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.
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4/2 = 2
clearest verbal form...
divide 4 by 2, giving the answer 2
divide 2 into 4, giving the answer 2
It's not the same usage as dividing a pizza into 4 [pieces], where you'd probably get 1/4 (a quarter) of a pizza as your share!
In math the term divide may have two different senses.
1) To use (a number) as a divisor. E.g: divided 5 into 35 = 7
5 is the divisor.
2) To subject (a number) to the process of division [by a divisior]. E.g: If you divide 6 by 2, you get 3
2 is the divisor.
10 divided into 100 = 10
100 divided by 10 = 10
Please check divide.
The expression of division using the word "into" comes from the form: "Two goes into four how many times?" Answer: two.
Dividing 2 by 4 means breaking(dividing) 2 into 4 equal parts ( 0.5 each).
You might think about it this way:
Have a look at this link for an example of "goes into": http://www.themathpage.com/arith/divide-whole-numbers.htm
My experience of "divide [number] into [number]" was solely as regional spoken idiom. In different math textbooks used ca. 1965 in public schools both in suburban Seattle and on the South Side of Chicago, "40/8" was written out as "forty divided by eight." Outside Seattle it was said the same way. In Chicago, though, it was said "eight divided into forty." The discrepancy offers a good lesson about relying on numerical rather than verbal expressions when math is involved.