Question

i) | Amit, I have an expression 3/8 +-5/7 which shows that: (a) rational numbers are closed under addition (b) rational number are not closed under addition (c) rational numbers are closed under multiplication (d)addition of rational numbers is ) not commutative​

Answer 1

The given expression shows that rational numbers are closed under addition

Given :

The numerical expression 3/8 + (-5)/7 = -19/56 ( Correction in the question )

To find :

The expression shows that

(a) rational numbers are closed under addition.

(b) rational numbers are not closed under addition.

(c) rational numbers are closed under multiplication.

(d) addition of rational numbers is not commutative.

Solution :

Step 1 of 3 :

Write down the given expression expression

The given expression is

$\displaystyle \sf{ \frac{3}{8} + \frac{( - 5)}{7} = - \frac{19}{56} }$

Step 2 of 3 :

Check validity of the expression

LHS

$\displaystyle \sf{ = \frac{3}{8} + \frac{( - 5)}{7} }$

$\displaystyle \sf{ = \frac{3}{8} - \frac{5}{7} }$

$\displaystyle \sf{ = \frac{21 - 40}{56} }$

$\displaystyle \sf{ = - \frac{19}{56} }$

= RHS

Hence the expression is true

Step 3 of 3 :

Choose the correct option

3/8 and (-5)/7 are rational numbers

Also - 19/56 is a Rational number

Thus the sum of two rational number is also a rational number

Above property is called Closure property for set of rational numbers under addition

Hence the correct option is (a) rational numbers are closed under addition.

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