Question

Which of the following property is represent by the statement -2/3+3/5=3/5+-2/3 Its option is: (a) Rational number are closed under addition (b) Rational number are closed multiplication (c) Addition of rational number is associative (d) Addition of rational number is communicative​

Answer 1

Solution :-

As we know that,

• Addition and multiplication of rational number is same in communicative .

so,

→ -2/3+3/5 = 3/5+-2/3

Solving LHS first,

→ (-2/3) + 3/5

taking LCM,

→ (-2 * 5 + 3 * 3) /15

→ (-10 + 9) / 15

→ (-1/15)

and,

→ 3/5 + (-2/3)

→ {3 * 3 + (-2) * 5} /15

→ (9 - 10) / 15

→ (-1/15)

Solving, RHS now,

→ 3/5 + (-2/3)

→ (3/5) - (2/3)

→ (3*3 - 2*5)/15

→ (9 - 10) / 15

→ (-1/15)

therefore ,

→ LHS = RHS .

Hence, we can conclude that, (d) Addition of rational number is communicative .

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

Which of the following property is represent by the statement

$\displaystyle \sf{ - \frac{2}{3} + \frac{3}{5} = \frac{3}{5} + \bigg( - \frac{2}{3} \bigg) }$

Its option is:

(a) Rational number are closed under addition

(b) Rational number are closed multiplication

(c) Addition of rational number is associative

(d) Addition of rational number is communicative

CONCEPT TO BE IMPLEMENTED

(a) Rational number are closed under addition

If a and b are two rational numbers then a + b is also a rational number

(b) Rational number are closed multiplication

If a and b are two rational numbers then a × b is also a rational number

(c) Addition of rational number is associative

If a, b, c are three rational numbers then

a + ( b + c ) = ( a + b) + c

(d) Addition of rational number is communicative

If a and b are two rational numbers then

a + b = b + a

EVALUATION

Here the given expression is

$\displaystyle \sf{ - \frac{2}{3} + \frac{3}{5} = \frac{3}{5} + \bigg( - \frac{2}{3} \bigg) }$

Let us take

$\displaystyle \sf{ a = - \frac{2}{3} \: \: and \: \: b = \frac{3}{5} }$

Now

LHS

= a + b

$\displaystyle \sf{ = - \frac{2}{3} + \frac{3}{5} }$

$\displaystyle \sf{ = \frac{ - 10 + 9}{15} }$

$\displaystyle \sf{ = - \frac{1}{15}}$

RHS

= b + a

$\displaystyle \sf{ = \frac{3}{5} + \bigg( - \frac{2}{3} \bigg) }$

$\displaystyle \sf{ = \frac{3}{5} - \frac{2}{3} }$

$\displaystyle \sf{ = \frac{9 - 10}{15} }$

$\displaystyle \sf{ = - \frac{1}{15} }$

∴ a + b = b + a

So Addition of rational number is communicative

FINAL ANSWER

Hence the correct option is

(d) Addition of rational number is communicative

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. Apply the distributive property to create an equivalent expression. 5*(−2w−4)

https://brainly.in/question/33967867

2. Prove that the inverse of the product of two elements of a group is the product of the inverses taken in the reverse order

https://brainly.in/question/22739109