Question

find the product of additive inverse and multiplication inverse of (-2)​

Answer 1

Answer:

-1

Step-by-step explanation:

First, let's make the concepts clear.

• additive inverse is:-

The number adds to 0.

• multiplicative inverse is:-

The number multiplies to 1.

Now, the additive inverse is 2 and multiplicative is -1/2.

Therefore their multiplication is now -1.

More Information

How to find such inverses?

• additive inverse:-

When added, the number becomes 0.

(-2) + x = 0

∴x = 2 is the additive inverse.

• multiplicative inverse:-

When multiplied, the number becomes 1.

(-2) × x = 1

∴x = -1/2 is the additive inverse.

Answer 2

Answer :–

• Additive inverse of –2 is 2.

• Multiplicative inverse of –2 is $\sf -\dfrac{1}{2}$

We know that,

Multiplicative inverse = $\sf \dfrac{b}{a}$

So we have,

→ –2

We also know that,

If we haven't any denominator so the value of denominator is 1.

I.e.,

→ $\sf \dfrac{-2}{1}$

Now, we have to find the multiplicative inverse of $\sf \dfrac{-2}{1}$.

So,

Multiplicative inverse of $\sf \dfrac{-2}{1}$ is $\sf -\dfrac{1}{2}$

Additional Information :–

★ Additive inverse →

✒️ If we take a positive number, when we add the same number with negative sign and when we add both the numbers we get 0.

✒️ In simple words, it is a sign changing of a number.

✒️ Let's take some examples to understand more about this :

• Additive inverse of –2 is +2.

→ –2 + 2 = 0

• Additive inverse of $\sf \dfrac{9}{11}$ is $\sf -\dfrac{9}{11}$

→ $\sf \dfrac{9}{11}$ + $\sf ( -\dfrac{9}{11} )$ = $\sf \dfrac{9}{11}$ – $\sf \dfrac{9}{11}$ = 0

• Additive inverse of 45 is –45.

→ 45 + (–45) = 45 – 45 = 0

★ Multiplicative Inverse →

✒️ When we multiply a number by its multiplicative inverse then it should be 1 as a result after multiplying both the numbers.

✒️ It is also known as Reciprocal.

✒️ It means, Multiplicative inverse / Reciprocal of $\sf \dfrac{a}{b}$ is $\sf \dfrac{b}{a}$

✒️ Let's take some examples :

• Multiplicative inverse of 3 is $\sf \dfrac{1}{3}$

→ $\sf 3 \times \dfrac{1}{3}$ = $\sf \dfrac{3}{3}$ = 1

• Multiplicative inverse of $\sf \dfrac{5}{8}$ is $\sf \dfrac{8}{5}$

→ $\sf \dfrac{5}{8}$$\sf \dfrac{8}{5}$ = 1

• Multiplicative inverse of $\sf - \dfrac{7}{9}$ is $\sf -\dfrac{9}{7}$

→ $\sf \cancel{-\dfrac{7}{9}}$ × $\sf \cancel{-\dfrac{9}{7}}$ = 1