Now that you’ve created your hypotheses, it’s time to prove them. First, look at the sum of two rational numbers. Let’s say they are two rational numbers, x and y. Because they’re rational, they can be written as a ratio of integers. Let x = and y = , 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. Statement Reason substitution Create common denominators. Simplify. Based on this sum and using the closure property of integers, what conclusion can you make about the sum of two rational numbers? Explain your answer.

Now that you've created your hypotheses, it's time to prove them. First look at the sum of two rational numbers. Let's say they are two rational numbers, x and y. Because they're rational, they can be written as a ratio of integers. Let [tex]x=\frac{a}{b}[/tex] and [tex]y=\frac{c}{d}[/tex], 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 in the figure below.

Based on the sum and using the closure property of integers, what conclusion can you make about the sum of two rational numbers? Explain your answer.

Answer: The sum of two rational numbers equals a rational number.

Step-by-step explanation: Rational number is defined as a number that can be made by dividing two integers.

Closure Property of Integers states the sum or subtraction of two integers always gives an integer.

Using the definition of rational and expanding the property, we can conclude that the sum of two rational numbers will result in a rational number, as demonstrated in the table below.