When “thinking mathematically,” most people think in proportions. For example, if someone is baking cookies and they want to make a double batch, they intuitively know they need to double the amount of all ingredients.
If someone was told a 100-horsepower engine, at full throttle, could make a certain car go 100 miles per hour, and was then asked how fast a 200-horsepower engine would make the same car go, he’s likely to answer 200 mph.