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How do you find the reciprocal of \[ - 5\dfrac{1}{3}\]

Last updated date: 20th Jun 2024
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Hint: We know that fraction is a part of whole. Here we are given with a mixed fraction. We have to convert this into an improper fraction first. For that we will multiply the denominator with the whole number and then add it to the numerator, this is the process. And when we write this with a denominator is the same. Mixed fraction to improper fraction \[ \Rightarrow \dfrac{{{\text{denominator multiply whole number + numerator}}}}{{{\text{denominator}}}}\]. Then to find the reciprocal we write the fraction as one divided by form. Then simplifying it we get the reciprocal of the given fraction.

Complete step by step solution:
Given that is a mixed fraction \[ - 5\dfrac{1}{3}\].
While converting into the improper fraction we will use the formula mentioned above.
Mixed fraction to improper fraction \[ \Rightarrow \dfrac{{{\text{denominator multiply whole number + numerator}}}}{{{\text{denominator}}}}\]
\[ - 5\dfrac{1}{3} \Rightarrow \dfrac{- 5 \times 3 + 1}{3}\]
On solving this we get,
\[ - 5\dfrac{1}{3} \Rightarrow \dfrac{{{\text{ - 15 + 1}}}}{3}\]
On adding the numbers in numerator
\[ - 5\dfrac{1}{3} \Rightarrow \dfrac{{ - 14}}{3}\]
Now to find the inverse we write the given fraction as,
\[{\text{inverse = }}\dfrac{{\text{1}}}{{{\text{ given fraction}}}}\]
\[{\text{inverse = }}\dfrac{{\text{1}}}{{\dfrac{{ - 14}}{3}}}\]
Rearranging and writing in standard form,
\[{\text{inverse = }}\dfrac{{ - 3}}{{14}}\]
This is our final answer.

Additional information:
Mixed fraction: It is a combination of whole number and fraction. It is written as \[a\dfrac{b}{c}\] where \[a\] is the whole number part and the fraction is \[\dfrac{b}{c}\].
Improper fraction: It is the type of fraction having numerator greater than denominator.
Proper fraction: It is the type of fraction having numerator less than denominator.Fractions are involved in mathematics and in the calculation part at the most.Percentage is one big concept that totally depends on the fraction.

Note: Here we first converted the mixed fraction into improper. After that when we go for inverse remember the denominator of the denominator becomes the numerator of the answer. How? See the example If a fraction is \[\dfrac{1}{{\dfrac{a}{b}}}\] where 1 is the numerator and \[\dfrac{a}{b}\] is the denominator then on simplifying it and writing in standard form means \[\dfrac{b}{a}\]. That’s it! Also note that always write minus sign in numerator. And if the fraction is like \[\dfrac{c}{{\dfrac{a}{b}}}\] then we can write, \[\dfrac{{c \times b}}{a}\].