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What is the quotient and remainder when $ 12000 $ is divided by $ 220 $ ?
Answer
The quotient is 54 and the remainder is 120.
Explanation
Division Table
|
| | | 0 | 0 | 0 | 5 | 4 |
2 | 2 | 0 | 1 | 2 | 0 | 0 | 0 |
| | – | 0 | | | | |
| | | 1 | 2 | | | |
| | | – | 0 | | | |
| | | 1 | 2 | 0 | | |
| | | | – | 0 | | |
| | | 1 | 2 | 0 | 0 | |
| | – | 1 | 1 | 0 | 0 | |
| | | | 1 | 0 | 0 | 0 |
| | | | – | 8 | 8 | 0 |
| | | | | 1 | 2 | 0 |
STEP 0: set up a division table
|
| | | | | | | |
2 | 2 | 0 | 1 | 2 | 0 | 0 | 0 |
STEP 1: DIVIDE 1 : 220 = 0 with a remainder of 1
|
| | | 0 | | | | |
2 | 2 | 0 | 1 | 2 | 0 | 0 | 0 |
STEP 2: MULTIPLY 0 · 220 = 0
|
| | | 0 | | | | |
2 | 2 | 0 | 1 | 2 | 0 | 0 | 0 |
| | | 0 | | | | |
STEP 3: SUBTRACT 1 - 0 = 1
|
| | | 0 | | | | |
2 | 2 | 0 | 1 | 2 | 0 | 0 | 0 |
| | – | 0 | | | | |
| | | 1 | | | | |
STEP 4: BRING DOWN
|
| | | 0 | | | | |
2 | 2 | 0 | 1 | 2 | 0 | 0 | 0 |
| | – | 0 | | | | |
| | | 1 | 2 | | | |
STEP 5: DIVIDE 12 : 220 = 0 with a remainder of 12
|
| | | 0 | 0 | | | |
2 | 2 | 0 | 1 | 2 | 0 | 0 | 0 |
| | – | 0 | | | | |
| | | 1 | 2 | | | |
STEP 6: MULTIPLY 0 · 220 = 0
|
| | | 0 | 0 | | | |
2 | 2 | 0 | 1 | 2 | 0 | 0 | 0 |
| | – | 0 | | | | |
| | | 1 | 2 | | | |
| | | | 0 | | | |
STEP 7: SUBTRACT 12 - 0 = 12
|
| | | 0 | 0 | | | |
2 | 2 | 0 | 1 | 2 | 0 | 0 | 0 |
| | – | 0 | | | | |
| | | 1 | 2 | | | |
| | | – | 0 | | | |
| | | 1 | 2 | | | |
STEP 8: BRING DOWN
|
| | | 0 | 0 | | | |
2 | 2 | 0 | 1 | 2 | 0 | 0 | 0 |
| | – | 0 | | | | |
| | | 1 | 2 | | | |
| | | – | 0 | | | |
| | | 1 | 2 | 0 | | |
STEP 9: DIVIDE 120 : 220 = 0 with a remainder of 120
|
| | | 0 | 0 | 0 | | |
2 | 2 | 0 | 1 | 2 | 0 | 0 | 0 |
| | – | 0 | | | | |
| | | 1 | 2 | | | |
| | | – | 0 | | | |
| | | 1 | 2 | 0 | | |
STEP 10: MULTIPLY 0 · 220 = 0
|
| | | 0 | 0 | 0 | | |
2 | 2 | 0 | 1 | 2 | 0 | 0 | 0 |
| | – | 0 | | | | |
| | | 1 | 2 | | | |
| | | – | 0 | | | |
| | | 1 | 2 | 0 | | |
| | | | | 0 | | |
STEP 11: SUBTRACT 120 - 0 = 120
|
| | | 0 | 0 | 0 | | |
2 | 2 | 0 | 1 | 2 | 0 | 0 | 0 |
| | – | 0 | | | | |
| | | 1 | 2 | | | |
| | | – | 0 | | | |
| | | 1 | 2 | 0 | | |
| | | | – | 0 | | |
| | | 1 | 2 | 0 | | |
STEP 12: BRING DOWN
|
| | | 0 | 0 | 0 | | |
2 | 2 | 0 | 1 | 2 | 0 | 0 | 0 |
| | – | 0 | | | | |
| | | 1 | 2 | | | |
| | | – | 0 | | | |
| | | 1 | 2 | 0 | | |
| | | | – | 0 | | |
| | | 1 | 2 | 0 | 0 | |
STEP 13: DIVIDE 1200 : 220 = 5 with a remainder of 100
|
| | | 0 | 0 | 0 | 5 | |
2 | 2 | 0 | 1 | 2 | 0 | 0 | 0 |
| | – | 0 | | | | |
| | | 1 | 2 | | | |
| | | – | 0 | | | |
| | | 1 | 2 | 0 | | |
| | | | – | 0 | | |
| | | 1 | 2 | 0 | 0 | |
STEP 14: MULTIPLY 5 · 220 = 1100
|
| | | 0 | 0 | 0 | 5 | |
2 | 2 | 0 | 1 | 2 | 0 | 0 | 0 |
| | – | 0 | | | | |
| | | 1 | 2 | | | |
| | | – | 0 | | | |
| | | 1 | 2 | 0 | | |
| | | | – | 0 | | |
| | | 1 | 2 | 0 | 0 | |
| | | 1 | 1 | 0 | 0 | |
STEP 15: SUBTRACT 1200 - 1100 = 100
|
| | | 0 | 0 | 0 | 5 | |
2 | 2 | 0 | 1 | 2 | 0 | 0 | 0 |
| | – | 0 | | | | |
| | | 1 | 2 | | | |
| | | – | 0 | | | |
| | | 1 | 2 | 0 | | |
| | | | – | 0 | | |
| | | 1 | 2 | 0 | 0 | |
| | – | 1 | 1 | 0 | 0 | |
| | | | 1 | 0 | 0 | |
STEP 16: BRING DOWN
|
| | | 0 | 0 | 0 | 5 | |
2 | 2 | 0 | 1 | 2 | 0 | 0 | 0 |
| | – | 0 | | | | |
| | | 1 | 2 | | | |
| | | – | 0 | | | |
| | | 1 | 2 | 0 | | |
| | | | – | 0 | | |
| | | 1 | 2 | 0 | 0 | |
| | – | 1 | 1 | 0 | 0 | |
| | | | 1 | 0 | 0 | 0 |
STEP 17: DIVIDE 1000 : 220 = 4 with a remainder of 120
|
| | | 0 | 0 | 0 | 5 | 4 |
2 | 2 | 0 | 1 | 2 | 0 | 0 | 0 |
| | – | 0 | | | | |
| | | 1 | 2 | | | |
| | | – | 0 | | | |
| | | 1 | 2 | 0 | | |
| | | | – | 0 | | |
| | | 1 | 2 | 0 | 0 | |
| | – | 1 | 1 | 0 | 0 | |
| | | | 1 | 0 | 0 | 0 |
STEP 18: MULTIPLY 4 · 220 = 880
|
| | | 0 | 0 | 0 | 5 | 4 |
2 | 2 | 0 | 1 | 2 | 0 | 0 | 0 |
| | – | 0 | | | | |
| | | 1 | 2 | | | |
| | | – | 0 | | | |
| | | 1 | 2 | 0 | | |
| | | | – | 0 | | |
| | | 1 | 2 | 0 | 0 | |
| | – | 1 | 1 | 0 | 0 | |
| | | | 1 | 0 | 0 | 0 |
| | | | | 8 | 8 | 0 |
STEP 19: SUBTRACT 1000 - 880 = 120
|
| | | 0 | 0 | 0 | 5 | 4 |
2 | 2 | 0 | 1 | 2 | 0 | 0 | 0 |
| | – | 0 | | | | |
| | | 1 | 2 | | | |
| | | – | 0 | | | |
| | | 1 | 2 | 0 | | |
| | | | – | 0 | | |
| | | 1 | 2 | 0 | 0 | |
| | – | 1 | 1 | 0 | 0 | |
| | | | 1 | 0 | 0 | 0 |
| | | | – | 8 | 8 | 0 |
| | | | | 1 | 2 | 0 |
STEP 19: SUBTRACT 1000 - 880 = 120
|
| | | 0 | 0 | 0 | 5 | 4 |
2 | 2 | 0 | 1 | 2 | 0 | 0 | 0 |
| | – | 0 | | | | |
| | | 1 | 2 | | | |
| | | – | 0 | | | |
| | | 1 | 2 | 0 | | |
| | | | – | 0 | | |
| | | 1 | 2 | 0 | 0 | |
| | – | 1 | 1 | 0 | 0 | |
| | | | 1 | 0 | 0 | 0 |
| | | | – | 8 | 8 | 0 |
| | | | | 1 | 2 | 0 |
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