Long division is a method for dividing large numbers, breaking it down into smaller, manageable steps. Here’s how you do it, drawing from the principles of the video "Long Division. DMSB. Grade 4 - YouTube":
Understanding the Basics of Long Division
Long division involves four key steps, often remembered with the acronym "DMSB" (Divide, Multiply, Subtract, Bring Down):
- Divide: Begin by dividing the first digit (or set of digits) of the dividend (the number being divided) by the divisor (the number you're dividing by). Write the result above the dividend, in the quotient (the answer).
- Multiply: Multiply the quotient you just wrote by the divisor. Write this result below the portion of the dividend you used for the division step.
- Subtract: Subtract the result of your multiplication from the portion of the dividend you used.
- Bring Down: Bring down the next digit of the dividend and place it next to the result of your subtraction. This creates a new number to repeat the process with. If there are no more digits to bring down, this indicates the end of the division process.
Step-by-Step Guide with an Example
Let's use an example: 876 divided by 4.
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Setup: Write the problem with the dividend (876) under the division symbol (a line with a rightward extending tail) and the divisor (4) outside on the left.
______ 4 | 876 -
Divide (Step 1): Begin by dividing the first digit of the dividend (8) by the divisor (4). 8 ÷ 4 = 2. Write the 2 above the 8 in the quotient.
2____ 4 | 876 -
Multiply (Step 2): Multiply the quotient (2) by the divisor (4). 2 x 4 = 8. Write the 8 below the first digit of the dividend.
2____ 4 | 876 8 -
Subtract (Step 3): Subtract the multiplied result (8) from the corresponding part of the dividend (8). 8 - 8 = 0.
2____ 4 | 876 8 --- 0 -
Bring Down (Step 4): Bring down the next digit of the dividend (7) and place it next to the result of the subtraction.
2____ 4 | 876 8 --- 07 -
Repeat the Process: Now repeat the steps:
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Divide: 7 ÷ 4 = 1 (with a remainder). Write the 1 above the 7 in the quotient.
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Multiply: 1 x 4 = 4. Write the 4 below the 7.
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Subtract: 7 - 4 = 3.
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Bring Down: Bring down the next digit (6).
21___ 4 | 876 8 --- 07 4 --- 36
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Final Cycle: Repeat the steps again:
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Divide: 36 ÷ 4 = 9. Write the 9 in the quotient above the 6.
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Multiply: 9 x 4 = 36. Write the 36 below the 36.
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Subtract: 36 - 36 = 0.
219 4 | 876 8 --- 07 4 --- 36 36 --- 0
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Result: Since the subtraction result is 0 and there are no remaining digits in the dividend, the long division is complete. The quotient is 219. Therefore, 876 divided by 4 is 219.
Key Takeaways
- Long division breaks down division into smaller, more manageable steps.
- The steps are repeated until all digits of the dividend have been used.
- Remainders are noted at the end, if the division isn't exact.
| Step | Action | Description |
|---|---|---|
| 1 | Divide | Divide a part of the dividend by the divisor, put result in the quotient. |
| 2 | Multiply | Multiply the divisor by the most recently added digit in the quotient. |
| 3 | Subtract | Subtract the product of the multiplication from the part of the dividend being worked on. |
| 4 | Bring Down | Bring down the next digit of the dividend to combine with the remainder from the subtraction. |
