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What is the quotient and remainder when $ 1575 $ is divided by $ 14 $ ?
Answer
The quotient is 112 and the remainder is 7.
Explanation
|
Division Table
|
| | | 0 | 1 | 1 | 2 |
| 1 | 4 | 1 | 5 | 7 | 5 |
| | – | 0 | | | |
| | | 1 | 5 | | |
| | – | 1 | 4 | | |
| | | | 1 | 7 | |
| | | – | 1 | 4 | |
| | | | | 3 | 5 |
| | | | – | 2 | 8 |
| | | | | | 7 |
STEP 0:
set up a division table
|
| | | | | | |
| 1 | 4 | 1 | 5 | 7 | 5 |
STEP 1: DIVIDE
1 : 14 = 0 with a remainder of 1
|
| | | 0 | | | |
| 1 | 4 | 1 | 5 | 7 | 5 |
STEP 2: MULTIPLY
0 · 14 = 0
|
| | | 0 | | | |
| 1 | 4 | 1 | 5 | 7 | 5 |
| | | 0 | | | |
STEP 3: SUBTRACT
1 - 0 = 1
|
| | | 0 | | | |
| 1 | 4 | 1 | 5 | 7 | 5 |
| | – | 0 | | | |
| | | 1 | | | |
|
STEP 4: BRING DOWN
|
| | | 0 | | | |
| 1 | 4 | 1 | 5 | 7 | 5 |
| | – | 0 | | | |
| | | 1 | 5 | | |
STEP 5: DIVIDE
15 : 14 = 1 with a remainder of 1
|
| | | 0 | 1 | | |
| 1 | 4 | 1 | 5 | 7 | 5 |
| | – | 0 | | | |
| | | 1 | 5 | | |
STEP 6: MULTIPLY
1 · 14 = 14
|
| | | 0 | 1 | | |
| 1 | 4 | 1 | 5 | 7 | 5 |
| | – | 0 | | | |
| | | 1 | 5 | | |
| | | 1 | 4 | | |
STEP 7: SUBTRACT
15 - 14 = 1
|
| | | 0 | 1 | | |
| 1 | 4 | 1 | 5 | 7 | 5 |
| | – | 0 | | | |
| | | 1 | 5 | | |
| | – | 1 | 4 | | |
| | | | 1 | | |
|
STEP 8: BRING DOWN
|
| | | 0 | 1 | | |
| 1 | 4 | 1 | 5 | 7 | 5 |
| | – | 0 | | | |
| | | 1 | 5 | | |
| | – | 1 | 4 | | |
| | | | 1 | 7 | |
STEP 9: DIVIDE
17 : 14 = 1 with a remainder of 3
|
| | | 0 | 1 | 1 | |
| 1 | 4 | 1 | 5 | 7 | 5 |
| | – | 0 | | | |
| | | 1 | 5 | | |
| | – | 1 | 4 | | |
| | | | 1 | 7 | |
STEP 10: MULTIPLY
1 · 14 = 14
|
| | | 0 | 1 | 1 | |
| 1 | 4 | 1 | 5 | 7 | 5 |
| | – | 0 | | | |
| | | 1 | 5 | | |
| | – | 1 | 4 | | |
| | | | 1 | 7 | |
| | | | 1 | 4 | |
STEP 11: SUBTRACT
17 - 14 = 3
|
| | | 0 | 1 | 1 | |
| 1 | 4 | 1 | 5 | 7 | 5 |
| | – | 0 | | | |
| | | 1 | 5 | | |
| | – | 1 | 4 | | |
| | | | 1 | 7 | |
| | | – | 1 | 4 | |
| | | | | 3 | |
|
STEP 12: BRING DOWN
|
| | | 0 | 1 | 1 | |
| 1 | 4 | 1 | 5 | 7 | 5 |
| | – | 0 | | | |
| | | 1 | 5 | | |
| | – | 1 | 4 | | |
| | | | 1 | 7 | |
| | | – | 1 | 4 | |
| | | | | 3 | 5 |
STEP 13: DIVIDE
35 : 14 = 2 with a remainder of 7
|
| | | 0 | 1 | 1 | 2 |
| 1 | 4 | 1 | 5 | 7 | 5 |
| | – | 0 | | | |
| | | 1 | 5 | | |
| | – | 1 | 4 | | |
| | | | 1 | 7 | |
| | | – | 1 | 4 | |
| | | | | 3 | 5 |
STEP 14: MULTIPLY
2 · 14 = 28
|
| | | 0 | 1 | 1 | 2 |
| 1 | 4 | 1 | 5 | 7 | 5 |
| | – | 0 | | | |
| | | 1 | 5 | | |
| | – | 1 | 4 | | |
| | | | 1 | 7 | |
| | | – | 1 | 4 | |
| | | | | 3 | 5 |
| | | | | 2 | 8 |
STEP 15: SUBTRACT
35 - 28 = 7
|
| | | 0 | 1 | 1 | 2 |
| 1 | 4 | 1 | 5 | 7 | 5 |
| | – | 0 | | | |
| | | 1 | 5 | | |
| | – | 1 | 4 | | |
| | | | 1 | 7 | |
| | | – | 1 | 4 | |
| | | | | 3 | 5 |
| | | | – | 2 | 8 |
| | | | | | 7 |
STEP 15: SUBTRACT
35 - 28 = 7
|
| | | 0 | 1 | 1 | 2 |
| 1 | 4 | 1 | 5 | 7 | 5 |
| | – | 0 | | | |
| | | 1 | 5 | | |
| | – | 1 | 4 | | |
| | | | 1 | 7 | |
| | | – | 1 | 4 | |
| | | | | 3 | 5 |
| | | | – | 2 | 8 |
| | | | | | 7 |
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