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Sagot :
The reciprocal of a rational number a/b is its multiplicative inverse, 1/(a/b) = b/a. That is, by definition of multiplicative inverse,
a/b • 1/(a/b) = 1
Then
1/(a/b) = b/(a/b • b) = b/a
So, the reciprocal of 17/19 is simply 19/17.
hello!
In order to find the reciprocal of a number, we should flop it over.
Now, "flopping over" is not the same as "changing the sign"
If we have a fraction, and we're asked to find its reciprocal, then the numerator and denominator switch places.
Please consult the following formula for more details:-
[tex]\sf{The~reciprocal~of~a~is~\frac{1}{a} }[/tex]
[tex]\sf{The~reciprocal~of~\frac{a}{b} ~is~\frac{b}{a} }}[/tex]
According to the [tex]Reciprocal~formula[/tex], the reciprocal of [tex]\displaystyle\frac{17}{19}[/tex] is:-
[tex]\sf{\displaystyle\frac{19}{17} }[/tex]
note:-
Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I'll comment and/or edit my answer :)
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