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Question
What is the quotient and remainder when $ 9725 $ is divided by $ 23 $ ?
Answer
The quotient is 422 and the remainder is 19.
Explanation
|
Division Table
|
| | | 0 | 4 | 2 | 2 |
| 2 | 3 | 9 | 7 | 2 | 5 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | – | 9 | 2 | | |
| | | | 5 | 2 | |
| | | – | 4 | 6 | |
| | | | | 6 | 5 |
| | | | – | 4 | 6 |
| | | | | 1 | 9 |
STEP 0: set up a division table
|
| | | | | | |
| 2 | 3 | 9 | 7 | 2 | 5 |
STEP 1: DIVIDE 9 : 23 = 0 with a remainder of 9
|
| | | 0 | | | |
| 2 | 3 | 9 | 7 | 2 | 5 |
STEP 2: MULTIPLY 0 · 23 = 0
|
| | | 0 | | | |
| 2 | 3 | 9 | 7 | 2 | 5 |
| | | 0 | | | |
STEP 3: SUBTRACT 9 - 0 = 9
|
| | | 0 | | | |
| 2 | 3 | 9 | 7 | 2 | 5 |
| | – | 0 | | | |
| | | 9 | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | |
| 2 | 3 | 9 | 7 | 2 | 5 |
| | – | 0 | | | |
| | | 9 | 7 | | |
STEP 5: DIVIDE 97 : 23 = 4 with a remainder of 5
|
| | | 0 | 4 | | |
| 2 | 3 | 9 | 7 | 2 | 5 |
| | – | 0 | | | |
| | | 9 | 7 | | |
STEP 6: MULTIPLY 4 · 23 = 92
|
| | | 0 | 4 | | |
| 2 | 3 | 9 | 7 | 2 | 5 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | | 9 | 2 | | |
STEP 7: SUBTRACT 97 - 92 = 5
|
| | | 0 | 4 | | |
| 2 | 3 | 9 | 7 | 2 | 5 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | – | 9 | 2 | | |
| | | | 5 | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 4 | | |
| 2 | 3 | 9 | 7 | 2 | 5 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | – | 9 | 2 | | |
| | | | 5 | 2 | |
STEP 9: DIVIDE 52 : 23 = 2 with a remainder of 6
|
| | | 0 | 4 | 2 | |
| 2 | 3 | 9 | 7 | 2 | 5 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | – | 9 | 2 | | |
| | | | 5 | 2 | |
STEP 10: MULTIPLY 2 · 23 = 46
|
| | | 0 | 4 | 2 | |
| 2 | 3 | 9 | 7 | 2 | 5 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | – | 9 | 2 | | |
| | | | 5 | 2 | |
| | | | 4 | 6 | |
STEP 11: SUBTRACT 52 - 46 = 6
|
| | | 0 | 4 | 2 | |
| 2 | 3 | 9 | 7 | 2 | 5 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | – | 9 | 2 | | |
| | | | 5 | 2 | |
| | | – | 4 | 6 | |
| | | | | 6 | |
|
STEP 12: BRING DOWN
|
| | | 0 | 4 | 2 | |
| 2 | 3 | 9 | 7 | 2 | 5 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | – | 9 | 2 | | |
| | | | 5 | 2 | |
| | | – | 4 | 6 | |
| | | | | 6 | 5 |
STEP 13: DIVIDE 65 : 23 = 2 with a remainder of 19
|
| | | 0 | 4 | 2 | 2 |
| 2 | 3 | 9 | 7 | 2 | 5 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | – | 9 | 2 | | |
| | | | 5 | 2 | |
| | | – | 4 | 6 | |
| | | | | 6 | 5 |
STEP 14: MULTIPLY 2 · 23 = 46
|
| | | 0 | 4 | 2 | 2 |
| 2 | 3 | 9 | 7 | 2 | 5 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | – | 9 | 2 | | |
| | | | 5 | 2 | |
| | | – | 4 | 6 | |
| | | | | 6 | 5 |
| | | | | 4 | 6 |
STEP 15: SUBTRACT 65 - 46 = 19
|
| | | 0 | 4 | 2 | 2 |
| 2 | 3 | 9 | 7 | 2 | 5 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | – | 9 | 2 | | |
| | | | 5 | 2 | |
| | | – | 4 | 6 | |
| | | | | 6 | 5 |
| | | | – | 4 | 6 |
| | | | | 1 | 9 |
STEP 15: SUBTRACT 65 - 46 = 19
|
| | | 0 | 4 | 2 | 2 |
| 2 | 3 | 9 | 7 | 2 | 5 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | – | 9 | 2 | | |
| | | | 5 | 2 | |
| | | – | 4 | 6 | |
| | | | | 6 | 5 |
| | | | – | 4 | 6 |
| | | | | 1 | 9 |
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