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Question
What is the quotient and remainder when $ 2223 $ is divided by $ 45 $ ?
Answer
The quotient is 49 and the remainder is 18.
Explanation
|
Division Table
|
| | | 0 | 0 | 4 | 9 |
| 4 | 5 | 2 | 2 | 2 | 3 |
| | – | 0 | | | |
| | | 2 | 2 | | |
| | | – | 0 | | |
| | | 2 | 2 | 2 | |
| | – | 1 | 8 | 0 | |
| | | | 4 | 2 | 3 |
| | | – | 4 | 0 | 5 |
| | | | | 1 | 8 |
STEP 0: set up a division table
|
| | | | | | |
| 4 | 5 | 2 | 2 | 2 | 3 |
STEP 1: DIVIDE 2 : 45 = 0 with a remainder of 2
|
| | | 0 | | | |
| 4 | 5 | 2 | 2 | 2 | 3 |
STEP 2: MULTIPLY 0 · 45 = 0
|
| | | 0 | | | |
| 4 | 5 | 2 | 2 | 2 | 3 |
| | | 0 | | | |
STEP 3: SUBTRACT 2 - 0 = 2
|
| | | 0 | | | |
| 4 | 5 | 2 | 2 | 2 | 3 |
| | – | 0 | | | |
| | | 2 | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | |
| 4 | 5 | 2 | 2 | 2 | 3 |
| | – | 0 | | | |
| | | 2 | 2 | | |
STEP 5: DIVIDE 22 : 45 = 0 with a remainder of 22
|
| | | 0 | 0 | | |
| 4 | 5 | 2 | 2 | 2 | 3 |
| | – | 0 | | | |
| | | 2 | 2 | | |
STEP 6: MULTIPLY 0 · 45 = 0
|
| | | 0 | 0 | | |
| 4 | 5 | 2 | 2 | 2 | 3 |
| | – | 0 | | | |
| | | 2 | 2 | | |
| | | | 0 | | |
STEP 7: SUBTRACT 22 - 0 = 22
|
| | | 0 | 0 | | |
| 4 | 5 | 2 | 2 | 2 | 3 |
| | – | 0 | | | |
| | | 2 | 2 | | |
| | | – | 0 | | |
| | | 2 | 2 | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 0 | | |
| 4 | 5 | 2 | 2 | 2 | 3 |
| | – | 0 | | | |
| | | 2 | 2 | | |
| | | – | 0 | | |
| | | 2 | 2 | 2 | |
STEP 9: DIVIDE 222 : 45 = 4 with a remainder of 42
|
| | | 0 | 0 | 4 | |
| 4 | 5 | 2 | 2 | 2 | 3 |
| | – | 0 | | | |
| | | 2 | 2 | | |
| | | – | 0 | | |
| | | 2 | 2 | 2 | |
STEP 10: MULTIPLY 4 · 45 = 180
|
| | | 0 | 0 | 4 | |
| 4 | 5 | 2 | 2 | 2 | 3 |
| | – | 0 | | | |
| | | 2 | 2 | | |
| | | – | 0 | | |
| | | 2 | 2 | 2 | |
| | | 1 | 8 | 0 | |
STEP 11: SUBTRACT 222 - 180 = 42
|
| | | 0 | 0 | 4 | |
| 4 | 5 | 2 | 2 | 2 | 3 |
| | – | 0 | | | |
| | | 2 | 2 | | |
| | | – | 0 | | |
| | | 2 | 2 | 2 | |
| | – | 1 | 8 | 0 | |
| | | | 4 | 2 | |
|
STEP 12: BRING DOWN
|
| | | 0 | 0 | 4 | |
| 4 | 5 | 2 | 2 | 2 | 3 |
| | – | 0 | | | |
| | | 2 | 2 | | |
| | | – | 0 | | |
| | | 2 | 2 | 2 | |
| | – | 1 | 8 | 0 | |
| | | | 4 | 2 | 3 |
STEP 13: DIVIDE 423 : 45 = 9 with a remainder of 18
|
| | | 0 | 0 | 4 | 9 |
| 4 | 5 | 2 | 2 | 2 | 3 |
| | – | 0 | | | |
| | | 2 | 2 | | |
| | | – | 0 | | |
| | | 2 | 2 | 2 | |
| | – | 1 | 8 | 0 | |
| | | | 4 | 2 | 3 |
STEP 14: MULTIPLY 9 · 45 = 405
|
| | | 0 | 0 | 4 | 9 |
| 4 | 5 | 2 | 2 | 2 | 3 |
| | – | 0 | | | |
| | | 2 | 2 | | |
| | | – | 0 | | |
| | | 2 | 2 | 2 | |
| | – | 1 | 8 | 0 | |
| | | | 4 | 2 | 3 |
| | | | 4 | 0 | 5 |
STEP 15: SUBTRACT 423 - 405 = 18
|
| | | 0 | 0 | 4 | 9 |
| 4 | 5 | 2 | 2 | 2 | 3 |
| | – | 0 | | | |
| | | 2 | 2 | | |
| | | – | 0 | | |
| | | 2 | 2 | 2 | |
| | – | 1 | 8 | 0 | |
| | | | 4 | 2 | 3 |
| | | – | 4 | 0 | 5 |
| | | | | 1 | 8 |
STEP 15: SUBTRACT 423 - 405 = 18
|
| | | 0 | 0 | 4 | 9 |
| 4 | 5 | 2 | 2 | 2 | 3 |
| | – | 0 | | | |
| | | 2 | 2 | | |
| | | – | 0 | | |
| | | 2 | 2 | 2 | |
| | – | 1 | 8 | 0 | |
| | | | 4 | 2 | 3 |
| | | – | 4 | 0 | 5 |
| | | | | 1 | 8 |
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