Explain why the rules for dividing integers are the same as the rules for multiplying integers.

Question

I do not get this one at all. If you could please explain this thoroughly I would greatly appreciate it. It is for a summer prealgebra class I am taking to get ahead.

Answer 1

The key concept here is RECIPROCAL.

 

The number 1/x is the reciprocal of the number x.

 

When a value y is multiplied by (1/x), we may write the expression as y/x, which is y divided by x.  The multiplication operation follows the same rules as the division operation [because they are the same operation expressed differently].

 

PLZ note (since you mentioned integers):  The rules for Integer Division usually disregard the remainder and keep the quotient (for example, 10\3 is 3;  the "\" is used by some computer languages for integer division).

Answer 2

Her's how divisions works in general. Actually division and multiplication are the same level operation in the order of operations for the same exact reason.

 

Every division problem can be changed into a multiplication problem!!!

 

Think of division of fractions.

 

8 ÷ 1/2 = 8*2/1.

12 ÷ 2/3 = 12 * 3/2

 

So since division can be converted into multiplication, it must have the same rules as multiplication.

 

Hope this helped.

Answer 3

negative multiplied by negative is positive

negative multiplied by positive is negative

positive multiplied by positive is positive

 

Multiplication is the inverse of division.  If multiplication follows these rules, then it works in the reverse way.  The reverse way of course will be division.

Answer 4

Explain why the rules for dividing integers are the same as the rules for multiplying integers.

 

 

The RULES THAT ARE THE SAME have to do with SIGN MANAGEMENT, i.e. whether the operation is multiplication or division, combining

 

(in that way) values with DIFFERING SIGNS yields a negative result, but with SAME signs yields a positive result--with the proviso that division by zero is not allowed, and multiplication by 0 yields zero (0 is unsigned).

 

Then, too, as others pointed out, multiplication by a fraction is the same as dividing by the reciprocal of that fraction, and vice versa.