hope it helps you even a little
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March 9th, 2014, 05:51 AM   #7
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Re: Fractions?

Many thanks, I think I see it now!
I know I am bad at maths, but that is why I have joined the forum to help me learn. At least I'm trying.
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