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Question
What is the quotient and remainder when $ 3500 $ is divided by $ 12 $ ?
Answer
The quotient is 291 and the remainder is 8.
Explanation
|
Division Table
|
| | | 0 | 2 | 9 | 1 |
| 1 | 2 | 3 | 5 | 0 | 0 |
| | – | 0 | | | |
| | | 3 | 5 | | |
| | – | 2 | 4 | | |
| | | 1 | 1 | 0 | |
| | – | 1 | 0 | 8 | |
| | | | | 2 | 0 |
| | | | – | 1 | 2 |
| | | | | | 8 |
STEP 0: set up a division table
|
| | | | | | |
| 1 | 2 | 3 | 5 | 0 | 0 |
STEP 1: DIVIDE 3 : 12 = 0 with a remainder of 3
|
| | | 0 | | | |
| 1 | 2 | 3 | 5 | 0 | 0 |
STEP 2: MULTIPLY 0 · 12 = 0
|
| | | 0 | | | |
| 1 | 2 | 3 | 5 | 0 | 0 |
| | | 0 | | | |
STEP 3: SUBTRACT 3 - 0 = 3
|
| | | 0 | | | |
| 1 | 2 | 3 | 5 | 0 | 0 |
| | – | 0 | | | |
| | | 3 | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | |
| 1 | 2 | 3 | 5 | 0 | 0 |
| | – | 0 | | | |
| | | 3 | 5 | | |
STEP 5: DIVIDE 35 : 12 = 2 with a remainder of 11
|
| | | 0 | 2 | | |
| 1 | 2 | 3 | 5 | 0 | 0 |
| | – | 0 | | | |
| | | 3 | 5 | | |
STEP 6: MULTIPLY 2 · 12 = 24
|
| | | 0 | 2 | | |
| 1 | 2 | 3 | 5 | 0 | 0 |
| | – | 0 | | | |
| | | 3 | 5 | | |
| | | 2 | 4 | | |
STEP 7: SUBTRACT 35 - 24 = 11
|
| | | 0 | 2 | | |
| 1 | 2 | 3 | 5 | 0 | 0 |
| | – | 0 | | | |
| | | 3 | 5 | | |
| | – | 2 | 4 | | |
| | | 1 | 1 | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 2 | | |
| 1 | 2 | 3 | 5 | 0 | 0 |
| | – | 0 | | | |
| | | 3 | 5 | | |
| | – | 2 | 4 | | |
| | | 1 | 1 | 0 | |
STEP 9: DIVIDE 110 : 12 = 9 with a remainder of 2
|
| | | 0 | 2 | 9 | |
| 1 | 2 | 3 | 5 | 0 | 0 |
| | – | 0 | | | |
| | | 3 | 5 | | |
| | – | 2 | 4 | | |
| | | 1 | 1 | 0 | |
STEP 10: MULTIPLY 9 · 12 = 108
|
| | | 0 | 2 | 9 | |
| 1 | 2 | 3 | 5 | 0 | 0 |
| | – | 0 | | | |
| | | 3 | 5 | | |
| | – | 2 | 4 | | |
| | | 1 | 1 | 0 | |
| | | 1 | 0 | 8 | |
STEP 11: SUBTRACT 110 - 108 = 2
|
| | | 0 | 2 | 9 | |
| 1 | 2 | 3 | 5 | 0 | 0 |
| | – | 0 | | | |
| | | 3 | 5 | | |
| | – | 2 | 4 | | |
| | | 1 | 1 | 0 | |
| | – | 1 | 0 | 8 | |
| | | | | 2 | |
|
STEP 12: BRING DOWN
|
| | | 0 | 2 | 9 | |
| 1 | 2 | 3 | 5 | 0 | 0 |
| | – | 0 | | | |
| | | 3 | 5 | | |
| | – | 2 | 4 | | |
| | | 1 | 1 | 0 | |
| | – | 1 | 0 | 8 | |
| | | | | 2 | 0 |
STEP 13: DIVIDE 20 : 12 = 1 with a remainder of 8
|
| | | 0 | 2 | 9 | 1 |
| 1 | 2 | 3 | 5 | 0 | 0 |
| | – | 0 | | | |
| | | 3 | 5 | | |
| | – | 2 | 4 | | |
| | | 1 | 1 | 0 | |
| | – | 1 | 0 | 8 | |
| | | | | 2 | 0 |
STEP 14: MULTIPLY 1 · 12 = 12
|
| | | 0 | 2 | 9 | 1 |
| 1 | 2 | 3 | 5 | 0 | 0 |
| | – | 0 | | | |
| | | 3 | 5 | | |
| | – | 2 | 4 | | |
| | | 1 | 1 | 0 | |
| | – | 1 | 0 | 8 | |
| | | | | 2 | 0 |
| | | | | 1 | 2 |
STEP 15: SUBTRACT 20 - 12 = 8
|
| | | 0 | 2 | 9 | 1 |
| 1 | 2 | 3 | 5 | 0 | 0 |
| | – | 0 | | | |
| | | 3 | 5 | | |
| | – | 2 | 4 | | |
| | | 1 | 1 | 0 | |
| | – | 1 | 0 | 8 | |
| | | | | 2 | 0 |
| | | | – | 1 | 2 |
| | | | | | 8 |
STEP 15: SUBTRACT 20 - 12 = 8
|
| | | 0 | 2 | 9 | 1 |
| 1 | 2 | 3 | 5 | 0 | 0 |
| | – | 0 | | | |
| | | 3 | 5 | | |
| | – | 2 | 4 | | |
| | | 1 | 1 | 0 | |
| | – | 1 | 0 | 8 | |
| | | | | 2 | 0 |
| | | | – | 1 | 2 |
| | | | | | 8 |
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