Question

Reasoning if you multiply two decimals that are less than 1,can you predict whether the product will be less thanor greater than either of the factors? Explain

Answer 1

• if both are positive, the result will be smaller than either
• if one is negative, the result is less than the positive number and greater than the negative number.
• if both are negative, the result is greater than either

Explanation:

The magnitude of a fraction of a fraction (their product) is always smaller than the magnitudes of either fraction. So, if both decimals are positive, the result is less than either factor.

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Negative numbers are less than 1, so there can be several cases of interest when one or both numbers are negative.

Both numbers negative

The product will be positive, so will be greater than either negative factor.

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One number negative, the other number positive

The product will be negative, so will be less than the positive factor and greater than the negative factor. (Multiplying a negative number by a positive fraction moves it closer to zero on the number line, hence to a value that is greater than the negative factor.)