Help needed with maths problem (ratios)

Hi all,

Because I'm not sure how else to put it, I will be writing centimetres squared and metres squared as - cm2 and m2 respectively.

The thing is, in my maths class today we were converting ratios into whole number ratios, one example was -

1.5 : 4

which we worked out by multiplying both sides by 2 to give -

3 : 8

So far so good.

Then we were given another one which was shown as follows -

340cm2 : 1m2

I said that since there are 100cm in a metre, you would start with -

3.4m2 : 1m2

multiply both sides by 10 -

34m2 :10m2

divide both sides by 2 to simplify to -

17m2 : 5m2

Apparently I'm wrong (some agreed with me, others said I was nowhere near) but no-one could properly explain why.

Any maths wizards able to clear this up please?

Many thanks,

Kaidan

ETA: does it matter if you look at cm2 as "square centimetres" or "centimetres squared"? I think this may have caused a few issues.

Originally posted by kai22


340cm2 : 1m2

I said that since there are 100cm in a metre, you would start with -

3.4m2 : 1m2

edit on 4/3/2013 by kai22 because: error

edit on 4/3/2013 by kai22 because: (no reason given)

There might be 100cm in a meter but 1 square metre = 10 000 square centimetres

Thats the problem

Im not a maths wizard, but i dont see anything wrong here you are correct.

When you divide 17 by 5 you get the same ratio of 3.4:1

So the answer provides the same argument but just different Units, you converted cm's that were already squared into metres squared.

reply to post by davespanners


That's one thing that was mentioned, but what I keep coming back to is -

10cm (length) x 10cm (width) would equal 100cm2

Now would that be 100 centimetres squared OR 100 square centimetres? Either way, would both be written as 100cm2? Further, in either case, would writing it as 1m2 be accurate at all?

Appreciate the help by the way

Kaidan

Then we were given another one which was shown as follows -

340cm2 : 1m2

I said that since there are 100cm in a metre, you would start with -

3.4m2 : 1m2

multiply both sides by 10 -

34m2 :10m2

divide both sides by 2 to simplify to -

17m2 : 5m2

Apparently I'm wrong (some agreed with me, others said I was nowhere near) but no-one could properly explain why.

Whether you convert the cm to m then compare, or the m to cm then compare....either way, you arrive at the 17 : 5 ratio. Looks correct to me. Maybe the instructor wanted you to avoid decimals, and convert the 1m to 100cm first? Either way, you get to the same answer.

reply to post by Gazrok


What they were saying is that to get to 340cm2, you would have a square that was 20cm long and 17cm wide, giving an area of 340cm2.

Also, 1m2 would be a square that was 1m long (100cm long) and 1m wide (100cm wide) giving an area of 1m2 or 10,000cm2.

So no matter how you look at 1m2 (as 1 metre squared or 1 square metre) it remains the same.

BUT!

After a look on google, I came by this example (emphasis is mine) -

Four square cm means an area equal to four squares of one centimeter by one centimeter. Four centimeter square is a square with sides four centimeter each. Thus the area of a four centimeter square is sixteen square centimeter.

So why can't I say that 340cm2 is 340 centimetres squared, as in a box that was 340cm along each side (or 3.4m along each side) ?

This difference may not mean I'm right, but surely it could make a considerable difference to the outcome?

reply to post by kai22


This might help.
There is a difference between square meters and meters squared in the sense of the English language, in maths it should be written unambiguously though as in the example in the link

I didn't think the problem was really going into as much depth...

but technically, 1 square meter = 10,000 square centimeters.

Now, you'd be comparing 340 square centimeters to 10,000 square centimeters, which would give you a 17 : 500 ration.

Check a conversion site or something, to double check me, but I believe this is correct.

reply to post by davespanners


Yeah, I can see now that the end result would be 17 : 500, not 17 : 5

I think I was being blunt converting cm to m, 340cm is 3.4m I just couldn't quite grasp how the square affected the whole thing.



Funnily enough, I came 2nd in class today with 95.5% on our calculus test... go figure

To save face, is there anyway at all that my original calculation would be right? It's always nice to find out you weren't completely wrong

Thanks again,

Kaidan

reply to post by kai22


Nothing on your math skill, the error was more in translating the verbiage into the correct units. I goofed it first time out too, and I got straight A's in Statistics....so don't feel bad.

reply to post by Gazrok


Thanks for being my fail-buddy

Though when I had 3 people all talking over each other - as well as over myself - it can be difficult to understand what they are all getting at.

Got there in the end though. I knew ATS would be beneficial at some point

Thanks to everyone involved, especially to davespanners

Kaidan