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\ Key Concept \	\             Closure property \
\ When you combine any two elements of the set, the result is also included in the set. \

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Select two different rational numbers and then determine whether the

addition is a rational number. Try some examples.

Find the Least Common Denominator (LCD) of improper fractionand.

Find the Least Common Multiple of 2 and 4.

Multiples of 2: 2 , 4 , 8 , 12 . . .

Multiples of 4: 4 , 8 , 12 . . .

The least common multiple of 2 and 4 is 8, the LCD is 4.

Rewrite each fraction using the least common denominator (LCD).

and

Rewrite the sum using the LCD.

                            (Add, )

Find the Least Common Denominator (LCD) of improper fractionand.

Find the Least Common Multiple of 3 and 4.

Multiples of 3: 3 , 6 , 9 , 12 . . .

Multiples of 4: 4 , 8 , 12 . . .

The least common multiple of 3 and 4 is 12, the LCD is 12.

Rewrite each fraction using the least common denominator (LCD).

and

Rewrite the sum using the LCD.

                            (Add, ) 

In the above examples, each time we get rational number. 

So the set of rational numbers is closed under addition.

The set of rational numbers is closed under addition.