Year 5 maths help (for me! - I have officially been left behind)

[MrsFogi]

My C in Maths GCSE is not quite cutting the mustard. Can someone tell me what the answer to this is (and better still explain in a KS2 way )?
"Compare these fractions by finding the lowest common denominator for each set: 2/3, 1/6, 2/12"
The teacher's worked example arrives at an answer of 8/12, 2/12, 2/12
I would have arrived at an answer of 2/6, 1/6, 1/6

2/6 = 1/3
The question has 2/3.
I think

2/3 = 8/12 but doesn't = 2/6
1/6 = 2/12
2/12 = 2/12

Actually my answer would be

4/6, 1/6, 1/6

My answer would be 4/6, 1/6, 1/6. I'm not sure why the teacher thinks 12 is the lowest common denominator for those fractions. 2/12=1/6

The teacher is wrong. 8/12, 2/12, 2/12 can be further reduced to 4/6, 1/6, 1/6.

Thanks all - sorry my typo re 2/6 (I promise I'm not that thick )! So by the sounds of it I can tell dd to go ahead and follow the route of 6 being the lowest denominator (I have not missed some new-fangled approach ).

I wouldn't have thought you were thick even if it wasn't a typo-it is really common to forget to multiply both the denominator and numerator of fractions when you're changing the denominator. I correct that mistake all the time. It'll be interesting to hear what the teacher's reasoning is that 12 is the lowest common denominator for that set.

www.khanacademy.org/search?search_again=1&page_search_query=lowest+common+denominator

Sorry guys but I need your help again - I think this maths teacher is trying to kill me. DD is stuck on this (and a page of similar fractions) and I'd love to have a clue how to explain how to tackle this but I am completely stumped. Can anyone tell me the answer (and working) to this so that I can then see if I can work out a few more before trying to explain it to DD tomorrow:
Lowest common denominator of 2/7, 1/3, 3/4, 4/9
I am loathe to tell DD I don't have a clue at this stage (I'm trying to continue some pretence of loving/being great at maths but this role modelling is getting more and more difficult ).

Haha. Wait until you have a year7! I can't even pretend to know what the heck is going on!

That's a tricky one. Because 7 is a prime you're looking for multiples of 7 that are also multiples of 4 and 9 (you don't need to worry about 3 because anything that's a multiple of 9 will also be a multiple of 3).

Are you sure there's not a typo? It seems very hard for year 5.

I struggled to help my yr 3 do hers yesterday I feel like I must have known it at some point but it has fallen out of my head, we were doing 3D shapes - how exactly in real life has it helped to know how many verticals and how many edges a triangular prism has?!

Either that's a typo or it would be easier by finding a common numerator instead. So:
2/7 = 12/42
1/3 = 12/36
3/4 = 12/16
4/9 = 12/27

If the numerators are the same then you can compare by looking at the denominator. Largest denominator = smallest fraction. Smallest denominator = largest fraction.

Sorry, just realised I forgot to put my answer which is 252! I might have missed a cancelling factor somewhere but I think the fractions work out as 72/252, 84/252,189/252 and 112/252. I'm sure there's a typo!

That's what I made it purple

If in doubt, multiply everything by everything that isn't a factor alreay.
So you want 974.
So 2/7 is multiplied top and bottom by 94
1/3 is by 374 (the three because 33 is nine, and already in there)
3/4 is top and bottom by 9*7
4/9 is x by 7 and 4

The denominators should all be the same, if you've done it right! Then cancel down if poss, but in this case not poss.

If you missed the fact that 3 was a factor of 9, everything would be bigger, and you might spot the multiple.

Are Y5 expected to do this on paper, or with calculator?

OK. Prime factorisation will work here:

1. Look at each denominator (bottom number) and see which prime numbers are multiplied to reach that number. Prime numbers are numbers which can only be divided by 1 and themselves. So 1,2,3,5,7,11,13,17, etc.

For 2/7: 1× 7
For 1/3: 1×3
For 3/4: 1×2×2
For 4/9: 1×3×3

2.Count how many times each prime number appears in each denominator:
1 appears once in each of the denominators.
2 appears twice in 4
3 appears once in 3 and twice in 9.

1. Write down the highest number of times that each of these factors appears in just one denominator:

1: 1appears once in every denominator. 2: 2 appears twice in 4 (2×2) 3: 3 appears twice in 9 (3×3) 7: 7 appears once in 7.

4.write each of these numbers, the highest number of times it appears (so you ignore the 3 in 3 because 9 has two threes):
1, 2, 2, 3, 3, 7

1. Multiply those numbers: 1×2×2×3×3x7=252.

This is the lowest common denominator.

1. Divide 252 by the bottom number, then multiply by the top numbers to work out the fractions:

252/7=36. 36x2=72 = 72/252 252/3=84. 84×1=84 = 84/252 252/4=63. 63x3=189 = 189/252 252/9=28. 28x4=112 = 112/252.

Y5 would do this without a calculator

I also think there might be a typo.

Here's how you do it:

Step 1) List all the multiples of 7, 3, 4 and 9 (the denominators)
Step 2) Find a multiple that is each of the times tables of those numbers
Step 3) Convert all of the original fractions to new fractions that have that denominator, (by multiplying the numerator of each by the same number as you did the denominator)
Step 3) List these fractions in order
Step 4) List the original fractions in order

In your OP, I think the teacher used 12 as the denominator, so that the pupils would not have to do any division to convert the original fractions. And 1/6 = 2/12.

I think your DD was probably meant to approach it by noticing that 1/3=3/9, meaning that she had 7ths, 9ths and quarters in the problem. 7x9x4=252.

Then using the fact, as greensand said, that 2/7 would only be multiplied by 9 and 4: 2x9x4=72

And so on.

It is a huge faff though. It would be much simple if you used numbers that had an easier lcm. And you'd demonstrate the same skills.

I suspect the teacher used 12 because it will always work to use the largest denominator if all the other denominators are factors of it. In order to use one of the smaller denominators you also have to take into account whether the numerator will cancel down too so it won't work in every situation.

For the purposes of comparing and ordering it doesn't really matter whether you use 6 or 12 so neither is really wrong.

Thanks for all the answers I will work through them (and may be back in a couple of hours if I have not "got" it (or if I have gone instance ). I think I need to get myself the KS2 maths course and start working through it to have the same level of maths as a 9 year old has these days.

OP

The thing is, your DD should know how to approach it. This should be practice. If she can't remember then make a note of it in her HW book. It's not your job to 'teach' her, as the teacher will have taught the technique in class