Write true (T) or false (F):
(i) In an improper fraction, the numerator is always greater than the denominator.
(ii) The product of two proper fractions can be an improper fraction.
(iii) Any improper fraction is always greater than any proper fraction.
(iv) Every unit fraction is equal to 1.
(v) The reciprocal of a proper fraction is an improper fraction.
(vi) The product of two proper fractions is always greater than each of the two proper fractions.
(vii) There exists a fraction whose multiplicative inverse is equal to the fraction itself.
(viii) The product of a proper fraction and and an improper fraction is always less than the improper fraction.

Question

Write true (T) or false (F):
(i) In an improper fraction, the numerator is always greater than the denominator.
(ii) The product of two proper fractions can be an improper fraction.
(iii) Any improper fraction is always greater than any proper fraction.
(iv) Every unit fraction is equal to 1.
(v) The reciprocal of a proper fraction is an improper fraction.
(vi) The product of two proper fractions is always greater than each of the two proper fractions.
(vii) There exists a fraction whose multiplicative inverse is equal to the fraction itself.
(viii) The product of a proper fraction and and an improper fraction is always less than the improper fraction.

KnowledgeBoat · Accepted Answer

(i) False Reason — In an improper fraction, the numerator may be equal to or greater than the denominator. (ii) False Reason — A proper fraction is less than 1. The product of two numbers less than 1 is always less than 1. Hence, it remains a proper fraction. (iii) True Reason — An improper fraction is greater than or equal to 1. A proper fraction is always less than 1. Therefore, any improper fraction is greater than any proper fraction. (iv) False Reason — A unit fraction is any fraction with a numerator of 1, such as . Only the fraction is equal to 1. (v) True Reason — In a proper fraction, the denominator is larger than the numerator. When you take the reciprocal, the larger number becomes the numerator, making it an improper fraction. (vi) False Reason — The product of two proper fractions is always less than each of them. (vii) True Reason — The number 1 can be written as the fraction . Its multiplicative inverse (reciprocal) is also , which is equal to the original fraction. (Similarly, or also shares this property). (viii) True Reason — A proper fraction is less than 1. When a number is multiplied by a fraction less than 1, the product becomes smaller than the original number.

Mathematics

Fractions

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