CLOSURE PROPERTY OF ADDITION OF RATIONAL NUMBERS -
The sum of two rational numbers is always a rational number.
If a/b and c/d are any two rational numbers, then (a/b + c/d) is also a rational number.
The closure property of addition states that when you add any two rational numbers, the result is always another rational number. In other words, the sum of any two rational numbers is also a rational number.
For example, let's take two rational numbers:-
a c
------- and -------
b d
where a, b, c, and d are integers and b and d are not equal to zero.
When you add these two rational numbers, you get:-
a c
------- + -------
b d
To find the sum, you need to find a common denominator and then add the numerators:-
ad bc
----------- + ------------
bd bd
Since both ad and bc are integers and bd is not zero, the result is also a rational number:-
(ad + bc)
-------------------
bd
So, the sum of two rational numbers ba and dc is another rational number (ad + bc)/bd. This demonstrates the closure property of addition for rational numbers.
For example:
1 3 1 3
1. If you add ----------- and -----------, the sum is ----------- + -----------
2 4 2 4
2 3
= ----------- + ------------
4 4
(2 + 3)
= ----------------
4
which is a rational number.
2 5
2. If you add − ----------- and -----------, the sum is which is also a rational number.
3 6
2 5
= - ---------- + -----------
3 6
(2 X 2) (5 X 1)
= - ----------------- + -----------------
(3 X 2) (6 X 1)
4 5 (-4 + 5)
= - ----------- + ----------- = -------------------
6 6 6
1
= ----------
6
No matter which rational numbers you add together, the result will always be rational. This is what is meant by the closure property of addition in rational numbers.