# What does "25% less than X" mean ?

How so? Typically, it’s either multiply, or multiply and add, depending on how its phrased. John has 5 cards. Mary has twice as many cards as John. Mary, therefore, has 10 cards. Mary has two times more cards than John. Now, here, it’s a bit of a language issue. It means either Mary has 15 cards or 10 cards. I think most people say it to mean the latter, but the former is the more literal interpretation (as shown in the recent Straight Dope thread on a word problem with this exact issue.) In neither case do I see how multiplication and subtraction comes into it, unless I am misunderstanding what you are saying.

5 times less or more would imply multiplying by 5. Plain and simple.

“Y is 11 times AS MUCH AS X” means Y = (?) * X

Please tell me what number is represented by (?), when the above statement is true.

No —
5 times MORE than
5 times as many as

There’s a difference -
MORE than means the delta is 5 times the original number

That’s why “5 times less than” - while it has slipped into usage as meaning 1/5 is poor construction.

Five times less than should actually be X - 5X… which would be (minus) 4X

If you want “five times less than” - you should use 20% of or “Only 1/5 of” or if you wanna be dramatic - “tumbled by 4/5” or “plummeted by 80%”

How many is five times AS MUCH AS twenty?

EXACTLY. Using “more than” or “less than” in a comparative statement of quantities means* that there is a delta between the quantities being compared. Having “(n) times” in the statement means** that the magnitude of that delta is (n) multiplied by whichever quantity is being used as the reference.

*I invite the alert reader to note that I used “means,” and not “implies.” There is a reason for this.

** See (*), above.

“Times less” is like “Divided more”. We could all agree that the form of words means some specific thing, but the words don’t naturally mean the right thing.

Again, regardless of whether it makes sense or not, “X times less than” is unambiguous, because it always means the same thing. How it came to mean that thing might be convoluted, but that’s what it means.

I think that was already abundantly acknowledged.

Well, no, as you see with the responses above, it’s ambiguous. But I’m most curious what you meant by “multiply first then subtract.” Subtract what?

Reading that in George Carlin’s newsman voice makes it hilarious!

/hijack

No it doesn’t. For a bunch of reasons.

The first reason is that you can’t translate things word for word. Yes, “times” generally means multiply, and “less than” generally means subtract, but putting them together makes a phrase that means “divide by”.

The second reason is that it makes plenty of sense that if “x times more than” means multiply by x, then “x times less than” means divide by x. Because division is the reciprocal of multiplication, so if you multiply in the “more” direction, then you divide in the “less” direction.

The third reason is that multiply first then subtract will change the sign of your result, which from context almost never makes any sense. When you have a supposedly “ambiguous” phrase with two possible interpretations, and one of them is nonsensical, then it’s not really that ambiguous. I say “I just flew in from New York” this morning, that phrase isn’t ambiguous because I didn’t specify that it was on a plane. Because the other interpretations are silly.

It is a sign of general innumeracy. Even when I know what the words mean, I can’t assume the author did, so I still don’t know for certain what they meant.

The unambiguous construction is “X is 5% of Y” The common construction is “X is 95% less than Y”.

“X is 20 times less than Y” is just pathetic. “X is 1/20th Y” is clear.

If “five times more than 20” is 5 x 20 = 100 what is “fifty percent more than 20?” Using the same logic it’s 10, which is clearly wrong.

However, if “five times more than 20” means 5 x 20 + 20 = 120. Then “fifty percent more than 20” mean 0.5 * 20 + 20 = 30. Which is clearly what is meant.

People seem to really dislike this phrasing, but that doesn’t make it

English is not a context free grammar. There really is no reason that “x % more than y” has to be parsed in exactly the same way as “x times more than y”. Both are unambiguous and reasonable in normal conversation. They simply aren’t consistent with each other.

x% more than y means Y + x/100
x times more than y means x * y
x times less than y means y / x

Just change your language. If something is “twice as slow” just say it’s “half as fast”. The only people who ever write ambiguous statements like these are journalists who don’t know math. I’ve never seen a legit scientist, engineer, or mathematician say “five times less”, unless something happened 100 times yesterday, and today it happened 95 times, or “five times less”.

Percentage wise, it makes sense. 25% less is 75% of the original number. Of course, when you’re talking percentages of percentages, you get more ambiguity, so don’t do that. Just say “the likelihood of rain increased to 50% today, up from 25% yesterday”.

“2 times more than” is not unambiguous.

this is utter tripe and uncontrovertibly wrong

MORE THAN means the difference between the two

50% more than 100 is 150.
Just substitute in numbers to see why
Today there are 5 times MORE people in the office than yesterday
there are 500% more people than yesterday
So there are 600 people in the office today

You could also say that rain is twice as likely today as yesterday.

Or

the likelihood of rain has doubled

This is actually one of my pet peeves and I hate imprecision is math…once this sort of thing starts to slip into common usage, and words stop having meaning - then the whole thing goes downhill.

You can already see here that while nobody is misunderstanding the actual meaning of “5 times less than”, SOME people are trying to use the reverse logic for 5 times more than - which is wrong wrong wrong.
And if we take “5 times more than” to mean the same as “5 times less than” - how then do we explain percentages?
My wife’s pay is 120% of mine
My wife gets paid 20% more than me
My brother earns 240% of my meager salary
my brother earns almost 2.5 times my salary.
My brother earns 1.4 times more than me.

All are easily understandable if you the words don’t shift in meaning

Once you allow the words to slip around then you get confusion - which makes math harder to understand, not easier.

The problem is, as much as I agree with you benganmo and that’s exactly how I solved that one word problem that was in a similar thread (about “what two times more” means in a word problem involving someone running four laps, i.e., that it’s 12), I actually can’t find any written usage in a cursory Google news search that shows anybody using “two times more” or such constructions to mean anything but “twice as many as.” So it appears the war has long been over and “two times more” means “twice as many as,” although I personally avoid “X times more” constructions all together.