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Q: Is the product of two numbers always greater than either number?

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Not always.

No.

No. If one of the numbers is 0 it is less; if one of the numbers is 1 it is the same as one of them; otherwise the product is greater than either

The product of any numbers greater one is greater than either.

The product of two digit numbers is always greater than either.

Yes, if both the numbers have the same sign. But not if only one of them is negative.

Not true if either of the numbers is negative.

One possible conjecture: The product is always an odd number. Another possible conjecture: The product is always greater than either of them. Another possible conjecture: Both odd numbers are always factors of the product. Another possible conjecture: The product is never a multiple of ' 2 '. Another possible conjecture: The product is always a real, rational number. Another possible conjecture: The product is always an integer.

The sum of two numbers will almost always be greater than either number. The only exception would be when dealing with two negative numbers.

Not if either of the numbers is between 0 and 1. 5*0.5 = 2.5 is not greater than 5 0.3*0.4 = 0.12 is smaller than both multiplicands.

Not always. Here are counterexamples: Cases involving 1: 1 x 1 = 1 1 x 3 = 3 Cases involving positive numbers less than 1: 0.5 x 10 = 5 0.5 x 0.5 = 0.25 Note that here we have positive numbers that are less than or equal to 1. When either number is less than 1, the product will not be greater than both numbers. Also, if either number is equal to 1, the product will be equal to the larger of the original numbers. A modified statement is the product P of two positive real numbers x and y such that x, y > 1, is greater than both x and y.

A positive number is any number greater than zero. 1 is a positive number, so is 2, 2.5, 3.14159, 11, 11.25 etc 0.5 is a positive number. The product of two positive numbers is the result of multiplying them together. * 2 x 3 = 6 (the product). In this case the product is greater than either number. But... * 0.5 x 0.25 is 0.125. ~In this case the product is actually smaller than either of the two numbers! * Or 0.5 x 10 = 5 . Here the product is greater than 0.5 but smaller than 10. So the answer is ...sometimes!

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