Answer:
Yes, rational numbers are closed under addition.
Step-by-step explanation:
Rational numbers are number that can be expressed in the form of fraction [tex]\frac{x}{y}[/tex], where x and y are integers and y ≠ 0.
Now, the closure property of addition of rational number states that if we add two rational number, then the sum of these two rational number will also be a rational number.
Let a and b be two rational number, then,
a+b = c, where c is the sum of and b
c is also a rational number.
Thus, rational numbers are closed under addition.
This can be explained with the help of a example.
[tex]\frac{1}{7} + \frac{2}{7}[/tex] = [tex]\frac{2}{7}[/tex]
It is clear that [tex]\frac{1}{7}, \frac{2}{7}, \frac{3}{7}[/tex] are rational numers.
Thus, rational numbers are closed under addition.
