Question

Prove the sum of two rational numbers is rational where a, b, c, and d are integers and b and d cannot be zero. Steps Reasons 1. a over b plus c over d Given 2. Multiply to get a common denominator 3. ad plus cb all over bd Simplify Fill in the missing step in the proof. ac over bd ad over b plus cb over d a plus c all over b plus d ad over bd plus cb over bd

Answer 1

step 2 is the 3rd option

Explanation:

Answer 2

ad+bc/bd is a rational number.

Explanation:

We know that the rational numbers are those numbers which can be written in p/q form. and q is not equal to zero

Lets say that a/b and c/d are two rational numbers and both the denominators b and d can not be zero.

We have given:

a/b + c/d

Now multiply the given term to get a common denominator

a/b + c/d = ad/bd +cb/db

Now if we simplify the given term we get:

a/b + c/d = ad/bd +cb/db

Take the L.C.M of the denominator.

ad/bd +cb/db

Notice that the denominators are same. Thus the term we get after taking L.C.M we get

=ad+cb/bd

=a/b + c/d = ad/bd +cb/db = ad+bc/bd

Since b and d are not equal to zero, bd is also not equal to zero.

And a,b,c,d are integers then bd,ad,bc, ad+ bc are also integers.

Thus the fraction ad+bc/bd is a rational number.