The sum of two rational numbers will always be

an irrational number.

an integer.

a rational number.

a whole number.

I think that the sum will always be a rational number

let's prove that

any rational number can be represented as a/b where a and b are integers and b≠0

and an integer is the counting numbers plus their negatives and 0

so like - 4,-3,-2,-1,0,1,2,3,4 ...

so, 2 rational numbers can be represented as

a/b and c/d (where a, b, c, d are all integers and b≠0 and d≠0)

their sum is

a/b+c/d=

ad/bd+bc/bd=

(ad+bc) / bd

to prove that the sum will always be a rational number, we must prove that

1. the numerator and denomenator will be integers

2. that the denomenator does not equal 0

alright

1.

we started with that they are all integers

ab+bc=?

if we multiply any 2 integers, we get an integer

like 3*4=12 or - 3*4=-12 or - 3*-4=12, etc

even 0*4=0, that's an integer

the sum of any 2 integers is an integer

lik 4+3=7, 3 + (-4) = - 1, 3+0=3, etc

so we have established that the numerator is an integer

now the denomenator

that is just a product of 2 integers so it is an integer

2. we originally defined that b≠0 and d≠0 so we're good

therfor, the sum of any 2 rational numbers will always be a rational number is the correct answer