Respuesta :
Answer:
So, adding two rationals is the same as adding two such fractions, which will result in another fraction of this same form since integers are closed under addition and multiplication. Thus, adding two rational numbers produces another rational number. Proof: "The product of two rational numbers is rational."
Sum of two rational numbers is always a rational number is always true .
What are rational numbers?
A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. For example, −3/7 is a rational number, as is every integer
According to the question
The sum of two rational numbers :
Case 1: Consider rational numbers with different denominator : [tex]\frac{4}{5} , \frac{2}{3}[/tex]
Sum of both rational numbers
= [tex]\frac{4}{5} + \frac{2}{3}[/tex]
= [tex]\frac{12 + 10 }{15}[/tex]
= [tex]\frac{22}{15}[/tex]
Case 2:Consider rational numbers with same denominator : [tex]\frac{4}{5} , \frac{1}{5}[/tex]
= [tex]\frac{4}{5} + \frac{1}{5}[/tex]
= [tex]\frac{5}{5}[/tex]
= [tex]\frac{1}{1}[/tex]
= 1
Sum in both cases are rational numbers
Hence, Sum of two rational numbers is always a rational number is always true .
To know more about rational number here:
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