Verify the closure property of rational numbers 5 /11and 3 /44 .
Answers
Here, a = \frac{-9}{11}
11
−9
and b = \frac{3}{5}
5
3
A. If a and b are two rational numbers and their sum c = a + b is also a rational number, then the two rational numbers a and b is said to satisfy Closure-Property of Addition.
a + b = \frac{-9}{11} + \frac{3}{5}
11
−9
+
5
3
= \frac{-45 + 15}{55}
55
−45+15
= \frac{-30}{55}
55
−30
which is also a rational number.
This means that the rational numbers are closed under addition.
B. If a and b are two rational numbers and their difference c = a - b is also a rational number, then the two rational numbers a and b is said to satisfy Closure-Property of Subtraction.
a - b = \frac{-9}{11} - \frac{3}{5}
11
−9
−
5
3
= \frac{-45 - 15}{55}
55
−45−15
= \frac{-60}{55}
55
−60
which is also a rational number.
This means that the rational numbers are closed under subtraction.
C. If a and b are two rational numbers and their product c = a x b is also a rational number, then the two rational numbers a and b is said to satisfy Closure-Property of Multiplication.
a x b = \frac{-9}{11}
11
−9
x \frac{3}{5}
5
3
= \frac{-27}{55}
55
−27
which is also a rational number.
This means that the rational numbers are closed under multiplication.
D. If a and b are two rational numbers and the quotient c = a ÷ b is also a rational number, then the two rational numbers a and b is said to satisfy Closure-Property of Division.
a ÷ b = \frac{-9}{11}
11
−9
÷ \frac{3}{5}
5
3
= \frac{-9}{11}
11
−9
x \frac{5}{3}
3
5
= \frac{-15}{11}
11
−15
which is also a rational number.
This means that the rational numbers are closed under division for the given set of numbers.
But we know that any rational number n, n ÷ 0 is not defined. So rational numbers are not closed under division.