My math teacher asked, and I'm soo... CONFUSED!!!?

Question

If A/B=C/D
Then [(A+B)/(A-B)]= [(C+D)/(C-D)]
We are supposed to explain why this is true... can you help? (We're supposed to be explaining to a 7th grader, make it understandable please) Thank You soooooo... much!!!

Answer 1

I don't know how much sense this will make, but try working it backwards.

(a + b)/(a - b) = (c + d)/(c - d)

(a + b)(c - d) = (c + d)(a - b)

ac + bc - ad - bd = ac + ad - bc - bd

Collecting similar terms, we get

bc - ad = ad - bc

2bc = 2ad

bc = ad

a/b = c/d, which is the other one.

If working backwards doesn't work, then you can simply repeat those steps in reverse order. Doing it that way is valid, even though the reason for the steps may not be obvious.

Hope this helps.

Answer 2

ok, let's put some numbers into it.
If A divided by B equals C divided by D so,
12/3 = 80/20 the answer is 4 in each case so we know they are equal

then :
[(12+3) / (12-3)] = [(80+20) / (80-20)] so...
15 / 9 = 100 / 60 which is....

1.666 for each

By giving you the a/b = c/d he/she is telling you the relationship (the numeric answer) between a/b is the same as is the relationship of c/d

So I guess to explain further start with the A/B and plug in some numbers like 10 (the A) divided by 2 (the B) equals 5. So you know A/B = 5 and if A/B and C/D are equal and have the same number as an answer (in this case 5) then the answer for C/D must also equal 5. And to do that you have an equation or a math problem that looks like this: C (a number) divided by D (a number) = 5

C/D = 5
now you just have to figure out a set of numbers for C and D

C / D = 5 so...if c divided by d = 5, c times something would have to equal D, which is the same as d times something would have to equal C
5 * D = C (D times 5 = C) so...pick a number
5 * 6 = C so...
5 * 6 = 30 so...
C=30 so... plug the numbers back into the equation

10/2=30/6
5=5

Does that help any? I know it can get confusing because how can a letter = a number, but remember the letters are only icons for the numbers and they can be moved around, added, subtracted, multiplied and divided according to the problem. Just take it step by step.

Answer 3

tellu gave a good answer, but here's another way to do this problem.

a/b = c/d, so a/b + 1 = c/d + 1 and so (a + b)/b = (c + d)/d.

Again, a/b = c/d, so a/b - 1 = c/d - 1 and so (a - b)/b = (c - d)/d.

Now divide these two equations.

[(a + b)/b]/[(a - b)/b] = [(c + d)/d]/[(c - d)/d].

The b's in the denominators on the left side cancel each other and the d's in the denominators on the right side also cancel each other, and finally you are left with (a + b)/(a - b) = (c + d)/(c - d).

Answer 4

if u cross multiply a/b = c/d becomes ad = bc.

then if u cross multiply (a+b)/(a-b) = (c+d) /(c-d), then it becomes ac-ad+bc-bd = ac+ad-bc-bd.

arranging terms on both sides, ac and bd gets cancelled.

so u will be left with 2ad = 2 bc, and cancelling 2 on each sides,
u get ad = bc. this is same as the first cross mulitiplication of a/b = c/d.

thats why both are same and equivalent. hope this helps sophie.

Answer 5

1/2=2/4
then 1+2/1-2=2+4/2-4
3/-1=6/-2

Answer 6

If it's an odd number, go to the back of the book. It might give you the answer.

Answer 7

i think its just part of equation for a set of problems that have to be pluged in you know what i mean. if you had like acutual problems that would be the eqution you would use

Answer 8

Ok, you can take a "backward" aproach, and just move around some stuff to demonstrate they are equal step-by-step:

(A+B)/(A-B) = (C+D)/(C-D)
(A+B)*(C-D) = (C+D)*(A-B)
AC+BC-AD-BD = AC+AD-BC-BD
AD+AD-BD+BD = AC-AC+BC+BC
2AD = 2BC
AD = BC
A/B = C/D