Comparison of Unit Fractions
Category : 5th Class
Comparison of Unit Fractions
Comparison of Unit Fractions
\[\frac{1}{P}\]and\[\frac{1}{Q}\]are unit fractions where P and Q are natural numbers. Lf P > Q then\[\frac{1}{P}<\frac{1}{Q}.\]
Compare between\[\frac{1}{5}\] and \[\frac{1}{7}.\] Which is greater?
Solution:
Compare between their denominators 5 < 7 ( 5 is smaller than 7) Therefore, \[\frac{1}{5}>\frac{1}{7}.\]
Comparison of Like Fractions
Like fractions have same denominator. The fraction which has greater numerator is greater. For example,\[\frac{5}{7}\]and\[\frac{3}{7}\]are like fractions and 5 > 3, therefore, \[\frac{5}{7}>\frac{3}{7}.\]
Is \[\frac{24}{71}\] greater than \[\frac{12}{71}?\]
Solution:
Both the fractions have same denominator and 24 > 12Therefore, \[\frac{24}{71}>\frac{12}{71}.\]
Comparison of Unlike Fractions
To compare unlike fractions, unlike fractions are converted into like fractions, Numerator and denominator of one fraction is multiplied with the denominator of other fraction and vice-versa. For example, \[\frac{P}{Q}\]and \[\frac{R}{Q}\]are unlike fractions thus\[\frac{P\times S}{Q\times S}\]and\[\frac{R\times Q}{S\times Q}\]are like fractions. Now compare the numerators.
Compare between \[\frac{3}{4}\] and\[\frac{5}{7}.\] which is greater?
Solution:
First convert\[\frac{3}{4}\]and\[\frac{5}{7}\] into like fractions \[\frac{3\times 7}{4\times 7}=\frac{21}{28}\]and\[\frac{5\times 4}{7\times 4}=\frac{20}{28}\] Now compare numerators 21 > 20, therefore\[\frac{21}{28}>\frac{20}{28}\]or\[\frac{3}{4}>\frac{5}{7}.\]
In which one of the following figures does the unshaded part represent?\[\frac{2}{5}?\]
(a)
(b)
(c)
(d)
(e) None of these
Answer: (c)
Explanation
In the figure, which has been shown in the option C, 3 part out of the 5 part is shaded. Therefore, fractional representation often shaded part is \[\frac{2}{5}.\]
Which one of the following options has correct fractional representation for the yellow part in the given figure?
(a) \[\frac{2}{7}\]
(b) \[\frac{1}{7}\]
(c)\[\frac{4}{7}\]
(d)\[\frac{5}{7}\]
(e) None of these
Answer: (b)
There are 2564577 fishes in a pond. If every third fish in the pond is rehu, what is the fractional representation of the number of rehu fishes out of the total fishes in the pond?
(a)\[\frac{454855}{2564577}\]
(b)\[\frac{456487}{2564577}\]
(c)\[\frac{457858}{2564577}\]
(d)\[\frac{854859}{2564577}\]
(e) None of these
Answer: (d)
Jack cuts a paper sheet into 8 equal pieces then he cuts each of the pieces into 8 equal pieces then again he cuts each of the pieces into 4 equal pieces. Now he colours 36 pieces with yellow colour, 108 pieces with red colour, and 54 pieces with blue colour. Which one of the following is the fractional representation for the coloured pieces out of total pieces?
(a)\[\frac{194}{200}\]
(b)\[\frac{198}{256}\]
(c)\[\frac{200}{256}\]
(d)\[\frac{222}{256}\]
(e) None of these
Answer: (b)
A question paper contains two types of questions objective and subjective. If fractional representation for the number of subjective questions is\[\frac{36}{80},\]find the number of objective questions the question paper contains.
(a) 44
(b) 116
(c) 36
(d) 80
(e) None of these
Answer: (a)
\[\frac{a}{b}\]is a fraction where b > a. \[\frac{a}{b}\]is a/an_____.
(a) Proper fraction
(b) Improper fraction
(c) Mixed fraction
(d) Unitfraction
(e) None of these
Answer: (a)
Explanation
According to the question denominator is greater than numerator, therefore,\[\frac{a}{b}\]is a proper fraction.
Convert the fraction \[\frac{15}{6}\]into mixed fraction and choose the correct option.
(a)\[2\frac{1}{6}\]
(b)\[2\frac{2}{6}\]
(c)\[2\frac{3}{6}\]
(d)\[3\frac{2}{6}\]
(e) None of these
Answer: (c)
Convert\[4\frac{1}{5}\]into improper fraction and choose the correct option.
(a)\[\frac{19}{5}\]
(b)\[\frac{20}{5}\]
(c)\[\frac{21}{5}\]
(d)\[\frac{22}{5}\]
(e) None of these
Answer: (c)
Choose the proper fraction from the following: \[\frac{22}{5},\frac{12}{7},\frac{8}{9},\frac{7}{6},\frac{5}{4}\]
(a)\[\frac{22}{5}\]
(b)\[\frac{5}{4}\]
(c)\[\frac{12}{7}\]
(d)\[\frac{8}{9}\]
(e) None of these
Answer:(d)
Which one of the following is not true about the mixed fraction?
(a) Mixed fraction is a sum of a whole number and a proper fraction
(b) When a mixed fraction is converted into an improper fraction, denominatorof the improper fraction and the fractional part in the mixed fraction is equal
(c) To convert a mixed fraction into an improper fraction, the whole number andthe numerator of the fraction part is multiplied and the result is added bythe denominator
(d) All of these
(e) None of these
Answer:(c)
Which one of the following fractions is in its lowest form?
(a)\[\frac{35}{60}\]
(b)\[\frac{95}{171}\]
(c)\[\frac{96}{171}\]
(d)\[\frac{39}{190}\]
(e) None of these
Answer: (d)
Explanation
HCF of 39 and 190 is 1. Therefore, \[\frac{39}{190}\]is in its simplest form.
Which one of the following is the reciprocal of\[7\frac{3}{16}?\]
(a)\[\frac{115}{16}\]
(b)\[\frac{16}{112}\]
(c)\[\frac{16}{115}\]
(d)\[7\frac{16}{3}\]
(e) None of these
Answer: (c)
Explanation
First convert the mixed fraction\[7\frac{3}{16}\]into an improper fraction Thus\[7\frac{3}{16}=\frac{115}{16}.\]and reciprocal\[\frac{115}{16}=\frac{16}{115}.\]
Which one of the following statements is not true?
(a) If a fraction is in its lowest form, HCF of numerator and denominator is 1.
(b) Reciprocal of a fraction has reversed numerator and denominator.
(c) Product of a fraction and its reciprocal is 1.
(d) Two improper fractions can never be like fractions.
(e) None of these
Answer: (d)
By which one of the following numbers numerator and denominator of \[\frac{1}{19}\]should be multiplied to get its one equivalent fraction?
(a) 7
(b) 5
(c) 19
(d) 11
(e) All of these
Answer: (e)
Find the fraction if numerator is 7 and denominator is one-fourth of 16.
(a)\[\frac{5}{7}\]
(b)\[\frac{7}{5}\]
(c)\[\frac{2}{7}\]
(d)\[\frac{7}{4}\]
(e) None of these
Answer:(d)
Compare \[\frac{11}{20}\]and \[\frac{22}{9}.\]which one is greater?
(a)\[\frac{22}{9}\]
(b)\[\frac{11}{20}\]
(c) Both are equal
(d) All of these
(e) None of these
Answer: (a)
Explanation \[\frac{11\times 9}{20\times 9}=\frac{99}{180}\]and\[\frac{22\times 20}{9\times 20}=\frac{440}{180}\] \[\because \]\[440>99.\]Therefore,\[\frac{11}{20}<\frac{22}{9}\]
Which one of the following fractions is greater than \[\frac{23}{55}?\]
(a)\[\frac{28}{63}\]
(b)\[\frac{22}{75}\]
(c)\[\frac{4}{11}\]
(d)\[\frac{13}{65}\]
(e) None of these
Answer: (a)
Explanation
\[\frac{23\times 63}{55\times 63}=\frac{1449}{3465}\]and\[\frac{28\times 55}{63\times 55}=\frac{1540}{3465}\] \[\because \]\[1449<1540.\]Therefore,\[\frac{1540}{3465}>\frac{1449}{3465}.\]
If, \[\frac{1}{P}>\frac{1}{Q}\]Which one of the following is not true?
(a)\[\frac{1}{P}\]and\[\frac{1}{Q}\]are unit fractions
(b) Q is greater than P
(c)\[\frac{1}{P\times Q}\]and\[\frac{1}{Q\times P}\]are like fractions
(d) \[\frac{1}{P}\]and\[\frac{1}{Q}\]are equivalent fractions If 2P = Q
(e) None of these
Answer: (d)
The fraction which represents the shaded part in the figure 1 is smaller than the fraction which represents the shaded part in the figure 2.
The above statement is____.
(a)True
(b) False
(c) Partly true
(d) All of these
(e) None of these
Answer: (b)
A bag contains a number of balls of different colours. Jack finds number of blue balls is greater than number of red balls. It means:
(a) The fraction which represents red balls out of total balls is greater than that of blue balls
(b) The fraction which represents blue balls out of total balls is greater thanthat of red balls
(c) The fraction which represents red balls out of total balls is equivalent to the fraction which represents blue balls out of total balls
(d) All of these
(e) None of these
Answer: (b)
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