Maths! Simplifying ratios as fractions?

KPeh · 1 Oct 2011 at 14:11

Hi

If I have a ratio which isn't straightforward, how can I figure out how to simplify it (or conversely, what the highest common multiple is)?

Eg: 152:121.6:212.8

The highest common multiple is 30.4, so it goes down to 5:4:7. But how do you figure that out? I was once told how to do this by converting them to fractions (I think, top heavy), but I've forgotten how.

Can anyone help? Thanks!

Lydzor · 1 Oct 2011 at 14:53

I'd just multiply each by 10 to give:

1520:1216:2128

then cancel down which leaves the figure you mentioned.

KPeh · 1 Oct 2011 at 15:01

Lydzor said:
I'd just multiply each by 10 to give:

1520:1216:2128

then cancel down which leaves the figure you mentioned.

Thanks, but that takes much too long - it's for a timed numerical reasoning exam (which I'm doing tomorrow...). Sadly the person who explained how to do it quickly originally to me is off on holiday atm..!

titaniumx3 · 1 Oct 2011 at 15:03

I think you mean highest common factor, not highest common multiple.

In order to simplify 152 : 121.6 : 212.8, I would begin my multiplying everything by 10, so that you're not dealing with decimals. Which gives:

1520 : 1216 : 2128

In order simplify this, there are several methods. You can divide by any common factor to make the numbers smaller and then repeat untill there are no more common factors (except 1). For example:

1520 : 1216 : 2128 (÷2)
760 : 608 : 1064 (÷2)
.
.
.
5 : 4 : 7

You could also factorise each number into primes, then use that to find the HCF and divide the ratio by that. So,

1520 = 2*2*2*2*5*19
1216 = 2*2*2*2*2*2*19
2128 = 2*2*2*2*7*19

Multiplying the common primes will give the HCF, i.e. 2*2*2*2*19 = 304. We can now divide the ratio by the HCF to simplify it to it's lowest terms:

1520 : 1216 : 2128 (÷304)
5 : 4 : 7

There are also other methods, that can easily be found with a quick search on google.

KPeh · 1 Oct 2011 at 15:06

Thanks titanium, but that's still not what I'm looking for. That was basically what I did find on google/youtube.

But you're right - I did mean highest common factor. Actually, that's not too important, the ratio just needs to be in its simplest form (and quickly) for the purposes of the exam.

Thanks

exhashdotdot · 1 Oct 2011 at 15:20

KPeh said:
Thanks titanium, but that's still not what I'm looking for. That was basically what I did find on google/youtube.

But you're right - I did mean highest common factor. Actually, that's not too important, the ratio just needs to be in its simplest form (and quickly) for the purposes of the exam.

Thanks

Dude, Titanium's way is probably the quickest way in your head with the smallest chance for error.

Mason- · 1 Oct 2011 at 15:26

Add them all together.

486.4

486.4/121.6 = 4

That's all I can think of atm. And all I can be arsed to work out but that gives one of them straight away.