Question

The multiplicative inverse of \[ - 3\dfrac{4}{7}\] is ?

Answer 1

Hint:The question above involves a mixed fraction and we need to find the multiplicative inverse of the fraction. First, we will convert the fraction into improper fraction and then we will find the multiplicative inverse. For that we should know the multiplicative inverse is the product of the number and its inverse such that the result is 1. So applying this we will find the answer.

Complete step by step answer:
Given the fraction is, \[ - 3\dfrac{4}{7}\] is a mixed fraction form.
Now we will find the improper fraction of the fraction above.
\[ - 3\dfrac{4}{7} = \dfrac{{7 \times \left( { - 3} \right) + 4}}{7} = \dfrac{{ - 17}}{7}\]
This is the improper fraction.
Now as we know that multiplicative inverse means \[a \times \dfrac{1}{a} = 1\].
Now we will apply this to the fraction above.
\[\dfrac{{ - 17}}{7} \times \dfrac{7}{{\left( { - 17} \right)}} = 1\]
Thus the multiplicative inverse is \[\dfrac{7}{{\left( { - 17} \right)}}\]. But we will shift the minus sign from the denominator to the numerator only.

Thus the final answer is \[\dfrac{{ - 7}}{{17}}\].

Note:In this question the part where students can get confused is only between multiplicative inverse and additive inverse. Additive inverse is the number when added with the given number gives zero as the final answer. Like if a is the given number then, \[ - a\] will be the additive inverse such that, \[a + \left( { - a} \right) = 0\].

And in case of multiplicative inverse \[a \times \dfrac{1}{a} = 1\] this should be followed.
The thing that is to be noticed is that in the additive inverse the sum should be zero and in the multiplicative inverse the product should be 1. Also be careful regarding the signs. The multiplicative inverse of a positive number is positive and that of negative is always negative.But this is exactly opposite in case of additive inverse.