Question

verify the closure property for addition and multiplication for the rational number -5/7 and 8/9​

Answer 1

➤ Answer :-

Closure property for addition :-

${\tt \longrightarrow \boxed{\tt\dfrac{( - 5)}{7} + \dfrac{8}{9}} = \boxed{\tt \dfrac{8}{9} + \dfrac{( - 5)}{7}}}$

Convert them into like fractions by taking the LCM of the denominators i.e, 9 and 7.

LCM of 7 and 9 is 63.

${\tt \longrightarrow \dfrac{( - 5) \times 9}{7 \times 9} + \dfrac{8 \times 7}{9 \times 7}}$

${\tt \longrightarrow \dfrac{( - 45)}{63} + \dfrac{56}{63} = \dfrac{( - 45) + 56}{63}}$

${\tt \longrightarrow \dfrac{11}{63} }$

Verification :-

${\tt \longrightarrow \dfrac{8}{9} + \dfrac{( - 5)}{7}}$

${\tt \longrightarrow \dfrac{8 \times 7}{9 \times 7} + \dfrac{( - 5) \times 9}{7 \times 9}}$

${\tt \longrightarrow \dfrac{56}{63} + \dfrac{( - 45)}{63} = \dfrac{56 + ( - 45)}{63}}$

${\tt \longrightarrow \dfrac{11}{63}}$

$\Huge\therefore$Closure property for addition is possible.

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Closure property for multiplication :-

${\tt \longrightarrow \boxed{\tt\dfrac{( - 5)}{7} \times \dfrac{8}{9}} = \boxed{\tt\dfrac{8}{9} \times \dfrac{( - 5)}{7}}}$

${\tt \longrightarrow \dfrac{( - 5) \times 8}{7 \times 9} = \dfrac{( - 40)}{63}}$

Verification :-

${\tt \longrightarrow \dfrac{8 \times ( - 5)}{9 \times 7}}$

${\longrightarrow\tt\dfrac{( - 40)}{63}}$

$\Huge\therefore$Closure property for multiplication is possible.

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More to know................

• Closure property is a mathematical problem. It is used to calculate the value of adding or multiplying the numbers by changing places.
• Closure property means solving the problem by changing the place of the numbers or fractions. It only works for addition and multiplication. It cannot be possible for subtraction and division. If we apply it for subtraction and division, the value will be changed.