Question

What should be added to (4/5) to get additive inverse of
(-1/5+4/3) ?​

Answer 1

Step-by-step explanation:

Given :-

The number = 4/5

To find :-

What should be added to (4/5) to get additive inverse of (-1/5+4/3) ?

Solution :-

Given number = 4/5

Let the required number be X

On adding X to 4/5 = (4/5)+X

According to the given problem

X+(4/5) = Additive inverse of (-1/5 +4/3)

Now

(-1/5)+(4/3)

LCM of 5 and 3 = 15

=> (-3+20)/15

=> 17/15

So , additive inverse of (-1/5 +4/3)

= additive inverse of 17/15

= -17/15

Therefore, X+(4/5) = -17/15

=> X = (-17/15)-(4/5)

LCM of 15 and 5 is 15

=>X = (-17-12)/15

=> X = -29/15

Therefore,the number = -29/15

Answer:-

The required number for the given problem is -29/15

Check:-

The number = -29/15

now on adding -29/15 to 4/5

=> (-29/15)+(4/5)

=> (-29+12)/15

=> -17/15 ------(1)

and

(-1/5)+(4/3)

LCM of 5 and 3 = 15

=> (-3+20)/15

=> 17/15

So , additive inverse of (-1/5 +4/3)

= additive inverse of 17/15

= -17/15------(2)

From (1) & (2)

The sum of 4/5 and -29/15 is equal to the

additive inverse of (-1/5+4/3) .

Verified the given relations in the given problem.

Used formulae:-

Additive inverse of a number :-

The sum of two rational numbers is the additive identity element i.e. 1 then they are Additive inverse to each other.

• The additive inverse of a is -a

• The additive inverse of -a is a

• a+(-a) = 0

• Additive identity element of the set of rational numbers is 1.