The closure property for rational numbers means that adding, subtracting, or multiplying any two rational numbers always results in another rational number. The set of rational numbers is closed under these three operations, but not for division by zero.
Closure property in detail
- Addition: The sum of any two rational numbers is a rational number.
- Example: 14+23=3+812=1112one-fourth plus two-thirds equals the fraction with numerator 3 plus 8 and denominator 12 end-fraction equals 11 over 12 end-fraction14+23=3+812=1112, which is a rational number.
- Subtraction: The difference between any two rational numbers is a rational number.
- Example: 47−59=36−3563=163four-sevenths minus five-nineths equals the fraction with numerator 36 minus 35 and denominator 63 end-fraction equals 1 over 63 end-fraction47−59=36−3563=163, which is a rational number.
- Multiplication: The product of any two rational numbers is a rational number.
- Example: 47×59=2063four-sevenths cross five-nineths equals 20 over 63 end-fraction47×59=2063, which is a rational number.
- Division: The quotient of two rational numbers is a rational number, with the exception of division by zero.
- Example: 47÷59=47×95=3635four-sevenths divided by five-nineths equals four-sevenths cross nine-fifths equals 36 over 35 end-fraction47÷59=47×95=3635, which is a rational number.
- Exception: Division by zero is undefined, so rational numbers are not closed under division by zero.
