Is an estimate for the quotient of a division problem involving decimals
always, sometimes, or never less than the actual quotient of the numbers? explain your reasoning.

Sometimes.

Explanation:

If two decimals are being divided by each other, that may result in either a larger number or a lesser number than the original dividends.

Say you're dividing two weird decimals like . Going through with this division gives you (I did calculate it) 175.177892211 ≈ 175. The estimation is around .18 less than the quotient.

But, if you divide two decimals that are like this: , in which the quotient is 0.15357356528 ≈ 0.2. This time, because the number next to the 1 is ≥5, it rounds up to a larger number. So, in this example, the estimation is larger than the actual quotient.

If the quotient's first number is followed by a number x≥5, the estimation will be larger than the actual quotient. If that number is x≤4, the estimation will be lower than the actual quotient. So, it depends (aka: your answer is sometimes).