is this answer 1? ab÷ab=?

Question

some people are arguing NO the answer is b*b

 

Answer 1

Good morning Jojo...from Dillingham, AK...have a great day at school.

Okay...great question.

Here is a good argument to use all those rules you know and use, but sometimes we all forget their titles.

Remember this Algebra Property...Inverse property of Multiplication, some will say Multiplicative Inverse. It basically states, any number, say a, when multiplied by its inverse, in this case 1/a, will equal 1. Let's check:

         1/a • a  =  1   RIGHT?    Do you understand how it works?

 

           1  • a   =  which is the same as    1   •   a    =    1 • a      Right?

           a                                                a       1           a • 1

 

The Identify property tells us that when we multiply any number, let's say a, is multiplied by 1, it equals the same number, so  a • 1 = a

So our equation above   

              1 • a   =   a   which is the same as   a ÷ a  = which equals 1

              a • 1        a

This confirms the other Algebra Property of Division: any number, in your case ab, divided by itself, again  ab, will equal 1. We can prove this using the first Identify property that if we multiply ab times 1 will equal ab.

This is how you prove     ab ÷ ab  =  1,    sorry it does not equal 2b