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Multiplying
By 111:
A. Multiplying by 111 is very similar to multiplying by 11 (see Multiplying by 11). When multiplying by 111 you add 3 digits together instead of 2. See below:
1. Write down the last digit.
2. Add the last 2 digits together. Write the answer, carry if necessary.
3. Add the last 3 digits together. Write the answer, carry if necessary.
4. Moving 1 digit at a time, move to the left and add 3 digits at a time until only the first 2 digits are left. Write the answers and carry.
5. Add the first 2 digits. Write the answer, carry if necessary.
6. Write down the first digit, carry if necessary.
B. Look at Ex [1] for an illustration of the above steps.
Ex [1] 8273 x 111 =_________.
a) Write down 3.
3
|
8 2 7 3
b) 7 + 3 = 10. Write down 0, carry *1.
*10
_|_
8 2 7 3
c) 2 + 7 + 3 = 12 + *1 = 13. Write down 3, carry *1.
12+*1
___|___
8 2 7 3
d) 8 + 2 + 7 = 17 + *1 = 18. Write down 8, carry *1.
17+*1
____|___
8 2 7 3
e) 8 + 2 = 10 + *1 = 11. Write down 1, carry *1.
10+*1
__|__
8 2 7 3
f) 8 + *1 = 9. Write down 9.
8+*1
|
8 2 7 3
g) The answer is 918303.
Ex [2] 32 x 111 =_________.
a) When multiplying by 111, you have to have at least 3 digits for this method to work, so think of 32 as 032.
b) Write down 2.
c) 2 + 3 = 5. Write down 5.
d) 0 + 2 + 3 = 5. Write down 5.
e) 0 + 3 = 3. Write down 3.
f) Since you do not write 0 in front of numbers, the final answer is 3552.