Most students asked why is that a b ÷ c d = a d b c I just told them: inverse the second fraction and multiply. Why? They ask me. I have no idea.Any logical answers to them kids?These day teachers just told students at secondary to memorise and no why is allowed in lessons. I think that is wrong. Putting people of studying maths.

Question

Most students asked why is that             a      b        ÷            c      d        =                    a        d                    b        c            I just told them: inverse the second fraction and multiply. Why? They ask me. I have no idea.Any logical answers to them kids?These day teachers just told students at secondary to memorise and no why is allowed in lessons. I think that is wrong. Putting people of studying maths.

amanhantmk · Accepted Answer

By definition,   x  ÷  y should be a number   z such that   x  =  y  zSo you just verify:                    a        d                    b        c              ×            c      d        =            a      b      Ultimately this works because of the associative and commutative laws of multiplication, but you don&#039;t have to tell the students that.&quot;Why&quot; should always be allowed.

Frederick Kramer · Accepted Answer

When you divide   x  ÷  y, it is the same as       x    y    =  x  ×      1    y  . Students familiar with fractions should be able to understand this. This is true no matter what   x or   y  are, even if they&#039;re fractions. Therefore,       a    b    ÷      c    d    =      a    b    ×      d    c    =            a      d              b      c