The division method, often referred to as long division, is a way to divide numbers, especially when the divisor has more than one digit. It involves a series of steps to break down the division problem into manageable parts. Here's a breakdown of the process:
Understanding the Terminology
According to the provided reference from the YouTube video "Long Division For Beginners | Step by Step", we use specific terms when discussing division:
- Dividend: This is the number that is being divided. In the example given (345 divided by 5), 345 is the dividend.
- Divisor: This is the number that you are dividing by. In the example, 5 is the divisor.
The Long Division Process
Here's a step-by-step guide on how to perform long division:
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Set Up the Problem:
- Draw the long division symbol (a sort of right parenthesis with a horizontal line over the dividend).
- Place the dividend (the number being divided) inside the division symbol, similar to how the video example places the "345 inside the bus".
- Place the divisor (the number you are dividing by) outside the division symbol, as shown with "the 5 goes outside" in the video.
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Divide:
- Start with the leftmost digit(s) of the dividend. Ask yourself how many times the divisor goes into this part of the dividend.
- Write the answer (the quotient) above the division symbol, aligning it with the digit(s) you used from the dividend.
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Multiply:
- Multiply the quotient you just wrote by the divisor.
- Write the product of this multiplication below the corresponding digits of the dividend.
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Subtract:
- Subtract the product from the corresponding portion of the dividend.
- Write the result of this subtraction below the line.
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Bring Down:
- Bring down the next digit of the dividend and write it next to the result of the subtraction. This forms your new working number.
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Repeat:
- Repeat steps 2-5 until there are no more digits left in the dividend to bring down.
- If after bringing down all digits, you have a number that the divisor cannot divide into evenly, the remainder is what's left over.
Example
Let's use the example given in the provided reference of 345 divided by 5.
| Step | Operation | Result |
|---|---|---|
| 1 | Set up the problem | 5 ) 345 |
| 2 | Divide: 5 into 3? No, 5 into 34? | 5 goes into 34 six times. Write "6" over the 4. |
| 3 | Multiply: 6 x 5 | Write "30" below the 34. |
| 4 | Subtract: 34 - 30 | 34 - 30 = 4. Write "4" below the line. |
| 5 | Bring Down: Bring down 5. | We have 45 as our new working number. |
| 6 | Divide: 5 into 45 | 5 goes into 45 nine times. Write a "9" next to the 6 over the division symbol |
| 7 | Multiply: 9 * 5 | Write "45" under our new working number |
| 8 | Subtract: 45 - 45 | 45 - 45 = 0. We have 0 and no more numbers to bring down. |
Therefore, 345 divided by 5 is 69.
Summary
Long division is a systematic way to break down more complex division problems. By following these steps you can solve divisions regardless of the size of the numbers involved. The main steps to remember are divide, multiply, subtract, bring down, and repeat.
