1. Verify the closure property of rational numbers (addition, subtraction, multiplication and division) for −9/ 11 and 3/ 5
Answers
Answer:
Here, a = and b =
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 = = = 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 = = = 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 = x = 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 = ÷ = x = 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.