Why is the quotient bigger than the dividend when dividing by a decimal?

Answer 1

The quotient of a division tell you how many times the divisor needs to be subtracted from the dividend to get a result of zero.

eg 10 ÷ 2 = 5 tells you that 2 needs to be subtracted 5 times from 10 to get 0: (1) 10 - 2 = 8; (2) 8 - 2 = 6; (3) 6 - 2 = 4; (4) 4 - 2 = 2; (5) 2 - 2 = 0.

With a divisor of 1, it can be subtracted exactly the same number of times as the dividend itself to get zero.

With a divisor greater than 1, each subtraction removes more than 1 and so less subtractions that the dividend will be required.

With a divisor less than 1 (and greater than 0) each subtraction removes less than 1; if it is subtracted the same number of times as the dividend there will be a remainder greater than zero which will require further subtractions before zero is reached.

eg 3 ÷ 0.6: (1) 3 - 0.6 = 2.4; (2) 2.4 - 0.6 = 1.8; (3) 1.8 - 0.6 = 1.2 [still have 1.2 to go]; (4) 1.2 - 0.6 = 0.6; (5) 0.6 - 0.6 = 0 → 3 ÷ 0.6 = 5.