Question

if the rational number a/b and c/d are equivalent, then_______​

Answer 1

Answer:

When Their Ratio Are Equal.

Step-by-step explanation:

One considers ordered pairs (a,b) of integers a and b for which b≠0. Two such pairs, (a,b) and (c,d), are called equivalent (equal) if and only if ad=bc. This is an equivalence relation, being reflexive, symmetric and transitive, and so partitions the set of all such pairs into equivalence classes.

How do you prove that the sum of any two rational numbers is rational?

A rational number is a number which can be expressed as the ratio (quotient) of two integers.

Let M and N be any two rational numbers and let S = M+N.

Then there exists integers a, b, c and d such that M = a/b and N = c/d.

So S = a/b+c/d

= ad/bd+bc/bd

So S = (ad+bc)/bd.

Let g = ad+bc and h = bd.

Then S = g/h.

Since a, b, c and are integers, g and h are integers.

Therefore S is a rational number.

So the sum of any two rational numbers is also a rational number.