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Question
What is the quotient and remainder when $ 9775 $ is divided by $ 42 $ ?
Answer
The quotient is 232 and the remainder is 31.
Explanation
|
Division Table
|
| | | 0 | 2 | 3 | 2 |
| 4 | 2 | 9 | 7 | 7 | 5 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | – | 8 | 4 | | |
| | | 1 | 3 | 7 | |
| | – | 1 | 2 | 6 | |
| | | | 1 | 1 | 5 |
| | | | – | 8 | 4 |
| | | | | 3 | 1 |
STEP 0: set up a division table
|
| | | | | | |
| 4 | 2 | 9 | 7 | 7 | 5 |
STEP 1: DIVIDE 9 : 42 = 0 with a remainder of 9
|
| | | 0 | | | |
| 4 | 2 | 9 | 7 | 7 | 5 |
STEP 2: MULTIPLY 0 · 42 = 0
|
| | | 0 | | | |
| 4 | 2 | 9 | 7 | 7 | 5 |
| | | 0 | | | |
STEP 3: SUBTRACT 9 - 0 = 9
|
| | | 0 | | | |
| 4 | 2 | 9 | 7 | 7 | 5 |
| | – | 0 | | | |
| | | 9 | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | |
| 4 | 2 | 9 | 7 | 7 | 5 |
| | – | 0 | | | |
| | | 9 | 7 | | |
STEP 5: DIVIDE 97 : 42 = 2 with a remainder of 13
|
| | | 0 | 2 | | |
| 4 | 2 | 9 | 7 | 7 | 5 |
| | – | 0 | | | |
| | | 9 | 7 | | |
STEP 6: MULTIPLY 2 · 42 = 84
|
| | | 0 | 2 | | |
| 4 | 2 | 9 | 7 | 7 | 5 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | | 8 | 4 | | |
STEP 7: SUBTRACT 97 - 84 = 13
|
| | | 0 | 2 | | |
| 4 | 2 | 9 | 7 | 7 | 5 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | – | 8 | 4 | | |
| | | 1 | 3 | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 2 | | |
| 4 | 2 | 9 | 7 | 7 | 5 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | – | 8 | 4 | | |
| | | 1 | 3 | 7 | |
STEP 9: DIVIDE 137 : 42 = 3 with a remainder of 11
|
| | | 0 | 2 | 3 | |
| 4 | 2 | 9 | 7 | 7 | 5 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | – | 8 | 4 | | |
| | | 1 | 3 | 7 | |
STEP 10: MULTIPLY 3 · 42 = 126
|
| | | 0 | 2 | 3 | |
| 4 | 2 | 9 | 7 | 7 | 5 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | – | 8 | 4 | | |
| | | 1 | 3 | 7 | |
| | | 1 | 2 | 6 | |
STEP 11: SUBTRACT 137 - 126 = 11
|
| | | 0 | 2 | 3 | |
| 4 | 2 | 9 | 7 | 7 | 5 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | – | 8 | 4 | | |
| | | 1 | 3 | 7 | |
| | – | 1 | 2 | 6 | |
| | | | 1 | 1 | |
|
STEP 12: BRING DOWN
|
| | | 0 | 2 | 3 | |
| 4 | 2 | 9 | 7 | 7 | 5 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | – | 8 | 4 | | |
| | | 1 | 3 | 7 | |
| | – | 1 | 2 | 6 | |
| | | | 1 | 1 | 5 |
STEP 13: DIVIDE 115 : 42 = 2 with a remainder of 31
|
| | | 0 | 2 | 3 | 2 |
| 4 | 2 | 9 | 7 | 7 | 5 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | – | 8 | 4 | | |
| | | 1 | 3 | 7 | |
| | – | 1 | 2 | 6 | |
| | | | 1 | 1 | 5 |
STEP 14: MULTIPLY 2 · 42 = 84
|
| | | 0 | 2 | 3 | 2 |
| 4 | 2 | 9 | 7 | 7 | 5 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | – | 8 | 4 | | |
| | | 1 | 3 | 7 | |
| | – | 1 | 2 | 6 | |
| | | | 1 | 1 | 5 |
| | | | | 8 | 4 |
STEP 15: SUBTRACT 115 - 84 = 31
|
| | | 0 | 2 | 3 | 2 |
| 4 | 2 | 9 | 7 | 7 | 5 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | – | 8 | 4 | | |
| | | 1 | 3 | 7 | |
| | – | 1 | 2 | 6 | |
| | | | 1 | 1 | 5 |
| | | | – | 8 | 4 |
| | | | | 3 | 1 |
STEP 15: SUBTRACT 115 - 84 = 31
|
| | | 0 | 2 | 3 | 2 |
| 4 | 2 | 9 | 7 | 7 | 5 |
| | – | 0 | | | |
| | | 9 | 7 | | |
| | – | 8 | 4 | | |
| | | 1 | 3 | 7 | |
| | – | 1 | 2 | 6 | |
| | | | 1 | 1 | 5 |
| | | | – | 8 | 4 |
| | | | | 3 | 1 |
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