Definition
Scaling
Scaling multiplies every matching quantity by the same factor.
Continue from this idea into connected AXIO math.
What it means
Think of one multiplier travelling through a set of matching amounts. If the number of snack bags is multiplied by 3, each ingredient amount must also be multiplied by 3. A factor greater than 1 scales up, a factor between 0 and 1 scales down, and a factor of 1 leaves the quantities unchanged. Adding the same amount to each quantity is not scaling.
Remember it
One multiplier travels to every matching amount.
Example
A mix for 2 snack bags uses 1 scoop of oats and 2 spoons of seeds. To make 6 bags, first find the factor: 6 ÷ 2 = 3. Multiply each matching amount by 3, so the new mix uses 3 scoops of oats and 6 spoons of seeds.
Watch for
Changing 1 scoop to 3 scoops but 2 spoons to 5 spoons is not one scaling, because the matching quantities did not use the same factor.
Common mix-up
Scaling is not the same as adding the same number. Multiplying 1 and 2 by 3 gives 3 and 6; adding 2 gives 3 and 4.
Exact meaning
Scaling is a multiplicative change in which every corresponding quantity is multiplied by the same positive scale factor, so proportional relationships among the quantities are preserved.