Is the following statement always, sometimes, or never true for numbers greater than zero: "In equivalent ratios, if the numerator of the first ratio is greater than the denominator of the first ratio, then the numerator of the second ratio is greater than the denominator of the second ratio."
I think I got it the answer is always true, but why
I don't know the answer to the question
I HAVE NO CLUE
What? I have noooo clue.
To determine if the statement is always, sometimes, or never true for numbers greater than zero, we can consider a counterexample.
Let's assume we have the equivalent ratios:
a/b = c/d
where a, b, c, and d are numbers greater than zero.
If the numerator of the first ratio (a) is greater than the denominator (b), then:
a > b
To maintain equivalence, the second ratio must also follow this pattern, where the numerator (c) is greater than the denominator (d):
c > d
For example, let's say a = 3 and b = 2. The first ratio is 3/2, and since 3 is greater than 2, it satisfies the condition. In order for the second ratio to be equivalent, the numerator (c) must also be greater than the denominator (d), such as 5/4. Therefore, in this case, the statement holds true.
If we take another example, let's say a = 2 and b = 4. The first ratio is 2/4, and since 2 is less than 4, it does not satisfy the condition. Even if we try to change the values in the second ratio, such as c = 1 and d = 3 to maintain equivalence, the statement still does not hold true.
Therefore, the statement is sometimes true for numbers greater than zero. It holds true when the numerator of the first ratio is greater than the denominator, but it does not hold true when the numerator is smaller or equal to the denominator.
look at some example
3/2= 6/4 = 60/40 = 12/8 = ..
what do you think?