Question

HELP ME ASAP ITS AN EMERGENCY Now that you've created your hypotheses, it's time to prove them. First, look at the sum of two rational numbers. Let's saythey are two rational numbers, x and y. Because they're rational, they can be wrxtten as a ratio of integers. Let x = andy = g, where a, b, c, and d are integers and b and d do not equal 0. The process for finding the sum x + y in terms of a, b, c,and d is shown.ReasonsubstitutionStatementx + y = 3 +(9) 4) + () (9)od + bareCreate common denominators.ad + bcSimplify.Based on this sum and using the closure property of integers, what conclusion can you make about the sum of tworational numbers? Explain your answer.В І uFont Sizes A - A-SE E 33xCharacters used: 0 / 15000

Answer 1

a/b + c/d = (a*d + b*c)/(b*d)

Closure property states:

If x and y are any two integers, xy will also be an integer:

Therefore:

a * b = integer

b * c = integer

b * d = integer

Also, addition and subtraction states that the sum or difference of any two integers will always be an integer too

So:

a*d + b*c = integer

We can conclude according to the previous information that:

a/b + c/d = (a*d + b*c)/(b*d) = rational number

Or, in another words:

the sum of two rational numbers is rational