# Divide 14 into 42.



## homotopy07

(1) Divide 14 into 42

(2) Divide 42 by 14.

Do these two sentences mean the same thing?

One of my English-Japanese dictionaries says (1) = (2).


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## bennymix

(1) is not usual phrasing.  {if it means 42/14}  
Sometimes we say '2 *goes into* 6, 3 times.  "2 goes into 6, how many times?"

{In the OP,  "14 goes into 42 how many times."}

Or delete 'goes'. 2 into 6 gives 3.

{Calculate 14 into 42.)


(2) is usual.


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## homotopy07

bennymix said:


> (1) is not usual phrasing.  {if it means 42/14}
> Sometimes we say '2 *goes into* 6, 3 times.  "2 goes into 6, how many times?"
> 
> {In the OP,  "14 goes into 42 how many times."}
> 
> Or delete 'goes'. 2 into 6 gives 3.
> 
> {Calculate 14 into 42.)
> 
> (2) is usual.


Thanks, bennymix. 

Do you think the following sentence is not normal?


Uncle Jack said:


> How many times can 30! be divided into 10?


"that divides" and "dividing"


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## dojibear

homotopy07 said:


> Do these two sentences mean the same thing?



Yes, they are the same. But you need to be careful with (1), because these two sound similar and both are common:

(1a) Divide 14 into 42. 
_14 goes into 42 three times. (42/14 = 3)_

(1b) Divide 14 into 42 parts. 
_How big is each part? (14/42 = 0.33 or 1/3)_

That is why "by" is safer and more common:

Divide 42 by 14 (42/14)
Multiply 42 by 14 (42x14)
Subtract 42 from 14 (14-42)
Add 14 to 42 (14+42)


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## dojibear

In math, 30! means "30 factorial", which is 1x2x3x4x5....x29x30. It is a large number


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## homotopy07

Thanks, dojibear.  Please look at the following sentences:


homotopy07 said:


> (5) How many times can 30! be divided evenly by 10?
> [my verbatim English translation of a problem from an entrance examination to a Japanese junior high school]
> (6) Find the exponent of the largest power of 10 that divides 30!.
> (7) Find the largest positive integer n such that 10ⁿ divides 30!


(8) How many times can 30! be divided into 10? [by Uncle Jack]

"that divides" and "dividing"

According to Uncle Jack, (6) and (8) mean the same thing. Do you agree?


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## bennymix

{Homotopy} (8) How many times can 30! be divided into 10? [by Uncle Jack]

I don't think this sentence is correct.  {I don't know if or where Uncle Jack said this.}


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## homotopy07

bennymix said:


> {I don't know if or where Uncle Jack said this.}


"that divides" and "dividing" (post #8)


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## dojibear

UJ says it in the middle of a paragraph. He does not have it marked "(8)"

I am not sure if it is a comment about example (5) or example (6). Either way, I think it is some kind of typo.

But I think it should be discussed in that thread, not in this different thread. Things get very confused if we have threads asking about comments in other threads, or we have to look at more than one thread to post a comment in this thread.


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## homotopy07

Thanks, dojibear. 

I thought I had to understand the use of "divide into" before asking a follow-up question to UJ, which is why I started this thread. I now think I understand the basic usage of "divide into" by virtue of your post #4.


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## dojibear

I started to comment in the other thread, but I stopped. It is possible that UJ uses "divide into" differently than I use it. That could be an AE/BE difference, or simply a regional difference. 

The only thing I'm sure I agree with is Uncle Jack's warning about using English grammar for arithmetic: 



Uncle Jack said:


> As I said in post #4, English can be quite poor when it comes to maths.


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## homotopy07

Thanks, dojibear. 

I thought "How many times can 30! be divided evenly by 10?" was natural because I had seen the following sentence:

The question becomes, how many times can 100! be divided by evenly by 5?
(Source)


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## Uncle Jack

"Divide into" is an awkward term, and I may well have misused it in another post. If you divide something into two, you halve it. If you divide it into four, you quarter it. If you divide 14 into 42, what do you do, exactly?


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## homotopy07

I now think my confusion has been cleared up. Thank you very much, Jack.


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## homotopy07

bennymix said:


> (1) is not usual phrasing.  {if it means 42/14}


Certainly, I have never seen a similar sentence to (1) in any of the following algebra/number theory books (if my memory serves me correctly).

Artin, _Algebra_, Pearson
Lang, _Algebra_, Springer
Rotman, _Advanced Modern Algebra_, AMS
Baker, _A Concise Introduction to the Theory of Numbers_, CUP



bennymix said:


> "2 goes into 6, how many times?"


How many times does 2 go into 6?

Is this sentence idiomatic?


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## bennymix

homotopy07 said:


> Certainly, I have never seen a similar sentence to (1) in any of the following algebra/number theory books (if my memory serves me correctly).
> 
> Artin, _Algebra_, Pearson
> Lang, _Algebra_, Springer
> Rotman, _Advanced Modern Algebra_, AMS
> Baker, _A Concise Introduction to the Theory of Numbers_, CUP
> 
> 
> How many times does 2 go into 6?
> 
> Is this sentence idiomatic?



Yes.


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## bennymix

Discussion of 'divide into' at stack exchange.
divide + "into" or "in"

It is NOT to be used as in (1) in the OP.   Several dictionaries support that "X divides into..."  mean that what follows are parts of  (i.e. smaller than)  X

DIVIDE | meaning in the Cambridge English Dictionary
_Knead the dough well, then divide it into four pieces.
_
I disagree with doji that his (1a) is "common".

[Doji post #4] (1a) Divide 14 into 42. 
_14 goes into 42 three times. (42/14 = 3)  _


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## elroy

homotopy07 said:


> (1) Divide 14 into 42
> 
> (2) Divide 42 by 14.
> 
> Do these two sentences mean the same thing?


 No. (1) means 14/42; (2) means 42/14.


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## homotopy07

bennymix said:


> Yes.





bennymix said:


> Discussion of 'divide into' at stack exchange.
> divide + "into" or "in"
> It is NOT to be used as in (1) in the OP.   Several dictionaries support that "X divides into..."  mean that what follows are parts of  (i.e. smaller than)  X
> DIVIDE | meaning in the Cambridge English Dictionary
> _Knead the dough well, then divide it into four pieces.
> _
> I disagree with doji that his (1a) is "common".
> [Doji post #4] (1a) Divide 14 into 42.
> _14 goes into 42 three times. (42/14 = 3)  _


Thank you very much, bennymix. 


elroy said:


> No. (1) means 14/42; (2) means 42/14.


Thank you very much, elroy.


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## kentix

homotopy07 said:


> How many times does 2 go into 6?
> 
> Is this sentence idiomatic?


I would say yes, but generally only when you are teaching a child very simple math with nice, round numbers that are easy to do in your head.

_How many times does 4 go into 12?
How many times does 27 go into 81?_

_What's 12 divided by 4?
What's 81 divided by 27?_

When you do grown-up math the number you are going to divide (and subtract from) comes first.

_What's 112 minus 68?_


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## homotopy07

kentix said:


> I would say yes, but generally only when you are teaching a child very simple math with nice, round numbers that are easy to do in your head.
> 
> _How many times does 4 go into 12?
> How many times does 27 go into 81?_
> 
> _What's 12 divided by 4?
> What's 81 divided by 27?_
> 
> When you do grown-up math the number you are going to divide (and subtract from) comes first.
> 
> _What's 112 minus 68?_


Thank you very much, kentix.


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## homotopy07

dojibear said:


> In math, 30! means "30 factorial", which is 1x2x3x4x5....x29x30. It is a large number


30! appears in the following problem:

Find the exponent of the largest power of 10 that divides 30!.

The fact that 30! is a large number is not an obstacle to solving this problem.

30÷5=*6
6*÷5=*1*.2
1.2÷5<1
*6*+*1*=*7*
30÷2=15>*7*
Hence, the answer is *7*.

(30! = 265252859812191058636308480000000.)


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## bennymix

homotopy07 said:


> 30! appears in the following problem:
> 
> Find the exponent of the largest power of 10 that divides 30!.
> 
> The fact that 30! is a large number is not an obstacle to solving this problem.
> 
> 30÷5=*6
> 6*÷5=*1*.2
> 1.2÷5<1
> *6*+*1*=*7*
> 30÷2=15>*7*
> Hence, the answer is *7*.
> 
> (30! = 265252859812191058636308480000000.)



For zeros:    
                   3 from the tens (10,20, 30)
                   4 from the fives (5,15, 25 [2])
                    7 total.

==
And for the record, we do NOT say, 10 divided into 30! equals 7.


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## Myridon

10 to the 32 divides into 30! with a remainder of 2.65....  (no one said evenly).


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## homotopy07

bennymix said:


> For zeros:
> 3 from the tens (10,20, 30)
> 4 from the fives (5,15, 25 [2])
> 7 total.


I guess 6th graders would prefer your explanation to mine.  (The problem is my English translation of one from an entrance examination to a Japanese junior high school, so the examinees were 6th graders.) I wrote my solution so that it can be applicable to the version with 30! replaced by 3000!, which is intended for junior high school students:

Find the exponent of the largest power of 10 that divides *3000!*.

3000÷5=*600*
600÷5=*120*
120÷5=*24*
24÷5=*4*.8
4.8÷5<1
*600*+*120*+*24*+*4*=*748*
3000÷2=1500>*748*
Hence, the answer is *748*.


bennymix said:


> And for the record, we do NOT say, 10 divided into 30! equals 7.


Thank you very much, bennymix. 


Myridon said:


> (no one said evenly).


Yes, I should have included "evenly". Thank you very much, Myridon.


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## bennymix

homotopy07 said:


> I guess 6th graders would prefer your explanation to mine.  (The problem is my English translation of one from an entrance examination to a Japanese junior high school, so the examinees were 6th graders.) I wrote my solution so that it can be applicable to the version with 30! replaced by 3000!, which is intended for junior high school students:
> 
> Find the exponent of the largest power of 10 that divides *3000!*.
> 
> 3000÷5=*600*
> 600÷5=*120*
> 120÷5=*24*
> 24÷5=*4*.8
> 4.8÷5<1
> *600*+*120*+*24*+*4*=*748*
> 3000÷2=1500>*748*
> Hence, the answer is *748*.
> 
> Thank you very much, bennymix.
> 
> Yes, I should have included "evenly". Thank you very much, Myridon.



Yes, nice work; it generalizes;  finds the powers of five in a given number.


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## homotopy07

bennymix said:


> Yes, nice work; it generalizes;  finds the powers of five in a given number.


Thanks a lot, bennymix.


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## Englishmypassion

And be careful while dealing with Indians, for whom _10 into 20_ is 200!


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## PaulQ

homotopy07 said:


> (1) Divide 14 into 42
> (2) Divide 42 by 14.
> 
> Do these two sentences mean the same thing?


Not to me - so my answer is "No". (1) appears ungrammatical and/or the wrong use of the verb "to divide."

"Divide 14 into ..." should be followed by, for example, "four parts".
Compare "Divide the cake into four slices and give one slice to each child."

In (2) *by *acts as an agentive preposition (It gives the means of the action of the verb.) This is correct.


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## homotopy07

homotopy07 said:


> The question becomes, how many times can 100! be divided *by* evenly by 5?
> (Source)


Sorry. 


Englishmypassion said:


> And be careful while dealing with Indians, for whom _10 into 20_ is 200!


Thank you very much, Englishmypassion. 


PaulQ said:


> Not to me - so my answer is "No". (1) appears ungrammatical and/or the wrong use of the verb "to divide."
> 
> "Divide 14 into ..." should be followed by, for example, "four parts".
> Compare "Divide the cake into four slices and give one slice to each child."
> 
> In (2) *by *acts as an agentive preposition (It gives the means of the action of the verb.) This is correct.


Thank very much, PaulQ.


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## prudent260

bennymix said:


> 2 into 6 gives 3.


Excuse me for restarting this thread.
*How should I ask the question?*
*How much* is 2 into 6? *What *is 2 into 6? I found both on Google Search, only one result for each one, and wonder which one is more idiomatic.
Thank you. 


Also I found this in the Oxford dictionary (divide | Definition of divide in English by Lexico Dictionaries): 
*3.2 *Find how many times (a number) is contained in another.
_‘divide 4 into 20’_

More example sentences

_‘If the hurricane was moving at 5 miles an hour and was expected to pass very close to your location, then divide 5 into 100. The answer is 20.’_
_‘How do you divide 6 into 612?’_
_‘If you divide 2 into 13983816 you get 6991908 or exactly half.’_


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## bennymix

I prefer  "What is 2 into 6?" and "divide 4 into 20", though I'm not so happy with the latter.


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## prudent260

bennymix said:


> I prefer  "What is 2 into 6?" and "divide 4 into 20", though I'm not so happy with the latter.



Thank you very much for the prompt answer.


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## Uncle Jack

prudent260 said:


> Excuse me for restarting this thread.
> *How should I ask the question?*
> *How much* is 2 into 6? *What *is 2 into 6? I found both on Google Search, only one result for each one, and wonder which one is more idiomatic.
> Thank you.
> 
> 
> Also I found this in the Oxford dictionary (divide | Definition of divide in English by Lexico Dictionaries):
> *3.2 *Find how many times (a number) is contained in another.
> _‘divide 4 into 20’_
> 
> More example sentences
> 
> _‘If the hurricane was moving at 5 miles an hour and was expected to pass very close to your location, then divide 5 into 100. The answer is 20.’_
> _‘How do you divide 6 into 612?’_
> _‘If you divide 2 into 13983816 you get 6991908 or exactly half.’_


As the previous discussion has said, the phrase "divide into" is very easy to misunderstand, and I suggest you do not use it. Certainly it used to be used, and you will find examples online and in dictionaries, but if you want to be unambiguously understood in modern English then I suggest you avoid it.

For the answer to calculations, "what" is usually a better question than "how much".


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## Andygc

I am astonished by those examples taken from lexico.com. I would *never *use these!! 


prudent260 said:


> _‘If the hurricane was moving at 5 miles an hour and was expected to pass very close to your location, then divide 5 into 100. The answer is 20.’_
> _‘How do you divide 6 into 612?’_
> _‘If you divide 2 into 13983816 you get 6991908 or exactly half.’_


Divide 5 into 100? That would be 0.05, wouldn't it?


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## Edinburgher

Andygc said:


> Divide 5 into 100? That would be 0.05, wouldn't it?


No, diving 5 *by* 100 would give 0.05, but dividing 5 *into* 100 gives 20.

I'm surprised to see BE-speakers unfamiliar with this "divide into" usage.  Baffling though it is (it had me confused when I first encountered it), it is nevertheless widespread.  Could it be peculiar to Scotland?


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## Andygc

I have never used it and can't remember ever having heard it. And my father was a Scot. If I divide one cake into 16 I get 16 pieces of cake. If I divide 5 into 100 I could, I suppose, get 100 little pieces of 0.05, but I wouldn't get 5 pieces of 20. Like others, if I want 20 I divide 100 by 5.

I echo the advice given earlier. If a learner of English doesn't want baffled looks, don't use _divide 5 into 100_.


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## Edinburgher

Andygc said:


> don't use _divide 5 into 100_.


I wholeheartedly support that advice.


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## Uncle Jack

Edinburgher said:


> I'm surprised to see BE-speakers unfamiliar with this "divide into" usage. Baffling though it is (it had me confused when I first encountered it), it is nevertheless widespread. Could it be peculiar to Scotland?


Well, I am familiar enough with this use of "into" from school ("three into five doesn't go", for example, meaning five divided by three is not an integer), and the usage might be fine in British schools, where nothing bad happens should someone misinterpret what you are saying, but I cannot recommend using "into" in any situation concerning division where a misunderstanding could have consequences.

Curiously, I note the the Open University still this wording in a page on long division: Numbers: Getting to grips with division, although not exactly in the form "divide _x_ into _y_".


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## Loob

Uncle Jack said:


> Curiously, I note the the Open University still this wording in a page on long division: Numbers: Getting to grips with division, although not exactly in the form "divide _x_ into _y_".


I think the OU is using "go into" rather than "divide into". Like others, I'm happy with that - it's when I see "divide into" that my brain starts turning somersaults.


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## RM1(SS)

homotopy07 said:


> (1) Divide 14 into 42
> 
> (2) Divide 42 by 14.
> 
> Do these two sentences mean the same thing?


I would say yes.


Edinburgher said:


> Baffling though it is (it had me confused when I first encountered it), it is nevertheless widespread. Could it be peculiar to Scotland?


I've heard it used here in the States.


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## pachanga7

I’m having the odd experience of stopping to question for the first time in my life how I would talk about division and hearing it rejected. 


homotopy07 said:


> (1) Divide 14 into 42
> 
> (2) Divide 42 by 14.
> 
> Do these two sentences mean the same thing?
> 
> One of my English-Japanese dictionaries says (1) = (2).


To me they are the same. We divide the divisor into the dividend, and the dividend by the divisor. 

As for potential confusion, I would distinguish some of the other examples given here by adding an object and making the number an adjective:

Let’s divide the proceeds into three equal parts. 
The walnut split cleanly into two pieces/halves. 

I don’t think I’d say “Divide 14 into 42 parts”, ever, whether in math class or outside of it. 

“In two” is a set phrase that I wouldn’t use in formal mathematical contexts but rather like this:

You broke my heart in two. 
The walnut split cleanly in two. 

We could also say “in half” in the above examples. 

Funny how these usages have never confused me!


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