Show that the given proportions are equivalent.
a+c / b+d = a-c / d-b
and a / b = c / d
16 years ago
16 years ago
a/b=c/d
->ad=bc
a+c / b+d = a-c / b-d
->(a+c)(b-d)=(a-c)(b+d)
->ab+cb-ad-dc=ab+ad-cb-cd
->2ad=2bc
so the given proportions are equivalent
16 years ago
whoops did it again lol.. no its a-c / b-d ...but i still don't know how to do it
16 years ago
do u understand my answer??
16 years ago
yeah i get it.. thanks some times i have brain farts and once i see it written out im like.. oh i should have known that. thanks again!!
11 months ago
To show that the given proportions are equivalent, we need to prove that one proportion can be algebraically manipulated to obtain the other proportion.
Let's start with the first proportion:
(a+c) / (b+d) = (a-c) / (d-b)
To manipulate this proportion, we can cross-multiply:
(a+c) * (d-b) = (a-c) * (b+d)
Expanding both sides:
ad - ab + cd - bc = ab + ad - cb - cd
Rearranging the terms:
ad - ab - ad + cb - bc - cd = 0
We can now combine like terms:
cb - bc - cd + ad - ab - ad = 0
Simplifying further:
cb - bc - cd - ab = 0
Now, let's work with the second proportion:
a / b = c / d
To manipulate this proportion, we can cross-multiply:
a * d = b * c
Now, let's compare the two equations we have obtained:
cb - bc - cd - ab = 0 (Equation 1)
a * d = b * c (Equation 2)
Upon comparison, we can see that Equation 1 is identical to Equation 2. Therefore, we have successfully shown that the given proportions are equivalent.