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Fractions: arithmetic and comparing
By louise on Monday, November 1, 1999 - 02:11 pm:

Is there an easy way to remeber how to add, subtract times and divide fractions cause i have my GCSE's this year had i can never remeber how to do them all and end up losing marks on my exams. AND!!! how do you do this question?

Three students took a french exam,
clair scored 2/3 of the total mark,
Ranjit scored 3/5 of the total mark,
nicola scored 5/8 of the total mark,
which student scored the highest mark?

My maths teacher has showed me but i didn't really understand what she was going on about and i dont want to ask her again as i hate her. If you do get round to showing me how to do this question, can you PLEASE tell me how to remember it easily!!!! PLEASES!

By Andrew Rogers (Adr26) on Monday, November 1, 1999 - 07:10 pm:

I don't know what works for most other people, but I always found fractions tricky at school as well.
I think the easiest way to remember what you do with fractions is to break them down into groups:

  • Adding & Subtracting
  • Multiplying
  • Special Rule for dividing


Firstly, for adding and subtracting what you need to do is make all the fractions the same. What I mean by this is if you think of (3/5) as 3 lots of (1/5) and (5/9) as 5 lots of (1/9), then to add or subtract these fractions you need to be able to say "How many (1/9)ths are there in a (1/5)th?" before you can compare them.

This bit is usually quite confusing, but fortunately there is a surefire way of finding out. What you do is you make each of (1/9) and (1/5) into another fraction with a different number at the bottom. In fact, if you make it so the same number is on the bottom then you can compare (1/5) and (1/9) like we said we needed to:

(1/5) = (1/5) * 1 = (1/5) * (9/9) = (9/45) = 9 lots of (1/45)

and

(1/9) = (1/9) * 1 = (1/9) * (5/5) = (5/45) = 5 lots of (1/45)

So (1/5) and (1/9) are really just different amounts of the same fraction, (1/45) !!! The wonderful thing is that you can do this for any fractions you like, if you just multiply the top & the bottom by the number from the other fraction. (Have a look again at the example to check you can understand what I mean).

Now we originally started with (3/5) and (5/9), which we now know are just:

3 lots of (1/5) = 3 * 9 lots of (1/45) = (27) * (1/45) = (27/45)

5 lots of (1/9) = 5 * 5 lots of (1/45) = (25) * (1/45) = (25/45)

So now we can say:

(3/5) - (5/9) = 27 lots of (1/45) take away 25 lots of (1/45) = 2 lots of (1/45) = (2/45)

And similarly we can add different fractions.


Phew !! We've done all the hard work, now for Multiplying.

This is dead easy, just take the two numbers from the top, multiply them together, and leave them on the top. Then take the numbers from the bottom of the fractions, multiply them togther, and leave them on the bottom, so:

(3/5) * (5/9) = {(3*5) / (5*9)} = (15/45) = (1/3)

(As (15/45) = (1*15)/(3*15) = (1/3)*(15/15) = (1/3)*1 = (1/3), cancelling down is just using this rule !!!)

Finally, we have division. Now the key to division by a fraction is this:

Take the fraction you are dividing by, turn it upside down, then just multiply like you would normally:

{(3/5) / (5/9)} = {(3/5) * (9/5)} = (3*9)/(5*5) = (27/25)


As for your original question, firstly take two of your fractions and make them have the same number on the bottom. Now do the same with the second of the new fractions and the third one. Now express the first fraction in terms of the number you have found for the other two. You should now have three fractions, all with the same number on the bottom, and should be able to see who has the biggest mark.

This is all quite tricky, so do write back if I've not explained anything properly,


Andrew
By p1259 on Thursday, November 4, 1999 - 08:46 pm:

Well, I'm probably just repeating what was said before, but I'm only in year nine and so I don't understand hard stuff like that! This is how I would explain it -

If 3 people have a mark, what we need to do is put them all in perspective - ie, make all three numbers out of the same number, if you see what I mean. All three marks have to be out of the same denominator (or the same bottom fraction number!)

So, the first person, Clair, got 2/3 right.
Ranjit got 3/5 right, and Nicola got 5/8 right.

If we then find a common denominator.

(I am presuming you know how to do this - using the prime numbers which make up the denominators. If you have no idea what I am going on about, either find the common denominator your own way, or send a message here and I will explain (I only know becasue my Mum is a maths teacher and she told me!))

I found the common denominator to be 120. We then put that into reality with the other numbers.

I.e - For Clair -

To get 120 we multiply 3 (the demoninator) by 40. We then do the same for the top number

2 do the same so x40
-
3 x40 to get 120

2/3
80/120

Our first answer is 80/120, so that means Clair has got 80 marks out of a possible 120 - quite good!

If you understand, then you do the same for the other two. If you don't then -

Ranjit scored 3/5

The common denominator is 120, so....

3 do the same x24
-
5 x 24 to get 72

3/5
72/120
So Ranjit scored 72 out of a possible 120

See? If not, it is probably my explaining!!!

Finally,
Nicola got 5/8 right.
To get to 120, we multiply 8 by 15, so we must do the same to the top

5/8
75/120

So, overall, Clair scored the best, because she got 80/120, while Radjit got 72/120, and Nicola got 75/120.

REMEMBER - WHATEVER YOU DO TO THE BOTTOM HALF, YOU MUST DO TO THE TOP TOO!

I hope I have got this right, but don't blame me if I haven't, it really isn't my fault!!!!

Hope this helps,

Rachel