The technique for
dividing any number by 11 mentally is simply to reduce a complex division to a
simple subtraction. You need to follow the steps below:
Step-1: Copy the first (left) digit from the dividend as it is and you have the first answer digit. Subtract it from the next digit of dividend and you have the second answer digit. Using the same logic, subtract this second answer digit from the next adjacent digit to get the third answer digit and continue the step with the other digits.
Step-2: Combine all except the last set of digit to get partial quotient. The last digit would be the Remainder, if there is a remainder.
Step-3: If any answer digit in any place except the last digit results in negative; subtract it from 10 and subtract 1 from its left digit. If last set of digit which happens to be the remainder results in negative, add 11 to it and subtract 1 from the partial quotient to get the final quotient and final remainder.
The whole
calculation can be done mentally at a very fast speed.
156
÷ 11
=?
Step 1: Copy the first (left) digit of the dividend as it is which is 1,
and you have the first answer digit. ->1
The next one would be the next digit of dividend that
is 5 minus this answer digit 1. So, 5 minus 1 is 4. ->1,4
The next answer digit would be the next digit of
dividend which is 6 minus this answer digit 4 that is 6-4 = 2. But do not write
2 as quotient, because this would be the remainder.
Step 2: Combine all except the last set of digit to get partial quotient
that is 14. The last digit finding 2 is the Remainder.
Answer: Quotient 14, Remainder 2
25789
÷ 11
=?
Start copying the
first (left) digit of the dividend as it is which is 2, and you have the first
answer digit. ->2
The next one would
be the next digit of dividend that is 5 minus this answer digit 2. So, 5 minus
2 is 3. ->2,3
The next answer
digit would be the next digit of dividend which is 7 minus this answer digit 3
that is 7-3=4. ->2,3,4
Now, using the same
logic, the next answer digit would be 8 minus 4, which is again 4. ->2,3,4,4
Next one would be 9
minus 4 that is 5. But do not write down 5 as quotient, because this would be
the remainder.
So, the answer
would be 2344 with a remainder 5.
25784
÷ 11
=?
Step 1: 2, 5-2, 7-3, 8-4, 4-4
Step 2: Quotient: 2,3,4,4; Remainder 0
Answer: 2344 with ‘NO’ Remainder
25352
÷ 11
=?
Step 1: 2, 5-2, 3-3, 5-0, 2-5
Step 2: Partial Quotient: 2,3,0,5; Remainder:
-3
Step 3: Final Quotient: 2305-1; Final Remainder
-3+11
Answer: Quotient
2304, Remainder 8
45062
÷ 11
=?
Step 1: 4, 5-4, 0-1, 6+1, 2-7
Step 2: Partial Quotient: 4,1,-1,7; Remainder:
-5
Step 3: Final quotient: 4097-1; final
remainder: -5+11
Answer: Quotient 4096, Remainder 6
68051
÷ 11
=?
6, 8-6, 0-2, 5+2,
1-7
6,2,-2,7,-6 =
6,20-2,7,-6 = 6,1,8,7,-6
Final quotient
(6187-1) and final remainder (-6+11)
Answer: Quotient
6186, Remainder 5
28250
÷ 11
=?
Quotient: 2, 8-2,
2-6, 5-(-4), Remainder: 0-9
Q: 2,6,-4,9 =
2,6-1,10-4,9 = 2,5,6,9 and R = -9
Final quotient
2569-1 = 2568 and final remainder -9+11 = 2
Answer: Quotient
2568, Remainder 2
I found this article very interesting but found the 3rd section, on how to divide by 11, a little confusing. However after a few goes I could see what was happening.
ReplyDeleteNow that I could see the way it was working I think I have come up with a simpler way. Please let me know if you agree.
Drop the first number then subtract it from the second number as you have done. But if the result is negative subtract one from the previous number and subtract the negative number from 11. Then continue to the next number.
28250 / 11
2, 8-2
2, 6, 2-6
2, 6, -4
2, 6-1, 11-4
2, 5, 7, 5-7
2, 5, 7, -2
2, 5, 7-1, 11-2
2, 5, 6, 9, r 0-9
2, 5, 6, 9-1, r 11-9
2568r2
In the number 1953577 I had a problem when I reached the second 5. I got -1 as the negative answer which when subtracted from 11 will give 10, so in that case which number will we add to the answer?
DeleteIn the number 1953577 I had a problem when I reached the second 5. I got -1 as the negative answer which when subtracted from 11 will give 10, so in that case which number will we add to the answer?
DeleteThat's right i think, and thanks.@Micheal_Punter
DeleteI solve it like that, suppose you get 6 and (-1) as 6 -1 consecutively... Then what I do is think like 60
ReplyDelete-1
Hence i get 59
and put it there for clarification i am setting this as an example:
1 9 5 3 5 7 7 becomes
1 8 -3 6 -1 8 -1 and (80 -3 = 77, 60-1 = 59) we get
1 77 59 7(since remainder's -ve)
Ans: 177597 remanider = 11-1 = 10
What about 3,168÷11? The first digit cannot be copied as is and be 3.
ReplyDelete