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Question
Verify the closure property for addition and multiplication for the rational numbers `(-5)/7` and `8/9`
Solution
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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