Question
What is the quotient and remainder when $ 32108 $ is divided by $ 9 $ ?
Answer
The quotient is 3567 and the remainder is 5.
Explanation
| Division Table | |||||
| 0 | 3 | 5 | 6 | 7 | |
| 9 | 3 | 2 | 1 | 0 | 8 |
| – | 0 | ||||
| 3 | 2 | ||||
| – | 2 | 7 | |||
| 5 | 1 | ||||
| – | 4 | 5 | |||
| 6 | 0 | ||||
| – | 5 | 4 | |||
| 6 | 8 | ||||
| – | 6 | 3 | |||
| 5 | |||||
|
STEP 0: set up a division table |
|||||
| 9 | 3 | 2 | 1 | 0 | 8 |
|
STEP 1: DIVIDE 3 : 9 = 0 with a remainder of 3 |
|||||
| 0 | |||||
| 9 | 3 | 2 | 1 | 0 | 8 |
|
STEP 2: MULTIPLY 0 · 9 = 0 |
|||||
| 0 | |||||
| 9 | 3 | 2 | 1 | 0 | 8 |
| 0 | |||||
|
STEP 3: SUBTRACT 3 - 0 = 3 |
|||||
| 0 | |||||
| 9 | 3 | 2 | 1 | 0 | 8 |
| – | 0 | ||||
| 3 | |||||
| STEP 4: BRING DOWN | |||||
| 0 | |||||
| 9 | 3 | 2 | 1 | 0 | 8 |
| – | 0 | ||||
| 3 | 2 | ||||
|
STEP 5: DIVIDE 32 : 9 = 3 with a remainder of 5 |
|||||
| 0 | 3 | ||||
| 9 | 3 | 2 | 1 | 0 | 8 |
| – | 0 | ||||
| 3 | 2 | ||||
|
STEP 6: MULTIPLY 3 · 9 = 27 |
|||||
| 0 | 3 | ||||
| 9 | 3 | 2 | 1 | 0 | 8 |
| – | 0 | ||||
| 3 | 2 | ||||
| 2 | 7 | ||||
|
STEP 7: SUBTRACT 32 - 27 = 5 |
|||||
| 0 | 3 | ||||
| 9 | 3 | 2 | 1 | 0 | 8 |
| – | 0 | ||||
| 3 | 2 | ||||
| – | 2 | 7 | |||
| 5 | |||||
| STEP 8: BRING DOWN | |||||
| 0 | 3 | ||||
| 9 | 3 | 2 | 1 | 0 | 8 |
| – | 0 | ||||
| 3 | 2 | ||||
| – | 2 | 7 | |||
| 5 | 1 | ||||
|
STEP 9: DIVIDE 51 : 9 = 5 with a remainder of 6 |
|||||
| 0 | 3 | 5 | |||
| 9 | 3 | 2 | 1 | 0 | 8 |
| – | 0 | ||||
| 3 | 2 | ||||
| – | 2 | 7 | |||
| 5 | 1 | ||||
|
STEP 10: MULTIPLY 5 · 9 = 45 |
|||||
| 0 | 3 | 5 | |||
| 9 | 3 | 2 | 1 | 0 | 8 |
| – | 0 | ||||
| 3 | 2 | ||||
| – | 2 | 7 | |||
| 5 | 1 | ||||
| 4 | 5 | ||||
|
STEP 11: SUBTRACT 51 - 45 = 6 |
|||||
| 0 | 3 | 5 | |||
| 9 | 3 | 2 | 1 | 0 | 8 |
| – | 0 | ||||
| 3 | 2 | ||||
| – | 2 | 7 | |||
| 5 | 1 | ||||
| – | 4 | 5 | |||
| 6 | |||||
| STEP 12: BRING DOWN | |||||
| 0 | 3 | 5 | |||
| 9 | 3 | 2 | 1 | 0 | 8 |
| – | 0 | ||||
| 3 | 2 | ||||
| – | 2 | 7 | |||
| 5 | 1 | ||||
| – | 4 | 5 | |||
| 6 | 0 | ||||
|
STEP 13: DIVIDE 60 : 9 = 6 with a remainder of 6 |
|||||
| 0 | 3 | 5 | 6 | ||
| 9 | 3 | 2 | 1 | 0 | 8 |
| – | 0 | ||||
| 3 | 2 | ||||
| – | 2 | 7 | |||
| 5 | 1 | ||||
| – | 4 | 5 | |||
| 6 | 0 | ||||
|
STEP 14: MULTIPLY 6 · 9 = 54 |
|||||
| 0 | 3 | 5 | 6 | ||
| 9 | 3 | 2 | 1 | 0 | 8 |
| – | 0 | ||||
| 3 | 2 | ||||
| – | 2 | 7 | |||
| 5 | 1 | ||||
| – | 4 | 5 | |||
| 6 | 0 | ||||
| 5 | 4 | ||||
|
STEP 15: SUBTRACT 60 - 54 = 6 |
|||||
| 0 | 3 | 5 | 6 | ||
| 9 | 3 | 2 | 1 | 0 | 8 |
| – | 0 | ||||
| 3 | 2 | ||||
| – | 2 | 7 | |||
| 5 | 1 | ||||
| – | 4 | 5 | |||
| 6 | 0 | ||||
| – | 5 | 4 | |||
| 6 | |||||
| STEP 16: BRING DOWN | |||||
| 0 | 3 | 5 | 6 | ||
| 9 | 3 | 2 | 1 | 0 | 8 |
| – | 0 | ||||
| 3 | 2 | ||||
| – | 2 | 7 | |||
| 5 | 1 | ||||
| – | 4 | 5 | |||
| 6 | 0 | ||||
| – | 5 | 4 | |||
| 6 | 8 | ||||
|
STEP 17: DIVIDE 68 : 9 = 7 with a remainder of 5 |
|||||
| 0 | 3 | 5 | 6 | 7 | |
| 9 | 3 | 2 | 1 | 0 | 8 |
| – | 0 | ||||
| 3 | 2 | ||||
| – | 2 | 7 | |||
| 5 | 1 | ||||
| – | 4 | 5 | |||
| 6 | 0 | ||||
| – | 5 | 4 | |||
| 6 | 8 | ||||
|
STEP 18: MULTIPLY 7 · 9 = 63 |
|||||
| 0 | 3 | 5 | 6 | 7 | |
| 9 | 3 | 2 | 1 | 0 | 8 |
| – | 0 | ||||
| 3 | 2 | ||||
| – | 2 | 7 | |||
| 5 | 1 | ||||
| – | 4 | 5 | |||
| 6 | 0 | ||||
| – | 5 | 4 | |||
| 6 | 8 | ||||
| 6 | 3 | ||||
|
STEP 19: SUBTRACT 68 - 63 = 5 |
|||||
| 0 | 3 | 5 | 6 | 7 | |
| 9 | 3 | 2 | 1 | 0 | 8 |
| – | 0 | ||||
| 3 | 2 | ||||
| – | 2 | 7 | |||
| 5 | 1 | ||||
| – | 4 | 5 | |||
| 6 | 0 | ||||
| – | 5 | 4 | |||
| 6 | 8 | ||||
| – | 6 | 3 | |||
| 5 | |||||
|
STEP 19: SUBTRACT 68 - 63 = 5 |
|||||
| 0 | 3 | 5 | 6 | 7 | |
| 9 | 3 | 2 | 1 | 0 | 8 |
| – | 0 | ||||
| 3 | 2 | ||||
| – | 2 | 7 | |||
| 5 | 1 | ||||
| – | 4 | 5 | |||
| 6 | 0 | ||||
| – | 5 | 4 | |||
| 6 | 8 | ||||
| – | 6 | 3 | |||
| 5 | |||||
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