To find the remainder using long division, you must continue the division process until you can no longer divide. The leftover amount that is less than the divisor is the remainder.
Here's a more detailed breakdown:
Steps for Long Division and Finding the Remainder
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Set Up the Problem: Write the dividend (the number being divided) inside the division symbol and the divisor (the number you're dividing by) outside the symbol.
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Divide: Begin dividing the leftmost digit (or digits) of the dividend by the divisor. Write the quotient above the division symbol.
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Multiply: Multiply the quotient by the divisor and write the result below the portion of the dividend you just divided.
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Subtract: Subtract the product from the part of the dividend.
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Bring Down: Bring down the next digit from the dividend next to the result of the subtraction.
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Repeat: Repeat steps 2-5 until all digits of the dividend have been used.
- According to our reference: To find the remainder, perform long division until the last digit is done.
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Identify the Remainder: Once you have brought down the last digit and completed the division as much as possible, the number left over after the last subtraction, if less than the divisor, is the remainder.
Example:
Let's say we're dividing 75 by 6:
| Steps | Calculations | Result |
|---|---|---|
| 1. Setup | 6 | 75 |
| 2. Divide | 6 goes into 7 once | 1 |
| 3. Multiply | 1 * 6 = 6 | 6 |
| 4. Subtract | 7 - 6 = 1 | 1 |
| 5. Bring Down | Bring down 5 | 15 |
| 6. Repeat Divide | 6 goes into 15 twice | 12 |
| 7. Multiply | 2 * 6 = 12 | 12 |
| 8. Subtract | 15 - 12 = 3 | 3 |
| Remainder | The leftover is 3 | Remainder: 3 |
Therefore, 75 divided by 6 is 12 with a remainder of 3.
Key Points:
- The remainder is always less than the divisor.
- If you get a remainder of 0, the division is exact.
Long division provides a systematic way to find both the quotient and the remainder when dividing numbers, which is particularly useful for larger numbers.
