Division Estimation Process

LONG DIVISION
I have seen too many students pick an answer for a division problem on a multiple choice test that does not contain the correct number of digits. There are only two possibilities for where to put the first digit of the quotient in a division problem. The placement of the first digit of the quotient depends on whether the first digit(largest part of number)of the divisor is smaller or larger that the first digit of the dividend.
12345 ÷ 823 There are three digits in the divisor 823….if you compare them to the first 3 digits in the dividend, then 123 ÷ 823 is less than 1, so the first digit of the quotient must begin over the 4th number in the dividend , in this case the 4. 1234 ÷ 823 will at least 1, so the first digit of the quotient must start above the 4, the 2nd digit above the 5, so the answer will be a two digit number plus the remainder, if there is a remainder.
Look at the following examples:
7896 ÷ 56 ...since 78 ÷56 is at least 1, then 1st digit of answer starts above the 8, and with 2 more digits left, 9 abd 6, the answer must be a 3 digit number plus a remainder if it exists.
7896 ÷ 87...since 78 ÷ 87 is less than 1 the, but 789 ÷87 is at least 1 the answer must start above the 9 and will be a two digit mumber plus a remainder if it exists.
56489 ÷ 673...since 564 ÷ 673 is less than 1, but 5648 ÷ 673 us at least 1, the answer must start above the 8 and will be a two digit answer, plus any remainder.
So…there are only two possibilities where the first digit of the answer (quotient) can go. Count the number digits in the divisor, and the 1st digit of the quotient must be over the corresponding number of digits in the dividend or over the next digit.
786 ÷ 79…one digit answer….1st digit is over the 6.
786 ÷ 56…two digit answer….1st digit is over the 8
(If there are 5 numbers in the divisor, the first digit of the answer must either be above the 5th or 6th digit of the dividend.
The actual numbers that make up the quotient can be obtained by doing an estimate….remember estimates are always done with the largest part of a number, and even though the estimate you obtain in division may not work out in that problem, the actual answer is rarely more than one number off from your esimate. The easiest way to practice division is to multiply two numbers on a calculator and then divide bothe the numbers into the product, so you can easily check your answer. An example would be 23 X 582 = 13386... now you have two division division you can work. 13389 ÷ 23 and 13389 ÷582.

An= estimation is used in every step of a division problem. As in all estimation problems, the largest part of the number is used in the estimate.


Determine how many digits are in the following division quotients.


13386 ÷23 = 1÷23 < 0 13÷23 < 0 133÷23 = a number higher than 0, so the 1st digit of the quotient starts above the 2nd 3, so their is a digit above the 2nd 3, a digit above the 8, and a digit above the 6....giving us a three digit number, so we know the quotient must be between 100 and 999 (all the three digit numbers.

75634 ÷ 34 = 7÷34 < 0 75÷34 = a number higher than 0, so th 1st digit of the quotient starts above the 5, a digit above the 6, a digit above the 3, and a digit above the 4, giving us a 4 digit number, so we know the quotient must be a four digit number. and must be between 1000 and 9999 (all the four digit numbers.





























































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