Can someone help me understand these fraction concepts?

Question

we are doing a little fraction work and I'm a little confused on a few problems. / treat these as a _____ on a fraction

1. 3/4(12a^2c) how would you do this one. How do you distribute the fraction.

2. a-4/5 divided by 10/3a-12. I think I've got the right answer 3a^2-24a+48/50 but I am unsure how to reduce it. is 3a^2-25a+24/25 right?

3.ab/(a-b)^2 divided by 1/a-b, i think i have a close answer it would be ab/a-b right so then that would become b/-b right? and that becomes -1/b? i'm not sure.

4.This last one have no idea on m^2-6m+5/m-1 divided by m-5/m-1. if you divide the denominators it would equal 1 right but how would you divide the numerators also if you use the reciprocal i don't know how to multiply the numerator then any help would be appreciated.

Answer 1

1. You really only need the coefficients - or the numbers in front of the variables. So they are 12 and 1. So just multiply 3/4 by 12 so thats 9 and 3/4 by 1 so thats 3/4. Then you put these new coefficients in and the answer should be (9a^2)(3/4c)

3. You're answer is wrong. First of all (working backwards) you can't ab / a-b does not simplify!!! One is multiplication and one is addition/subtraction. It's a simple but crucial mistake. And to divide two fractions, you DON'T multiply them - though it may seem that way. You must flip the second fraction ( 1/a-b will become a-b/1) and, THEN, multiply. So that would be ab(a-b)/a-b^2. Only then can you simplify...

= ab(a-b)/(a-b)(a-b)

= ab/(a-b) <--- final answer

Answer 2

think of it like this...you have one sub thats the whole, cut the sub in half one half is a 1/2 cut one of the half's in half thats a quater