If you liked Multiplication by 11,
you'll enjoy seeing how to take that idea one step farther. Here's a quick way
to multiply by 111.
Multiplying a 2-digit number by 111
Add the two digits and write this digit
TWO TIMES in between the original digits of the number. However, if the sum of
the two digits is more than single digit (>9); write the units digit and add
the carried to left digit. Some examples:
23x111= 2553
41x111= 4551
If the sum of the two digits is not a single digit, remember to carry.
Example: 111 × 58 =?
1. Write
down the ones digit. 8
2. Add
the tens and ones; carry, if any. 38 (5 + 8 = 13)
3. Repeat
the previous step (and add carry) 438 (5 + 8 + 1 = 14)
4. Write
the tens digit (add carry, if any) 6438 (5 + 1 = 6)
So, 111 × 58 = 6,438
And, 57x111= 6327; since 5+7=12, you
have to carry the one twice.
Multiplying a multi-digit (more than two) number by 111
If the number you are multiplying by
111 is a three-digit number, say ABC, then the answer will have five digits
(though it may be six if there is a carry involved):
the first digit is A,
the second digit is A+B,
the third digit is A+B+C,
the fourth digit is B+C,
the fifth digit is C.
Again, you must remember to carry if
any of these sums is more than one digit.
Because
of the carries, it may be easier to do the sums and write the answer down from
right to left.
For example: 111 × 234=?
Use right-to-left “sweeps” of 1, 2, 3, 2, and 1 digit. The
units digit of the answer will always be the units digit of the given number.
So,
1. For rightmost (Unit) digit of the answer; write down 4.
2. For 2nd right (Tens) digit; 3 + 4 = 7.
3. For 3rd right (hundreds) digit of the answer; 2 + 3
+ 4 = 9.
4. For 4th right digit of the answer; 2 + 3 = 5.
5. For 5th right (in this case the leftmost) digit; 2.
So, 111 × 234=
25,974
Thus 123 x 111 = 13653;
And, 241 x 111 = 26751
And for an example where carrying is
needed, 358x111=39738
Remember that whenever the sum is a
two-digit number, the units digit is the answer portion and the tens digit is
carried and added to the left digit.
Similarly,
If
the number you are multiplying by 111 is more than 3-digit number, such as
659,845; the same procedure is to be followed, adding up to three adjacent
digits together.
659,845 X 111 =?
For rightmost (Unit) digit of the answer; write down 5.
For second-right (tens) digit; 5 + 4 = 9.
For 3rd right (hundreds) digit of the answer; 5 + 4 + 8
= 17; write 7, carry 1.
The
three digits of the answer from right to left we have found thus far are 795
Now
begin adding the digits of the given number in groups of three and continue the
process until the last two digits, 65, are reached.
4 + 8 + 9 = 21 plus carried 1 = 22; write 2, carry 2
8 + 9 + 5 = 22 + carried 2 = 24; write 4, carry 2
9 + 5 + 6 = 20 + carried 2 = 22; write 2, carry 2
The
2nd leftmost digit of the answer will be, 5+6=11 + carried 2 = 13; write 3, carry 1
The
leftmost digit of the answer will be, 6 + carried 1 = 7
So, 659,845
X 111 =73,242,795
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