Generic question on division

[miiike]

May I ask:

how may we formulate the following statement, since I have seen variations to it. That greatly confuses me. Also, do kindly explain why the answer.

- x divides y
- x divided by y

Thank you

 

[tkhunny]

Those are very different statements/expressions.

"x divides y" means y = x*q for 'q' an integer. In other words, y is an integer multiple if x.

3 divides 12. We have 12 = 3*4 and 4 is an integer
5 does not divide 12. We have 12 = 5*2 + 2 and 12 = 5*3 - 3. There is no integer between 2 and 3.

"x divided by y" is just an expression for the division x/y.

15/3 = 5
15/4 = 3.75 or 3 remainder 3, if you like.

 

[miiike]

Those are very different statements/expressions.

"x divides y" means y = x*q for 'q' an integer. In other words, y is an integer multiple if x.
"x divided by y" is just an expression for the division x/y.

Thank you. In that case, may i conclude that whenever i see 'x divides y':
y is automatically larger than x?
so that x may be divided by y?

 

[miiike]

Could also be equal.

Thank you. now it's clear