# Does “less than” really mean “subtracted from”, or is it bad English?

I got involved in a discussion about some Math problems provided in the local primary school education:

• 20 more than 543 is 563
• 25 less than 261 is 236
• 155 less than 310 is 155
• 355 more than 1233 is 1588

Some of us (including me) argued that this is unclear or incorrect English, while others said that it is correct or that we are not creative if we do not understand it (huh?).

In my own Math education, I have learnt that "less than" and "more than" (or rather, "greater than") are comparative operators. However, in the above, they are used as manipulative operators (subtraction or addition) - a usage I never learnt.

At first I thought this must be something peculiar with the Singapore Math education, as those who argued that this is incorrect are mostly foreigners, while the other side is made up of mostly locals.

After some searching for similar use on the Internet, the two instances I could find are an exercise paper from Math Activities Resource Center, Mt. San Antonio College, Walnut, CA (USA) [link], and a lecture paper from Professor Weissman's Algebra Classroom [link].

In the exercise paper, the lecturer also mentions that "less than" is different from "is less than", in that "less than" is used to mean subtraction (where the numbers are inverted), whereas "is less than" is used to compare two numbers.

In the lecture paper, it is mentioned that "3 is less than 7" translates to "3<7", "3 less than 7" translates to "7-3" and "3 less 7" translates to "3-7".

I want to hear from some experts regarding how correct and/or widespread this kind of usage of these terms is. No matter how many times I read the examples back to myself I feel it's odd and wrong to use it this way, and that the correct usage for manipulation should be:

• 20 added to 543 is 563
• 25 subtracted from 261 is 236
• 155 subtracted from 310 is 155
• 355 added to 1233 is 1588

Whereas the correct usage for comparison should be:

• 20 more than 543 is False
• 25 less than 261 is True
• 155 less than 310 is True
• 355 more than 1233 is False
• `25 less than 261 is True`. No. `Is 25 less than 261?` might be `true`, but `25 less than 261` is saying how much less than 261. – starsplusplus Jan 23 '14 at 11:20
• True and False can only apply to propositions containing verbs. The mathematical equals is a verb, as is is less than. – Tim Lymington Jan 23 '14 at 14:16
• Both this word order and the inverted word order are correct English. I heard both in school and, as you state in response to Pete Kirkham, one "sounds normal" to you and me both. Using the reverse introduces cognitive dissonance, as does any unusual inversion of word order. This may be simply a technique to draw attention to the facts; my teachers certainly did this purposefully. But it does not make it grammatically incorrect. – shipr Jan 23 '14 at 19:15
• It's important to understand that "less than" and "less than" don't mean the same thing. – Hot Licks Oct 25 '16 at 0:51

The paper you found describing the difference between less than meaning subtraction and is less than meaning comparison is correct. Here are some examples from published English works I found in the Corpus of Contemporary American English. (more than query) (less than query):

For example, children need to learn that numbers later in the count list have larger quantities and that numbers themselves have magnitudes (e.g., 4 is one more than 3 and one less than 5)

— Jordan, Nancy et al. “Validating a Number Sense Screening Tool for Use in Kindergarten and First Grade: Prediction of Mathematics Proficiency in Third Grade” School Psychology Review, 2010

As the number of killings has crept this year to 95 -- seven more than the total for all of 2004 -- the city has only sporadically increased foot and bicycle patrols, key elements of any community policing plan.    — Jaxon Van Derbeken, Chronicle Staff Writer. San Francisco Chronicle, December 21, 2005

A month before your trip, you see a newspaper ad showing fares for the same trip are \$100 less than what you paid.
— Rosato, Donna. USA Today, October 8, 1996

The four-cam, 32-valve engine produces 280 horsepower, 15 less than the Northstar, and it drives the rear wheels through a new four-speed automatic transmission.

— Schuon, Marshall. New York Times “ABOUT CARS; With a New V8, Lincoln Introduces an All-New Mark VIII”, November 11, 1992

These are standard English usages, so get used to them.

• Nice answer but I'd like to see the difference between everyday language and formal math pointed out a little more. Most mathematicians probably wouldn't use `less than`. The same way you wouldn't say `A month before your trip, you see a newspaper ad showing fares for the same trip are what you paid substracted by 100\$.`. – André Stannek Jan 23 '14 at 14:32
• I'd say mathematicians use "less than" meaning "subtracted from" in spoken language. In publications I think they mostly use "-". – Zane Jan 23 '14 at 15:13
• 25 fewer than 100 is 75 sounds better than 25 less than 100 is 75, but I'd consider that a bit pedantic to complain about. Using fewer in this context seems to be gaining a lot of ground. – Martijn Jan 23 '14 at 15:48
• @AndréStannek as Zane says, formal math uses symbols, not words. Also, I'm not a mathematician, so I can't speak for them. That would be a question for math.SE. – nohat Jan 23 '14 at 17:07
• @Martijn as for less vs. fewer, see my highly-rated answer elsewhere. I'd wager that, without any kind of data to back it up, a claim about a usage that "seems to be gaining a lot of ground" is almost certainly just an example of the recency illusion. – nohat Jan 23 '14 at 17:11

Yes, if you are talking in strict mathematical terms, `less than` is a exclusively comparative operator.

However, outside mathematics, in everyday language, it is normal use it both as a comparative operator as well as to state a quantified difference. That means both these phrases are correct:

I have less apples than you.

I have ten apples less than you.

In the first case, I am just comparing the amount of apples we both possess, but in the second case I am quantifying the difference. In mathematics, I could describe that situation as:

My amount of apples is 10 subtracted from your amount of apples

Or

X = Y - 10

Since your examples come from a primary school environment, I do not find it strange that more natural language is used rather than strict mathematical language in order to teach children the basics of calculus.

`25 less than 261 is 236` is much closer to what a child would hear in everyday speech (1 apple less than 5 is 4 apples) and as such it leaves the child to ponder the actual numbers rather than a new jargon (I am not sure many primary school kids are familiar with the vocabulary of subtraction, multiplication and addition).

Indeed, for multiplication I would expect lines like

3 times 4 is 12

3 multiplied by 4 equals 12

As a matter of fact, the former is the exact form in which I was taught to memorize my tables of multiplication (albeit in Dutch, not English).

• Agreed. My children were taught both ways: less than and minus early on. – anongoodnurse Jan 23 '14 at 7:56
• Argh. Less is not the same as fewer. – Andrew Leach Jan 23 '14 at 12:27
• The mathematical symbol (not strictly an operator) should be pronounced is less than. – Tim Lymington Jan 23 '14 at 14:07

One the one side, constructs of the form "a is b-a less than b" are common as English statements. Similarly "a is b-a below b", "a is b-a from b", inside, outside, under etc. where you are comparing quantities and can have a sentence which either indicates the truth of the comparison or the magnitude of the difference.

Many such quantified comparisons can include the difference. "the diver is below the surface" and "the diver is six fathoms below the surface"; "the church was outside the city wall", "the church was three miles outside the city wall", "Anne is less than ten years old", "Ann is one day less than ten years old" are all common.

But the examples you give are "b-a less than b is a" are a backwards "six fathoms below the surface is the diver"; "three miles outside the city wall is the church", "one day less than ten years old is Anne" are unusual word orders.

If they were intended as questions, then either "what is 25 less than 261?" or on a page "_ is 25 less than 261" to fill in the blank would be more normal phrasing.

• You touched on something I forgot to add. Indeed, `a is b less than c` seems correct to me due to the word order, but not `b less than c is a`, which seems rather odd. – ADTC Jan 23 '14 at 13:35

25 subtracted from 261 is 236 is clear. Because we know what subtraction is, we don't give it a second thought.

However, 25 less than 261 is 236 is also clear. If one thinks concretely about what is said, it reads (to me)

25 fewer than/taken away from 261 is 236.

One can also express it as "236 is 25 less than 261"

Arguably, the 'subtract' binary operation in maths covers three different situations. I'll start by covering the easier situation with the 'add' operation:

(a) Combine a number of elements from set A with a number from set B {3 + 4 = 7}

(b) Increase a base figure by a certain amount {3 --- (+4) ---> 7} {3 has been transformed (increased) to 7}

For the corresponding subtraction:

(c) Split a quantity into two sub-quantities, taking off a chosen number, and identify what's left {7 - 4 = 3} {7 has been partitioned into 4 and 3}

(d) Reduce a quantity by a chosen number to leave a reduced number {7 ---(-4) --->3} {7 has been transformed (reduced) to 3}

(e) Identify how much greater one number is than a second {7 - 4 = 3} {7 is 3 more than 4; 4 is 3 less than 7}.

The model for working out 'the answer' to c, d and e is of course identical, usually written 7 - 4 = 3. This convenience masks the type of situation being modelled. (Though often, especially in the teaching of maths, operations are shown over arrows to indicate transformations rather than splittings / finding differences. Ferrers graphs may be used to show partitions.)

The language used (minus, subtract, take, take away, less / less than // add, plus, and / more than) can correspond either to the general model or to the actual situation being modelled.

That's a shorthand way of stating a rather plain sentence of the format:

A notch less than perfect is not good enough.

[A notch] less than [perfect] is [not good enough.]

 less than  is .

or rephrasing:

A number by 25 less than the number 261 is the number 236.

In the USA in an everyday usage setting NOBODY ever uses the expression "25 less than 3 = 22." That is a confusing statement. You will hear "25 less 3 = 22" infrequently although it is correct usage to describe a subtraction operation.

The correct usage would be to say "25 minus 3 = 22" or "3 subtracted from 25 = 22 or "subtracting 3 from 25 = 22."

The terms "more than" or "less than" are pretty much only used as a comparison operator as in "3 is less than 25."

That's just here in the USA. Other English speaking countries may have their own syntax that would make your version correct.

• The syntax in question is not `25 less than 3 is 22`, which would be wrong, but rather `3 less than 25 is 22`, which is entirely understandable and acceptable in US English, despite being less common than `25 minus 3 is 22`. – WinnieNicklaus Jan 23 '14 at 18:28

Seems to be common in English schools. As a child of the age they use this type of language on is hardly likely to understand the semantics and hardly likely to understand the complexities of an unusual grammatical construct, they just learn 'less than' as one meme meaning the operation subtract. Some then get confused when the word than is used in the comparative because their reading skills are not good or honed and they jump to conclusions. Why not keep concepts simple at age 5? I think this is just change for changes sake and muddies the waters for kids.

In the same vein, no longer using the passive to describe chemistry experiments loses a cross-training opportunity yet we are now expecting children to learn about gerunds in primary school.

• Welcome to ELU.SE. Mary, while your answer is fitting, this site strives to provide objective answers. As it stands your answer seems purely subjective and could be improved by adding references. Take the tour or have a look at the help center to find out more about good answers. – Helmar Oct 8 '16 at 9:27