Answer

Verified

448.2k+ views

**Hint**: We start solving this problem by finding the additive inverse of the obtained number after multiplying given numbers. Then we find the multiplicative inverse of the other given number and then multiply obtained results to obtain the final answer.

**:**

__Complete step-by-step answer__Additive inverse of a number is a real number which sums up to the given number and gives zero.

Let us consider the definition of additive inverse.

Let a and b be two real numbers. Then we say b is the additive inverse of a, if

$ a+b=0 $ .

Let us consider the given number $ \dfrac{-2}{7}\times \dfrac{4}{5} $ as a.

Now, we need to find the additive inverse of a that is b.

Then, by the definition above, we get

\[\begin{align}

& \Rightarrow \left( \dfrac{-2}{7}\times \dfrac{4}{5} \right)+b=0 \\

& \Rightarrow \left( \dfrac{-8}{35} \right)+b=0 \\

& \Rightarrow b=-\left( \dfrac{-8}{35} \right) \\

& \Rightarrow b=\dfrac{8}{35} \\

\end{align}\]

So, the additive inverse of $ \dfrac{-2}{7}\times \dfrac{4}{5} $ is \[\dfrac{8}{35}\].

Now, let us consider the definition of Multiplicative Inverse.

Multiplicative inverse of a number is nothing but the reciprocal of the number, i.e., the multiplicative inverse of x is $ \dfrac{1}{x} $ .

We need to find the multiplicative inverse of $ \dfrac{13}{21} $ .

So, from the definition above, we get

\[\begin{align}

& \Rightarrow \dfrac{1}{\dfrac{13}{21}} \\

& \Rightarrow \dfrac{21}{13} \\

\end{align}\]

Now, we need to multiply the both obtained results to get the required result.

So, multiplying them we get

\[\Rightarrow \dfrac{8}{35}\times \dfrac{21}{13}\]

As both 21, 35 are divisible by 7 we reduce them. Then we get

\[\begin{align}

& \Rightarrow \dfrac{8}{5}\times \dfrac{3}{13} \\

& \Rightarrow \dfrac{24}{65} \\

\end{align}\]

Therefore, the product of additive inverse $ \dfrac{-2}{7}\times \dfrac{4}{5} $ of and multiplicative inverse of $ \dfrac{13}{21} $ is \[\dfrac{24}{65}\].

Hence the answer is \[\dfrac{24}{65}\].

**Note**: While finding the additive inverse of $ \dfrac{-2}{7}\times \dfrac{4}{5} $ , there is a chance of making mistake by finding additive inverse for both the numbers and multiply them like

Additive inverse of $ \dfrac{-2}{7} $ is $ \dfrac{-2}{7}+x=0\Rightarrow x=-\left( \dfrac{-2}{7} \right)=\dfrac{2}{7} $ .

Additive inverse of $ \dfrac{4}{5} $ is $ \dfrac{4}{5}+x=0\Rightarrow x=-\left( \dfrac{4}{5} \right)=-\dfrac{4}{5} $ .

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

How do you graph the function fx 4x class 9 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

What organs are located on the left side of your body class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell