given that a/b=c/b,decide whether it is true or not that a/b=b/d. explain your reasoning
To determine whether the statement "a/b = b/d" is true or not given that "a/b = c/b", we can manipulate the given information and compare the two statements.
Given: a/b = c/b
To compare it with "a/b = b/d", we need to convert the equation "a/b = c/b" into a form that involves both b and d.
To do this, we can cross-multiply:
a*d = b*c
Now we can compare this with the statement "a/b = b/d":
a/b = b/d
In order for both statements to be true, the cross multiplication in both equations should be equivalent.
So, let's cross-multiply the second equation:
a*d = b*b
Simplifying this equation:
a*d = b^2
Comparing this with the first equation, we can see that the cross multiplication does not match:
a*d ≠ b*c or a*d ≠ b^2
Therefore, we can conclude that the statement "a/b = b/d" is not always true given that "a/b = c/b".