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Question
What is the quotient and remainder when $ 9711 $ is divided by $ 13 $ ?
Answer
The quotient is 747 and the remainder is 0.
Explanation
|
Division Table
|
| | | 0 | 7 | 4 | 7 |
| 1 | 3 | 9 | 7 | 1 | 1 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | – | 9 | 1 | | |
| | | | 6 | 1 | |
| | | – | 5 | 2 | |
| | | | | 9 | 1 |
| | | | – | 9 | 1 |
| | | | | | 0 |
STEP 0: set up a division table
|
| | | | | | |
| 1 | 3 | 9 | 7 | 1 | 1 |
STEP 1: DIVIDE 9 : 13 = 0 with a remainder of 9
|
| | | 0 | | | |
| 1 | 3 | 9 | 7 | 1 | 1 |
STEP 2: MULTIPLY 0 · 13 = 0
|
| | | 0 | | | |
| 1 | 3 | 9 | 7 | 1 | 1 |
| | | 0 | | | |
STEP 3: SUBTRACT 9 - 0 = 9
|
| | | 0 | | | |
| 1 | 3 | 9 | 7 | 1 | 1 |
| | – | 0 | | | |
| | | 9 | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | |
| 1 | 3 | 9 | 7 | 1 | 1 |
| | – | 0 | | | |
| | | 9 | 7 | | |
STEP 5: DIVIDE 97 : 13 = 7 with a remainder of 6
|
| | | 0 | 7 | | |
| 1 | 3 | 9 | 7 | 1 | 1 |
| | – | 0 | | | |
| | | 9 | 7 | | |
STEP 6: MULTIPLY 7 · 13 = 91
|
| | | 0 | 7 | | |
| 1 | 3 | 9 | 7 | 1 | 1 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | | 9 | 1 | | |
STEP 7: SUBTRACT 97 - 91 = 6
|
| | | 0 | 7 | | |
| 1 | 3 | 9 | 7 | 1 | 1 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | – | 9 | 1 | | |
| | | | 6 | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 7 | | |
| 1 | 3 | 9 | 7 | 1 | 1 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | – | 9 | 1 | | |
| | | | 6 | 1 | |
STEP 9: DIVIDE 61 : 13 = 4 with a remainder of 9
|
| | | 0 | 7 | 4 | |
| 1 | 3 | 9 | 7 | 1 | 1 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | – | 9 | 1 | | |
| | | | 6 | 1 | |
STEP 10: MULTIPLY 4 · 13 = 52
|
| | | 0 | 7 | 4 | |
| 1 | 3 | 9 | 7 | 1 | 1 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | – | 9 | 1 | | |
| | | | 6 | 1 | |
| | | | 5 | 2 | |
STEP 11: SUBTRACT 61 - 52 = 9
|
| | | 0 | 7 | 4 | |
| 1 | 3 | 9 | 7 | 1 | 1 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | – | 9 | 1 | | |
| | | | 6 | 1 | |
| | | – | 5 | 2 | |
| | | | | 9 | |
|
STEP 12: BRING DOWN
|
| | | 0 | 7 | 4 | |
| 1 | 3 | 9 | 7 | 1 | 1 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | – | 9 | 1 | | |
| | | | 6 | 1 | |
| | | – | 5 | 2 | |
| | | | | 9 | 1 |
STEP 13: DIVIDE 91 : 13 = 7 with a remainder of 0
|
| | | 0 | 7 | 4 | 7 |
| 1 | 3 | 9 | 7 | 1 | 1 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | – | 9 | 1 | | |
| | | | 6 | 1 | |
| | | – | 5 | 2 | |
| | | | | 9 | 1 |
STEP 14: MULTIPLY 7 · 13 = 91
|
| | | 0 | 7 | 4 | 7 |
| 1 | 3 | 9 | 7 | 1 | 1 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | – | 9 | 1 | | |
| | | | 6 | 1 | |
| | | – | 5 | 2 | |
| | | | | 9 | 1 |
| | | | | 9 | 1 |
STEP 15: SUBTRACT 91 - 91 = 0
|
| | | 0 | 7 | 4 | 7 |
| 1 | 3 | 9 | 7 | 1 | 1 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | – | 9 | 1 | | |
| | | | 6 | 1 | |
| | | – | 5 | 2 | |
| | | | | 9 | 1 |
| | | | – | 9 | 1 |
| | | | | | 0 |
STEP 15: SUBTRACT 91 - 91 = 0
|
| | | 0 | 7 | 4 | 7 |
| 1 | 3 | 9 | 7 | 1 | 1 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | – | 9 | 1 | | |
| | | | 6 | 1 | |
| | | – | 5 | 2 | |
| | | | | 9 | 1 |
| | | | – | 9 | 1 |
| | | | | | 0 |
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