Is half of an amount stated as 50% less or 100% less? [closed]

I've struggled with this concept and have generally interpreted it one way for all of my life, which leads me to believe people are incorrect when they state the other form. And honestly I'm not really sure this is even the correct SE site but I figured there wasn't a better choice.

Here it is:

If I have a basket of 10 apples and I remove 5 apples, do I have 50% fewer apples? Or 100% fewer apples? I tend to consider the correct phrasing by performing: (original amount as a fraction / (new amount as a fraction) - 1) * 100%

So therefore 5 apples is now 0.5 of what I previously had, giving ((1 / .5) - 1) * 100%, giving 100% less. I think this phrasing I choose is motivated by the fact that when someone says: Basket A has 10 apples and basket B has 20 apples, therefore basket B has 100% more apples. So it leads me to believe twice as much is 100% more, and then half as much would be 100% less. It would not make sense to me if twice as many apples were 100% more, yet half as many apples were 50% less.

Where this gets confusing

If my interpretation above is correct, then I commonly see people making the mistake when dealing with different amounts that don't make this obvious. For instance about a year ago, a professor of mine said: Processor A runs at 9/10 the speed of processor B, therefore it is 10% slower. I raised my hand and explained it should be 11.1% slower since (1 / 0.9) - 1 * 100% gives 11.1%, arguing that if processor B ran at half the speed, we wouldn't claim it ran 50% slower

He agreed, but I'm still not sure I use this phrase correctly.

Going along the same lines, I generally struggle with the differences between % of an amount vs. % more than an amount, for amounts greater than 100.

It seems logical than 50% of is plain multiplcation. Therefore Qty A is 50% of Qty B means Qty A = Qty B * 0.5. And also 50% more than would be 100% + 0.5 * amount, so Qty A is 50% more than Qty B means Qty A = 1.00 + Qty B * 0.5.

So if that is true, then of means pure multiplication, while more than means multiplication by 2nd amount and added to the original.

But this seems to be very confusing for amount larger than 100%.

For example: Qty A is 200% of Qty B So Qty A = Qty B * 2? And Qty A is 200% more than Qty B is Qty A = 1.00 + 2 * Qty B? That means the phrasing 200% more than really means 3x as much!

closed as off-topic by Drew, Centaurus, Marthaª, tchrist♦, 200_successMar 18 '15 at 11:04

• This question does not appear to be about English language and usage within the scope defined in the help center.
If this question can be reworded to fit the rules in the help center, please edit the question.

• Basically the only thing in this question that isn’t completely wrong and off basis is the last paragraph. Colloquially, you’ll hear people say (if A = 200 and B = 100) that “A is 200% more than B”; but logically speaking, A is 200% of B, but only 100% more than B. You’re correct there. Everything else you say is just wrong. Percentages are calculated based on the original amount, not on the amount after performing a mathematical operation. You have 50% fewer apples, Processor A runs 10% slower. Your professor shouldn’t have agreed, ’cause you were wrong. – Janus Bahs Jacquet Mar 18 '15 at 1:10
• I'm voting to close this question as off-topic because it is a question about arithmetic, not English. – Drew Mar 18 '15 at 1:13
• @JanusBahsJacquet Good to know! I had that suspicious feeling that was the case. – krb686 Mar 18 '15 at 1:13
• I have to agree with Drew: while the sloppiness of English often leaves room for math-centered questions to be fully on topic on ELU, in this case your confusion is with the basic math involved, not with the language used to describe it, and thus your question is off-topic. – Marthaª Mar 18 '15 at 3:15
• @Drew This is not a question about arithmetic. All the math is fine, it's just the wrong math for the phrase. It's a question about which mathematical concept is represented by an English phrase in common usage. – DCShannon Mar 18 '15 at 4:29

The correct expression is 50% fewer generally, as 50% of 10 is of course 5, while 100% less would be exactly zero.

Notice that 100% more would be 20 and that 50% more would be 15.

Then again, 100% of the original would be the same (10), while 300% would be 30.

• So then twice as many is 100% more or 200% of, and half as many is both 50% fewer AND 50% of? – krb686 Mar 18 '15 at 1:07
• Yes, that is correct. 50% less is the same as 50% of, however 25% less than 100 is 75, which is more than 25% of 100 which is 25. – veryRandomMe Mar 18 '15 at 1:09
• @krb686: That's right, since 100% - 50% = 50% – sumelic Mar 18 '15 at 1:10

I was a high school math teacher for a little while, and explaining the connection between English phrases like this and the corresponding math is a huge part of teaching story problems. Most of the math teachers I spoke with at the time agreed that these concepts should be taught in both English and math classes, and the English teachers were beginning to have story problem segments in their classes.

The more than/less than phrases are based on addition and subtraction, and the of phrasing is based on multiplication.

x% more than / x% less than

The phrase more than indicates addition, and the phrase less than indicates subtraction. When we say 50% more we mean to add 50% of the original amount. Similarly, when we say 50% less, we mean to subtract 50% of the original value.

x% more than y = y + y*(x/100)

So 50% more than 10 is 10 + 5 = 15, and 250% more than 10 is 10 + 25 = 35.

Note that the difference between the 250% more value and the 50% more value is 35 - 15 = 20, which is 200% of the original value. This is as it should be, as 250% - 50% = 200%.

x% less than y = y - y*(x/100)

So 50% less than 10 is 10 - 5 = 5. We don't often say less than with a percentage greater than 100%, but 250% less than 10 is 10 - 25 = -15.

Common Confusion

I do sometimes see this phrasing used incorrectly when speakers attempt to reverse statements. This will lead to one speaker saying something along the lines of "we had 20% more revenue this year than last year", and then another speaker will say something like "...last year we had 20% less revenue", but this second statement is not correct.

This is because if A is x% less than B, it is not the case that B is x% more than A. Example:

• 8 is 20% less than 10. 10 is 25% more than 8.
• 9 is 10% less than 10. 10 is 11.1% more than 9.
• 5 is 50% less than 10. 10 is 100% more than 5.
• 5 is 75% less than 20. 20 is 300% more than 5.

I expect you probably noticed this, and concluded that you were getting one of the numbers wrong because the values did not match. It's okay, they're not supposed to match.

Note: The only place I can think of where I've seen percentages handled in the way you describe is in the math of some video games. The phrasing of the effects in question is usually not 50% less but instead something like 50% reduced _____. Specifically, in the Borderlands series of games, having a 100% reduction in something results in 50% as much of the thing. For instance, 100% damage reduction results in taking 50% damage, 200% damage reduction results in taking 33% damage, 300% damage reduction results in taking 25% damage, and so on.

• Your answer explains where, how, and why the OP could be confused by a seemingly obvious mathematical "definition". – Mari-Lou A Mar 18 '15 at 6:34
• The fact that you were teaching this in a math class, and not an English class, is significant. Beyond translating basic words such as percent, reduced, and fewer from English to arithmetic, this is not a question about English. The same would be true for a question about a logic problem (also typically in a math class or a philosophy class, not an English class): there is a basic translation of words such as and and or to logic, but beyond that it is about logic, not English. – Drew Mar 18 '15 at 13:32
• @Drew At the time I was teaching, it was becoming clear that students struggling with story problems were doing so because of English deficiencies at least as much as because of mathematical ones. To correct this, the English teachers were beginning to have story problem segments in their classes where they would elaborate on the connection between English phrases and mathematical ideas. – DCShannon Mar 18 '15 at 19:18
• @DCShannon: I believe you. Students need to be taught basic English - as well as elementary math jargon such as percent, increment, and reduced by 10%. Likewise introductory biology & physics jargon, economics jargon, etc. And this is so no matter how simple such jargon might seem to those who are familiar with it. None of us hatches from the egg knowing such things. IMHO, teaching such jargon is not for this site, in general. Likewise, teaching basic English. But mine is just one opinion. – Drew Mar 18 '15 at 23:25