[alancalverd (OP)]

I've just seen a TV advert for a detergent that requires "four times less scrubbing" to remove grease.

Now one times A equals A  so one times less A = 0. No problem with that.

But what does 4 times less A mean? Does the detergent remove the grease from next week's dinner too?

[Bored chemist]

It's what happens when maths meets advertising.
Many products now offer remove or kill "up to 100%" of something.
I dare say it's accurate... the range includes zero.

[evan_au]

I think it is shorthand for "one quarter of"
- But understandable by people who are comfortable with the counting numbers, but uncomfortable with fractions...

I suspect that the quantity that is reduced to a quarter is the mechanical energy of scrubbing - perhaps this new product chemically reacts or dissolves the dirt, much better than (say) water.

It is possible that "one quarter of the energy expended in scrubbing" translates into "one quarter of the time spent scrubbing"
- However, I am sure that it does not mean that it removes dirt, three-quarters of which has not yet been generated

[vhfpmr]

Four times more: multiply by four
Four times less: divide by four, i.e. less, by  a factor of four.

[Bored chemist]

Four times more: multiply by four
Four times less: divide by four, i.e. less, by  a factor of four.

The problem is it's unorthodox use of language.
We use "less" for subtraction and "times" for multiplication.

[vhfpmr]

Four times more: multiply by four
Four times less: divide by four, i.e. less, by  a factor of four.

The problem is it's unorthodox use of language.
We use "less" for subtraction and "times" for multiplication.

Minus is the opposite of plus, less is the opposite of more.

[Bored chemist]

Four times more: multiply by four
Four times less: divide by four, i.e. less, by  a factor of four.

The problem is it's unorthodox use of language.
We use "less" for subtraction and "times" for multiplication.

Minus is the opposite of plus, less is the opposite of more.

Your observation seems the opposite of useful.

[alancalverd (OP)]

Four times more: multiply by four
Four times less: divide by four, i.e. less, by  a factor of four.

So one times less = ?

[varsigma]

With numbers, doesn't "times" mean iterated addition?

Like 3 times 6 is 3 added six times, right? LIkewise "times less" means iterated subtraction, i.e. division.

What if the product only gives me 3.2 times less whatever? How do I logically deal with that? Or if I can't determine how close to 4 times less my individual result is? I invoke statistics, of course.

[Bored chemist]

Four times more: multiply by four
Four times less: divide by four, i.e. less, by  a factor of four.

So one times less = ?

It probably = bad grammar.
One time fewer.

[alancalverd (OP)]

LIkewise "times less" means iterated subtraction

So 1 times less = 0
and n times less (n>1) = ?

[paul cotter]

Four times less is obviously=−3. So the real question is how one does −3 scrubbing sessions?

[Zer0]

It's Obviously the Opposite of...
" Four times More " .

ps - : )~

[alancalverd (OP)]

However I  interpret "opposite", whether by arithmetic or geometry, it still implies that the detergent will remove grease  that doesn't exist yet.

Oddly, that would work if you wash up in a bowl, because you could save the scummy cold water for another day, but this advert was for dishwasher capsules so it would all get flushed away the first time you used it. 

[paul cotter]

Maybe it removes negative grease, so you end up with plates covered in gank?

[paul cotter]

Maybe it strips the grease, the glaze, the pattern and half the base ceramic as if it were a bath of molten sodium hydroxide? That adds up to four times.

[Petrochemicals]

Four times, less scrubbing. Scrubbing required by Brand Y ? 4= the ammount of scrubbing you will have to do with Brand X minus the Scrubbing required by Brand Y ----->  5(scrubbing brand y) = scrubbing brand X.


But it could also be

Scrubbing required by Brand X?4= the ammount of scrubbing you will have to do with Brand Y.

[alancalverd (OP)]

However you phrase it, 1 times less than Y  is obviously  Y - Y = 0, whatever Y may be, so 4 times less is Y- 4Y = - 3Y, which invokes the concept of negative scrubbing.

[Zer0]

Good Point @ PC!

The process of Scrubbing perhaps has a Specific lower limit.

For an Object A____B

say 4 times from point A to B, n similarly 4 return strokes from B to A.
Total = 8

' Four Times Less '
8/4 = 2

ps - I don't get maths, Sorry if it makes No sense.

* Whatever the liquid/gel/solution is in question, it seems pretty acidic...
I'd suggest using gloves..
Made of Steel.

[alancalverd (OP)]

 No. "Less" means "subtract". Look at this standard invoice:

Goods delivered as specified              $500

Less deposit received in advance       $200 

Total now due                                      $300

By your bizarre arithmetic you'd invoice for $500/200 = $2.50 and be out of business in a week.