Divide two into four and Divide two by four

Question

Why "divide two into four" equals to two and "divide two by four" equals to one half?

Correct if I am wrong, but this what I have learned recently.

Answer 1

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. As Jez says, it means exactly the same as "divide 2 by 4" - which gets 197 hits in Google Books as against only 4 for the first link (a format we tend to avoid in writing because of the scope for confusion). It's important to note that you could rephrase the sum as how many 2s are there in 4?.

This isn't the same usage as divide a pizza into 6 - we all know perfectly there are no pizzas in 6!

Answer 2

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.

Answer 3

"Divide 2 into 4" and "divide 2 by 4" seem semantically identical (2 / 4) to me; I don't recognize the former's meanining as 4 / 2.

Answer 4

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: Given a division problem:
A
---
B

The expression is either "B into A" (bottom to top) or "A divided by B" (top to bottom)

Have a look at this link for an example of "goes into": http://www.themathpage.com/arith/divide-whole-numbers.htm