If a and b are any real numbers such that 0<a<1<b, which of the following must be true ov the value ab??

Again, what are your alternatives?

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To determine which of the given options must be true for the value of ab, we need to understand the properties of multiplying numbers between 0 and 1. Here's how you can work through it:

1. Recall that when you multiply two numbers with the same sign, the result is always positive.
2. In this case, both a and b are greater than 0, so ab will always be positive.
3. Since a and b are both between 0 and 1, multiplying them will yield a smaller number than either a or b individually.
- For example, if a = 0.5 and b = 0.8, then ab = 0.5 * 0.8 = 0.4, which is smaller than both a and b.
- This holds true for any real numbers a and b such that 0 < a < 1 < b.
4. Therefore, the option that must be true is that ab < a and ab < b.

In summary, when a and b are any real numbers such that 0 < a < 1 < b, the value of ab will always be positive and smaller than both a and b.