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

Factor changes are not additions or subtractions.

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.

As we shall see next, the above mathematics shows a ** factor
change 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,

*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, read across:

Initial Quantity |
Final Quantity |
Factor Change |
Since |

3 m | 30 m | 10 | (3 m)(10) = 30 m |

40 s | 10 s | 1/4 or 0.25 | (40 s)(1/4) = 10 s |

4.6 m/s | 12.8 m/s | 12.8/4.6 or about 2.78 | (4.6 m/s)(12.8/4.6) = 12.8 m/s |

5.3 kg | 1.1 kg | 1.1/5.3 or about 0.21 | (5.3 kg)(1.1/5.3) = 1.1 kg |

Notice that the factor change in a quantity can easily be calculated by taking the final quantity and dividing it by the initial quantity. For example:

- If a quantity starts out with a value of 7.2 (initially)
- And that quantity changes to a value of 9.6 (finally)
- Then the factor change is (9.6 / 7.2), or about 1.3
- Because 7.2 times (9.6 / 7.2) equals 9.6

Proportions can be defined in terms of factor changes.

Factor changes are important to understand when discussing proportions. Here is some related material: