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Find the reciprocal of \[\dfrac{3}{5},\dfrac{9}{{10}},\dfrac{3}{9},\dfrac{7}{4}\] and \[\dfrac{9}{2}\], also classify them as proper, improper fractions.

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Last updated date: 21st Jul 2024
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Answer
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Hint: Here the question is related to the topic, fractions. First we have to determine the reciprocal of each fractions and then we have to classify them as proper and improper fractions. First we know about the reciprocal and definition of proper and improper fractions. Hence we get required solution for the question

Complete step by step solution:
In Mathematics, reciprocal means an expression which when multiplied by another expression, gives unity (1) as a result. The reciprocal of any quantity is, one divided by that quantity, it is also called the multiplicative inverse.
For any number ‘a’, the reciprocal will be \[\dfrac{1}{a}\].
Now consider the given question
\[\dfrac{3}{5},\dfrac{9}{{10}},\dfrac{3}{9},\dfrac{7}{4}\] and \[\dfrac{9}{2}\]
In fractions, to determine the reciprocal we interchange the numerator value to the denominator value.
The reciprocal of \[\dfrac{3}{5}\] is \[\dfrac{5}{3}\]. The reciprocal of \[\dfrac{9}{{10}}\] is \[\dfrac{{10}}{9}\]. The reciprocal of \[\dfrac{3}{9}\] is \[\dfrac{9}{3}\]. The reciprocal of \[\dfrac{7}{4}\] is \[\dfrac{4}{7}\]. The reciprocal of \[\dfrac{9}{2}\] is \[\dfrac{2}{9}\].
Now we must classify these fractions as proper and improper fractions.
First we know the definition of proper and improper fractions:
Proper fraction: A fraction where the numerator is less than the denominator.
Improper fraction: A fraction where the numerator is greater than the denominator.
Therefore the proper fractions are \[\dfrac{4}{7}\] and \[\dfrac{2}{9}\].
The improper fractions are \[\dfrac{5}{3}\], \[\dfrac{{10}}{9}\] and \[\dfrac{9}{3}\].
Hence we have determined the solution for the given question.

Note: To solve these kinds we must know about actual definitions. If we go wrong with definition means then the solution will be wrong. Suppose in the question if they mention the inverse instead of reciprocal the same methodology is implemented to determine the reciprocal.