If you multiply a non zero whole number by a decimal less than one would the product be less than or greater than the whole number?

Answer 1

It depends on the signs of the two numbers.

The answer is tricky when at least one number is negative because you have to remember that "less than" means "farther to the left on the number line" and NOT "greater in magnitude". E.g. -20 is less than -4 because -20 is farther to the left even though its magnitude (absolute value) is greater.

There are four possible cases:

1. Whole number and decimal are both positive: The product is less than the whole number. The decimal reduces the magnitude of the product, so the product is to the left of the whole number on the number line. E.g. 0.5 * 10 = 5, which is less than 10.
2. Whole number positive, decimal negative. The product less than the whole number. A negative times a positive is ALWAYS negative, so regardless of its magnitude the product is to the left of the positive whole number on the number line. E.g. 15 * (-0.2) = -3 and -3 < 15
3. Whole number negative, decimal negative. The product is greater than the whole number. The product is negative but like in Case 1, the magnitude of the product is smaller, so the product is to the right of the whole number on the number line. E.g. (-8) * 0.3 = -2.4 and -8 < -2.4
4. Whole number negative, decimal negative. The product is greater than the whole number. A negative times a negative is positive, and ANY positive number is always greater than any negative number regardless of magnitude. E.g. (-0.25) * (-12) = +3 and -12 < +3