Partial quotients
An alternative to long division is the partial quotients method, also called the chunking method. It looks a bit like long division, but the calculation is simpler and clearer, especially for students who have difficulty with traditional long division.
Example partial quotients
We will explain partial quotient division using an example. You will then also understand why it is also called the chunking method. You always take a chuck out of the number to be divided. Ultimately, you always work as close to 0 as possible.
In our example we divide the number 936 by 8. We write this as follows:
| 8 | 9 | 3 | 6 | ||||
We are now going to take a chunk out of the number to be divided (936). This chunk can be different for everyone; the point is that you determine how often the divisor 8 fits into a part of the large number. For example, the number 800 is smaller than 936 and our divisor 8 fits into it 100x. We then write this as follows:
| 8 | 9 | 3 | 6 | ||||
| 8 | 0 | 0 | × | 1 | 0 | 0 | |
Now we subtract this 800 from our large number 936 and we are left with 136:
| 8 | 9 | 3 | 6 | ||||
| - | 8 | 0 | 0 | × | 1 | 0 | 0 |
| 1 | 3 | 6 | |||||
Now we are going to divide the remaining 136 further. The number 80 is smaller than 136 and our divisor 8 fits in here 10 times. This looks like this:
| 8 | 9 | 3 | 6 | ||||
| - | 8 | 0 | 0 | × | 1 | 0 | 0 |
| 1 | 3 | 6 | |||||
| 8 | 0 | × | 1 | 0 |
We subtract this 80 from 136 and we are left with 56:
| 8 | 9 | 3 | 6 | ||||
| - | 8 | 0 | 0 | × | 1 | 0 | 0 |
| 1 | 3 | 6 | |||||
| - | 8 | 0 | × | 1 | 0 | ||
| 5 | 6 |
As for the remaining 56, you may quickly see that our 8 fits in here 7 times (8 × 7 = 56). When we then subtract this 56, we are left with 0. This looks like this:
| 8 | 9 | 3 | 6 | ||||
| - | 8 | 0 | 0 | × | 1 | 0 | 0 |
| 1 | 3 | 6 | |||||
| - | 8 | 0 | × | 1 | 0 | ||
| 5 | 6 | ||||||
| - | 5 | 6 | × | 7 | |||
| 0 |
Because we are left with 0, we cannot divide our large number any further, so our division is complete. The result of the division is the sum of numbers to the right of the large bracket. So we add:
So the answer is 117:
We write the result above the dividend, the complete calculation then looks like this:
| 1 | 1 | 7 | |||||
| 8 | 9 | 3 | 6 | ||||
| - | 8 | 0 | 0 | × | 1 | 0 | 0 |
| 1 | 3 | 6 | |||||
| - | 8 | 0 | × | 1 | 0 | ||
| 5 | 6 | ||||||
| - | 5 | 6 | × | 7 | |||
| 0 |
Just like with long division, you can also have a remainder with column division. In this example, we had no remainder (after the last chunk, we had 0).
Partial quotients method vs Chunking
In the US, the partial quotients method is used in many elementary schools as an alternative to traditional long division. This method encourages students to solve the problem in steps by subtracting large chunks of the number based on estimates.
In the UK, the term "chunking" is common. Again, it involves gradually subtracting larger parts of the number, without going straight to the exact quotient as in long division.
Both methods are therefore largely the same, although the way in which they are worked out, or in other words how they are written down, can differ between countries.
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