Why is the sum of two rational numbers always rational?

Select from the options to correctly complete the proof. /

Let / and / represent two rational numbers. This means a, b, c, and d are (integers, natural numbers, imaginary numbers), and b is not (zero, rational, negative) and d is not (zero, rational, negative). The product of the numbers is / where bd is not 0. Because integers are closed under (addition, subtraction, multiplication, division), / is the ratio of two integers making it a rational number.

Question

Mathematics

Jordan

5 July, 05:15

Why is the sum of two rational numbers always rational?

Select from the options to correctly complete the proof. /

Let / and / represent two rational numbers. This means a, b, c, and d are (integers, natural numbers, imaginary numbers), and b is not (zero, rational, negative) and d is not (zero, rational, negative). The product of the numbers is / where bd is not 0. Because integers are closed under (addition, subtraction, multiplication, division), / is the ratio of two integers making it a rational number.

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Gideon Warner · Answer 1

The sum of two rational numbers always rational

The proof is given below.

Step-by-step explanation:

Let a/b and c / d represent two rational numbers.

This means a, b, c, and d are integers.

And b is not zero and d is not zero.

The product of the numbers is ac/bd where bd is not 0.

Because integers are closed under multiplication

The sum of given rational numbers a/b + c/d = (ad + bc) / bd

The sum of the numbers is (ad + bc) / bd where bd is not 0.

Because integers are closed under addition

(ad+bc) / bd is the ratio of two integers making it a rational number.