Question

What will be multiplicative inverse of a rational number \(\frac{5}{19}\) multiplied by its additive inverse ?
1. \(- \frac{361}{25}\)
2. \( \frac{361}{25}\)
3. \(\frac{381}{25}\)
4. \(-\frac{381}{25}\)

Answer 1

Correct Answer - Option 1 : \(- \frac{361}{25}\)

Concept:

• Additive inverse is what number you add to a given number to make the sum zero. For example, if we take the number 3 and add -3 to it, the result is zero. Hence, the additive inverse of 3 is -3. 

• The multiplicative inverse of a number is defined as a number which when multiplied by the original number gives the product as 1. 

Calculation:

The additive inverse of \(\frac{5}{19}\)is \(\frac{-5}{19}\).

According to the question,

\(\Rightarrow ​​​\frac{5}{19} \times ​\frac{-5}{19}\)

\(​\Rightarrow \frac{-25}{361}\)

Now, the multiplicative inverse of \(\frac{-25}{361}\) = \(- \frac{361}{25}\)

So, \(- \frac{361}{25}\) is the multiplicative inverse of a rational number \(\frac{5}{19}\) multiplied by its additive inverse.