Factor Change
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When a quantity gets larger or smaller, we say that it changes.
For example, the volume of a certain liquid in a container can change from 3 quarts to 12 quarts. One could simply imagine extra liquid being poured into the container taking the volume from 3 quarts to 12 quarts.
Factor changes are not additions.
We can talk about this change in volume in several ways. One way is to say that 9 quarts were added, since 3 quarts plus 9 quarts is equal to 12 quarts. Talking about the change this way, however, is not talking about it in terms of a factor change. This is talking about the change as an additive change, not a factor change.
Factor changes are multiplications.
To understand factor change, think about it this way: 3 times 4 equals 12. So, times 4 is the multiplier that changes the 3 quarts into 12 quarts. We say, therefore, that the volume changed by a factor of 4.
Factor changes are always discussed in terms of the multiplier that takes you from the initial quantity to the final, or changed, quantity.
A factor change of three (3):
If a distance changed from 5 meters to 15 meters, we would say that there was a factor change of 3 in the distance, since 5 times 3 is 15. We could also say, "The distance changed by a factor of 3."
A factor change of one half (1/2):
If a speed changed from 40 m/s to 20 m/s, we would say that the speed changed by a factor of 1/2. This is because 40 times 1/2 equals 20.
Again, the factor change in a quantity is the multiplier that takes you from the initial value of some quantity to the final, or changed, value of that quantity.
Here are some more examples:
| Initial Quantity | Final Quantity | Factor Change |
| 3 m | 30 m | 10 |
| 40 s | 10 s | 1/4 or 0.25 |
| 4.6 m/s | 12.8 m/s | 12.8/4.6 or about 2.78 |
| 5.3 kg | 1.1 kg | 1.1/5.3 or about 0.21 |
Notice that the factor change in a quantity can easily be calculated by taking the final quantity and dividing it by the initial quantity.
Proportions can be defined in terms of factor changes.
Factor changes are important to understand when discussing proportions. Here is some related material:
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