Why do you change the sign when you divide fractions

Question

why do you have to change the sign when you divide fractions in math why can you just leave it the same 

 

 

 

 

 

 

 

 

 

 

 

 

Answer 1

WHY do you change signs ??

 

Example:  (2/3)÷(4/5)=

 

               (2/3)

               ------ =

               (4/5)

 

multiply the numerator and the denominator by the reciprocal of the denominator

 

               (2/3)(5/4)

               ------------ =

               (4/5)(5/4)

 

               (2/3)(5/4)

               ------------ =         (4/5 and 5/4 are reciprocals whose product is 1)

                      1

 

               (2/3)(5/4) =         (any number divided by 1 is that number)

 

               (2*5)/(3*4)=10/12=5/6   (or simplify before multiplying)

               (1*5)/(3*2)=5/6   (2/2=1 and 4/2=2)

 

You don't have to do all this work, you simply use the rule "dividing by a number is the same as multiplying by it's reciprocal." Now, however, you know why you change the sign from division to multiplication.

 

 

 

Answer 2

If you divide a number by another, regardless of whether either is a fraction, you don't "change signs."

 

To quote Jaime Escalante, a negative times (or divided by) a negative is a positive;

a negative divided by a positive is negative;

a positive divided  by a negative is negative.

 

Consider this illustration:   -4 ÷ -2 = -4/(-2).  You could multiply it by 1 without changing its real value.

So since -1 ÷  -1 must equal one (it's something by itself), when you multiply both its numerator and denominator by -1, you get 4 ÷ 2 which equals 2 (positive).

 

Or perhaps you meant to ask why is (a/b) ÷  (c/d) = (a/b)(d/c), which is "to divide a fraction by another, multiply the first fraction by the RECIPROCAL of the other fraction."