1. terminology question

In mathematics, when something is a factor 4 better/worse, does it mean that compared with something else, it is 4 times larger in value.

Will

In mathematics, when something is a factor 4 better/worse, does it mean that compared with something else, it is 4 times larger in value.

Will
you mean if a=4b this equivalent to a=b+b+b+b then a is 4times larger than b if b equal 1 then a equal 4
since you need four amount of b to put the equality I wish it is clear

if

$\displaystyle a=\frac{b}{4}$ here b is 4 times larger than a since the quarter of b equal a it is clear I think

In mathematics, when something is a factor 4 better/worse, does it mean that compared with something else, it is 4 times larger in value.

Will
If I understand your question correctly, the answer is basically yes, you are correct. Suppose for instance that Laundry Detergent A is 4 times more effective at removing stains that Laundry Detergent B. That means that if Detergent B removes 20% of all stains, then Detergent A removes 80% of stains.

Hope that's clear.

4. Originally Posted by AlephZero
If I understand your question correctly, the answer is basically yes, you are correct. Suppose for instance that Laundry Detergent A is 4 times more effective at removing stains that Laundry Detergent B. That means that if Detergent B removes 20% of all stains, then Detergent A removes 80% of stains.

Hope that's clear.
Is it though?
Purely on a semantical point - and I'm not disagreeing with your answer, but if, say, a box of cornflakes contains 1kg of cornflakes, then a box that contains 4 times as many would contain 4kg, right? But would a box that contains 4 times more contain 5kg?

5. That is what I would say. "Four times as much" is 4x. "Four times more" is x+ 4x= 5x.

Of course, I have no idea which of those "factor 4 better/worse" is supposed to mean!

(Oh, and "4 more or less" is $\displaystyle x\pm 4$.)

6. Originally Posted by Unenlightened
Is it though?
Purely on a semantical point - and I'm not disagreeing with your answer, but if, say, a box of cornflakes contains 1kg of cornflakes, then a box that contains 4 times as many would contain 4kg, right? But would a box that contains 4 times more contain 5kg?
You're quite right; I should have chosen my words better.

No wonder I am constantly fleeced at the grocery store!