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No.

A rational number is ANY number that can be represented as one integer over a second integer (which cannot be zero). There is no requirement that the top integer is less than the bottom integer (an improper fraction is still a rational number - all integers are rational numbers as they can be represented as an improper fraction with a 1 as the denominator).

Only if both rational numbers are less than 1 will the result of multiplying them together be less than both of them.

If one rational number is greater than 1 and the other less than 1, then the result of multiplying them together is greater than the number less than 1 and less than the number greater than 1.

If both rational numbers are greater than 1, then the result of multiplying them together is greater than both of them.

Q: When you multiply two rational numbers will you always get a number that is smaller than the two factors?

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All numbers between negative one and zero are negative. When you multiply a number by a negative it becomes negative. Also, all numbers between negative one and zero are decimals. When you multiply a number by a decimal it becomes smaller. Thus, when you multiply a rational number by a number between negative one and zero, it becomes smaller and negative.

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Look for factors. Start with small factors, such as 2, 3, 5, 7. Once you find a factor, divide the number by that factor to get the other factor. Continue looking for smaller factors for this smaller factor.

Answer: It will be greater than both the numbers. Answer: It may be greater, equal, or less than the numbers. Examples: 2 x 3 = 6 (greater than both factors) 0.5 x 0.4 = 0.2 (smaller than both factors)

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All numbers between negative one and zero are negative. When you multiply a number by a negative it becomes negative. Also, all numbers between negative one and zero are decimals. When you multiply a number by a decimal it becomes smaller. Thus, when you multiply a rational number by a number between negative one and zero, it becomes smaller and negative.

It is the smallest non-negative rational number. Negative numbers are rational and are smaller.

The product of two rational numbers, X and Y, is smaller than either of them if both are between 0 and 1.

There weren't any numbers given below.

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Look for factors. Start with small factors, such as 2, 3, 5, 7. Once you find a factor, divide the number by that factor to get the other factor. Continue looking for smaller factors for this smaller factor.

It's because decimals are really fractions and all numbers get smaller when you multiply them by fractions.

Generally yes, but not in all cases. The largest prime number has over 22 million digits but only two factors whereas 60 has six times as many factors.

If you mean the product, that's by definition. A composite number has smaller factors. If you multiply two positive integers, none of which is 1, together, then it follows that the product has smaller factors - namely, the numbers you multiplied together.

there are infinitely many positive rational and irrational numbers smaller than .0001. Try .00001. Or how about π/100000.

Answer: It will be greater than both the numbers. Answer: It may be greater, equal, or less than the numbers. Examples: 2 x 3 = 6 (greater than both factors) 0.5 x 0.4 = 0.2 (smaller than both factors)