Tell whether the following statement is always,sometimes, or never true for numbers greater than 0. Explain.
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.
always
if a/b = c/d
and a/b > 1
then c/d > 1
Bruh what???
The statement is sometimes true for numbers greater than 0.
To understand why, let's first define what equivalent ratios are. Equivalent ratios are two or more ratios that have the same value when simplified. For example, 1:2 and 2:4 are equivalent ratios because both simplify to 1:2.
Now, when the numerator of the first ratio is greater than the denominator, it means that the value of the first ratio is greater than 1. For example, if we have a ratio of 3:2, the value of this ratio is 3/2, which is greater than 1.
When we have equivalent ratios, it means that the two ratios represent the same relationship between quantities, just in different terms. So if the value of the first ratio is greater than 1, it doesn't necessarily mean that the value of the second ratio will also be greater than 1. It all depends on the specific numbers used in the ratios.
To illustrate this, consider the example of 3:2 as the first ratio. If we want an equivalent ratio, we can multiply both the numerator and denominator by the same non-zero number. Let's say we multiply by 2: 3(2):2(2) = 6:4. In this case, the numerator of the second ratio is greater than the denominator.
However, if we chose a different set of numbers, such as 5:2 as the first ratio, multiplying by the same number for equivalence would give us 5(2):2(2) = 10:4. In this case, the numerator of the second ratio is still greater than the denominator.
Therefore, we can see that the statement is sometimes true because the relationship between the numerator and denominator can vary depending on the specific numbers chosen for the ratios.