Question

The ratios a:b and b:c are equivalent to one another

Select all the statements that must be true

1. a=c

2. b/a = c/b

3. b-a = c-b

4. a
5. if a=b, then b=c

Answer 1

2. b/a = c/b

5. if a=b, then b=c

Answer 2

2 and 5

Explanation:

We have rations:

a:b=b:c, we can write that also like

a/b=b/c. Now we know that:

axc=bxb i.e

c=bxb/a, i.e. c/b=b/a then statmen 2 is TRUE.

Statmen 1 is not tru, because if a=c than we have a:b=b:a an it is true only if b=a, but we don’t have that information.

Statmen 3: suppose that

a:b=b:c=k, where k is some number. From that we get:

a=kb and c=b/k.

So b-a=b-kb=(1-k)b

And c-b=b/k-b=(1/k-1)b, these two statmen are equal only if k=1, i,e a=b=c but we dont have that information, so 3 is not true.

4. I think it is missing something??

5. If a=b than a:b=b:b=1, so it is b:c=1, i.e b=c, statement 5 is TRUE