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Question
What is the quotient and remainder when $ 2014 $ is divided by $ 11 $ ?
Answer
The quotient is 183 and the remainder is 1.
Explanation
Division Table
|
| | 0 | 1 | 8 | 3 |
1 | 1 | 2 | 0 | 1 | 4 |
| – | 0 | | | |
| | 2 | 0 | | |
| – | 1 | 1 | | |
| | | 9 | 1 | |
| | – | 8 | 8 | |
| | | | 3 | 4 |
| | | – | 3 | 3 |
| | | | | 1 |
STEP 0: set up a division table
|
| | | | | |
1 | 1 | 2 | 0 | 1 | 4 |
STEP 1: DIVIDE 2 : 11 = 0 with a remainder of 2
|
| | 0 | | | |
1 | 1 | 2 | 0 | 1 | 4 |
STEP 2: MULTIPLY 0 · 11 = 0
|
| | 0 | | | |
1 | 1 | 2 | 0 | 1 | 4 |
| | 0 | | | |
STEP 3: SUBTRACT 2 - 0 = 2
|
| | 0 | | | |
1 | 1 | 2 | 0 | 1 | 4 |
| – | 0 | | | |
| | 2 | | | |
STEP 4: BRING DOWN
|
| | 0 | | | |
1 | 1 | 2 | 0 | 1 | 4 |
| – | 0 | | | |
| | 2 | 0 | | |
STEP 5: DIVIDE 20 : 11 = 1 with a remainder of 9
|
| | 0 | 1 | | |
1 | 1 | 2 | 0 | 1 | 4 |
| – | 0 | | | |
| | 2 | 0 | | |
STEP 6: MULTIPLY 1 · 11 = 11
|
| | 0 | 1 | | |
1 | 1 | 2 | 0 | 1 | 4 |
| – | 0 | | | |
| | 2 | 0 | | |
| | 1 | 1 | | |
STEP 7: SUBTRACT 20 - 11 = 9
|
| | 0 | 1 | | |
1 | 1 | 2 | 0 | 1 | 4 |
| – | 0 | | | |
| | 2 | 0 | | |
| – | 1 | 1 | | |
| | | 9 | | |
STEP 8: BRING DOWN
|
| | 0 | 1 | | |
1 | 1 | 2 | 0 | 1 | 4 |
| – | 0 | | | |
| | 2 | 0 | | |
| – | 1 | 1 | | |
| | | 9 | 1 | |
STEP 9: DIVIDE 91 : 11 = 8 with a remainder of 3
|
| | 0 | 1 | 8 | |
1 | 1 | 2 | 0 | 1 | 4 |
| – | 0 | | | |
| | 2 | 0 | | |
| – | 1 | 1 | | |
| | | 9 | 1 | |
STEP 10: MULTIPLY 8 · 11 = 88
|
| | 0 | 1 | 8 | |
1 | 1 | 2 | 0 | 1 | 4 |
| – | 0 | | | |
| | 2 | 0 | | |
| – | 1 | 1 | | |
| | | 9 | 1 | |
| | | 8 | 8 | |
STEP 11: SUBTRACT 91 - 88 = 3
|
| | 0 | 1 | 8 | |
1 | 1 | 2 | 0 | 1 | 4 |
| – | 0 | | | |
| | 2 | 0 | | |
| – | 1 | 1 | | |
| | | 9 | 1 | |
| | – | 8 | 8 | |
| | | | 3 | |
STEP 12: BRING DOWN
|
| | 0 | 1 | 8 | |
1 | 1 | 2 | 0 | 1 | 4 |
| – | 0 | | | |
| | 2 | 0 | | |
| – | 1 | 1 | | |
| | | 9 | 1 | |
| | – | 8 | 8 | |
| | | | 3 | 4 |
STEP 13: DIVIDE 34 : 11 = 3 with a remainder of 1
|
| | 0 | 1 | 8 | 3 |
1 | 1 | 2 | 0 | 1 | 4 |
| – | 0 | | | |
| | 2 | 0 | | |
| – | 1 | 1 | | |
| | | 9 | 1 | |
| | – | 8 | 8 | |
| | | | 3 | 4 |
STEP 14: MULTIPLY 3 · 11 = 33
|
| | 0 | 1 | 8 | 3 |
1 | 1 | 2 | 0 | 1 | 4 |
| – | 0 | | | |
| | 2 | 0 | | |
| – | 1 | 1 | | |
| | | 9 | 1 | |
| | – | 8 | 8 | |
| | | | 3 | 4 |
| | | | 3 | 3 |
STEP 15: SUBTRACT 34 - 33 = 1
|
| | 0 | 1 | 8 | 3 |
1 | 1 | 2 | 0 | 1 | 4 |
| – | 0 | | | |
| | 2 | 0 | | |
| – | 1 | 1 | | |
| | | 9 | 1 | |
| | – | 8 | 8 | |
| | | | 3 | 4 |
| | | – | 3 | 3 |
| | | | | 1 |
STEP 15: SUBTRACT 34 - 33 = 1
|
| | 0 | 1 | 8 | 3 |
1 | 1 | 2 | 0 | 1 | 4 |
| – | 0 | | | |
| | 2 | 0 | | |
| – | 1 | 1 | | |
| | | 9 | 1 | |
| | – | 8 | 8 | |
| | | | 3 | 4 |
| | | – | 3 | 3 |
| | | | | 1 |
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