Question

The numerical expression 3/8 + (-5)/7 = -19/56 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.

Answer 1

Answer:

Option (a) is correct

rational numbers are closed under addition.

Step-by-step explanation:

Given : expression $\frac{3}{8}+\frac{-5}{7}=\frac{-19}{56}$

Solving the left side of  given expression $\frac{3}{8}+\frac{-5}{7}$

we get,

LCM (7, 8) = 56

$\frac{7\times 3+(-5) \times 8}{56}$

Simplify , we get

$\frac{7\times 3-5\times 8}{56}$

$\frac{21-40}{56}$

$\frac{-19}{56}$

Which is same as left side

Also sum of two rational number is again a rational number

Thus, rational numbers are closed under addition.

Option (a) is correct

Answer 2

Answer:

Option (a) rational numbers are closed under addition.    is correct

Step-by-step explanation:

Given: expression  

Solving the left side of the given expression  we get,

LCM (7, 8) = 56

After simplifying, we get

Which is the same as L.H.S

Also, the sum of two rational number is also a rational number

Thus, rational numbers are closed under addition.