You subtract partial products in division to break down a larger division problem into a series of smaller, more manageable steps. You repeatedly estimate how many times the divisor goes into the dividend, multiply that estimate by the divisor (the partial product), and then subtract that partial product from the dividend. This process continues until you reach a remainder that is smaller than the divisor.
Here's a breakdown of the process:
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Estimate: Look at the dividend and divisor. Estimate how many times the divisor can go into the dividend. This is your first partial quotient.
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Multiply: Multiply your estimated partial quotient by the divisor. This is your partial product.
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Subtract: Subtract the partial product from the dividend. This leaves you with a new, smaller dividend.
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Repeat: Repeat steps 1-3 with the new dividend. Continue estimating, multiplying, and subtracting until the remaining number is less than the divisor.
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Add Partial Quotients: Add all the partial quotients you found in each step. This sum is the quotient (the answer to the division problem).
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Remainder: If you have a number remaining that is less than the divisor, that is your remainder.
Example:
Let's say you want to divide 104 by 8.
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Estimate: You know 8 goes into 104 at least 10 times. So, our first partial quotient is 10.
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Multiply: 10 * 8 = 80 (This is our first partial product)
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Subtract: 104 - 80 = 24
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Repeat: Now we divide 24 by 8. We know 8 goes into 24 exactly 3 times. Our next partial quotient is 3.
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Multiply: 3 * 8 = 24 (This is our second partial product)
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Subtract: 24 - 24 = 0
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Add Partial Quotients: 10 + 3 = 13.
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Remainder: We have a remainder of 0.
Therefore, 104 / 8 = 13.
In essence, using partial products allows you to approximate the answer piece by piece, making division easier to understand and perform, especially with larger numbers. You're breaking down the larger division problem into a series of smaller multiplication and subtraction problems.
