Fractions Question

[nomiddlename]

Okay - so wasn't sure where to post this but I'm currently doing a course at home and have to go over level 2 maths.

I cannot fathom for the life of me a fractions question.
I'd been doing really well until this one and can't work out how they've cancelled out some of the figures.

so it's:

9/15 x 10/24. They reckon you can cancel it down to 3/5 x 5/12 but why?

Please don't tell me I'm thick.....I know that maths is my weakest subject!!
TIA

Oh whoops - just realised why - see, I am thick!

You can divide the top and bottom by the same number, and the fraction will be the same. So 9/15, divide top and bottom both by 3, you get 3/5.

Okay - how about this one....

they say 3/7 x 21 (21/1) cancels down to:

3/1 x 3/1 = 9/1 = 9

I cannot see how they cancel out the 7 to get 1 or the 21 to get 3 ???

oh - other than dividing by 7 but it seems random. You see, the facts don't stay in my head and then, once I've stared at it, I suddenly see it. I think I'm number dyslexic. Going now because I think I'm making myself look even more thick than I already am!

I cant see how they broke it down either but 3/7x21/1=63/7=9,so I get the answer but not the break down,perhaps somebody will come along and enlighten us.

Phew - not just me then. Perhaps it's s typo?

I think that the point is that you need to recognise that:

3/7 x 21/1 is the same as 3/1 x 21/7

Once you get to that bit of enlightenment, then it is easier to make the leap to dividing 21/7 by 7 on top and bottom, to give

3/1 x 3/1 = 9

Does that help?

Not a typo. If you have fractions separated by a multiplication sign you can cancel any one number from the top with any one number from the bottom by dividing by the same number.

They have divided the 7 on bottom of first fraction to get one and divided 21 on top of second fraction to give the three. Does that help?

You do divide AND multiply by 7; 3/7 x 21/1 = 3/(7/7) x (21/7)/3 =3/1 x3/1=9 does this make sense

Aha - mrshocuspocus hit the nail on the head I think.
Well, you all did but that's what I wasn't getting. I did think it was a bit weird being able to divide by one number from one side and another from the other iyswim?

Thank you

You're welcome - I'm a secondary maths teacher so any other questions then just shout!