Question

How will you find the additive inverse and multiplicative inverse of 1.5?

Answer 1

Hint: We are given a term 1.5, we will first simplify 1.5, we get \[1.5=\dfrac{3}{2}\], then to find additive inverse and multiplicative inverse, to do so we will learn about additive identity, then additive inverse using certain examples, similarly, we will learn about multiplication identity and then about multiplication inverse. We will work with certain examples to get a grip and then finally we will find a multiplicative inverse of 1.5.

Complete step by step answer:
We are given a term as 1.5, we are asked to find the multiplicative inverse and additive inverse of the given number 1.5.
To answer this, we need to have knowledge of what additive inverse and the multiplicative inverse are.
Firstly, we will learn about the additive inverse, before this we will know the meaning of additive identity, it is the term which when added to any number will always give you base as the same number i.e. if a is any number, then e is the additive identity of e+a = a.
We have an additive identity as 0.
If we add anything to zero it will always give us the same number.
For example, 0+2 = 2, 0+3 = 3, 0-1 = -1.
Now additive inverse of any number says 'a' is the number 'b' such that, if we add a and b we will get additive identity (0).
In simple terms, b is the additive inverse of a if a+b = 0.
So, for our term 1.5, we will find the additive inverse.
Let b be the additive inverse of 1.5, so by definition, b+1.5 = 0.
Subtracting 1.5 both sides we get $ b+1.5-1.5=0-1.5 $ .
Further simplifying we get b = -1.5
So additive inverse of 1.5 is -1.5
Now we will learn about the multiplicative inverse, earlier we have learned about multiplicative identity, a number is said to be a multiplicative identity if we multiply any number with that, it will give us the same number.
One multiplicative identity is 1 always, as we multiply 1 with any term we get the same term back. For example $ 1\times 2=2,1\times \left( -3 \right)=-3 $ etc.
Now, multiplicative inverse for any number say 'a' is the number b if we multiply a with b and we get multiplicative identity i.e. for any number a, b is multiplicative identity if $ a\times b=1 $.
Now for our term 1.5, let b be a multiplicative identity of 1.5 then by definition, $ b\times 1.5=1 $.
Divide both sides by 1.5 we get $ b=\dfrac{1}{1.5} $ .
Simplifying we get $ b=\dfrac{2}{3} $ .

Note:
Shortcut method to find the additive inverse is that, for any term a, additive inverse is simply given as -a, while for non-zero term, a multiplicative inverse is given as $ \dfrac{1}{a}\left( a\ne 0 \right) $ . So for example, 2, additive identity of 2 is -2 and multiplicative identity is $ \dfrac{1}{2} $ .