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प्रश्न
Verify the closure property for addition and multiplication for the rational numbers `(-5)/7` and `8/9`
उत्तर
closure property for addition
Let a = `(-5)/7` and b = `8/9`
a + b = `(-5)/7 + 8/9`
= `((-5 xx 9) + (8 xx 7))/(7 xx 9)`
= `(-45 + 56)/63`
= `11/63` is in Q.
i.e. a + b = `(-5)/7 + 8/9`
= `11/63` is in Q.
∴ Closure property is true for addition of rational numbers.
Closure property for multiplication
Let a = `(-5)/7` and b = `8/9`
a × b = `(-5)/7 xx 8/9`
= `(-40)/63` is in Q.
∴ Closure property is true for multiplication of rational numbers.
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संबंधित प्रश्न
Closure property is not true for division of rational numbers because of the number
Give an example and verify the following statement.
The collection of all non-zero rational numbers is closed under division
Rational numbers are closed under addition and multiplication but not under subtraction.
Give one example each to show that the rational numbers are closed under addition, subtraction and multiplication. Are rational numbers closed under division? Give two examples in support of your answer.
