.
Since @josgarithmetic presented his answers I N C O R R E C T L Y, let me do it in correct way:
a. Negative 3 times a number w -3w
b. Negative 3 divided by a number w
c. A number w divided into negative 3 =
d. The quotient of negative 3 and a number w
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After reading the post by @greenestamps, I have a question:
In the post by @josgarithmetic, the line c) says w/(-3) = -3/w
I S I T C O R R E C T ? I S T H I S E Q U A L I T Y C O R R E C T ?
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To learn the subject, I first looked into my textbooks in Algebra (that I have many from library sales . . . ).
I found that NO ONE textbook uses this form "divide a number into the other number" or even mention it.
Then I made my search in the Internet. I found this site and some discussion in it. I placed it below.
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https://english.stackexchange.com/questions/58209/divide-two-into-four-and-divide-two-by-four
English Language & Usage Stack Exchange is a question and answer site for linguists, etymologists,
and serious English language enthusiasts.
QUESTION // asked by someone Feb 16 '12 at 6:17
Why does "divide two into four" equal two, and "divide two by four" equal one half?
Correct if I am wrong, but this what I have learned recently.
ANSWER 1
As a AmE speaker from NE US, I have to say that I have a hard time recalling EVER hearing someone say "divide X into Y."
I would not have been able to answer this question from someone without clarification of what they were asking.
– horatio Feb 16 '12 at 19:12
ANSWER 2
OP's confusion arises because "divide 2 into 4" is an idiomatic usage meaning perform a division operation,
using 2 as the divisor, and 4 as the dividend.
ANSWER 3
For me (an American) divide 2 into 4 is not the same as divide 2 by 4. This one: divide 2 into 4 uses 2 as the divisor,
as you say: 4/2 ... but divide 2 by 4 I take to mean use 4 as the divisor, 2/4 .
– GEdgar Jul 10 '13 at 20:59
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Getting familiarity with the issue, I conclude that this form practically is never used in Math and in Math/Algebra textbooks.
It is the area where linguists, etymologists, and English language enthusiasts make their exercises, when they have nothing to do.