Division with repeated subtraction involves subtracting the divisor from the dividend repeatedly until you reach zero or a number less than the divisor. The number of times you subtract is the quotient (the answer to the division problem).
Understanding the Process
The core idea is to find out how many times a specific number (the divisor) fits into another number (the dividend).
- Dividend: The number being divided.
- Divisor: The number you are dividing by.
- Quotient: The result of the division.
- Remainder: The amount left over if the divisor doesn't divide the dividend evenly.
Steps for Division Using Repeated Subtraction
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Start with the dividend. Write down the number you want to divide.
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Subtract the divisor. Subtract the divisor from the dividend.
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Keep Subtracting. Subtract the divisor from the result of the previous subtraction. Continue this process.
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Count the Subtractions. Keep track of how many times you subtract the divisor.
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Stop When You Reach Zero or a Remainder. Stop subtracting when you reach zero (meaning the divisor divides the dividend evenly) or when you get a number smaller than the divisor (this is your remainder).
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The number of times you subtracted the divisor is the quotient.
Example
Let's say we want to divide 12 by 3 (12 ÷ 3). We'll use repeated subtraction. The reference mentions the example of 12 - 3.
- Start with 12.
- 12 - 3 = 9 (1st subtraction)
- 9 - 3 = 6 (2nd subtraction)
- 6 - 3 = 3 (3rd subtraction)
- 3 - 3 = 0 (4th subtraction)
Since we subtracted 3 four times to reach 0, 12 ÷ 3 = 4.
Another Example with a Remainder
Let's divide 14 by 3 (14 ÷ 3) using repeated subtraction.
- Start with 14.
- 14 - 3 = 11 (1st subtraction)
- 11 - 3 = 8 (2nd subtraction)
- 8 - 3 = 5 (3rd subtraction)
- 5 - 3 = 2 (4th subtraction)
Now we have 2, which is less than our divisor 3. So, we stop. We subtracted 3 four times, and we have a remainder of 2. Therefore, 14 ÷ 3 = 4 with a remainder of 2.
Summary
- Repeated subtraction is a simple way to understand division.
- It involves repeatedly subtracting the divisor from the dividend until you reach zero or a remainder.
- The number of subtractions gives you the quotient.
