**Category : **5th Class

**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\[\frac{3}{4}>\frac{5}{7}.\]

- Development of Egyptian fraction occurred in the middle kingdom of Egypt.
- The Hindus are believed to be the first group to represent fractions with numbers rather than words.
- Early Hindu mathematicians (Brahmagupta and bhaskara) wrote fractions as we do today.
- Earlier, in fractions bar was not used just one number above the other indicates a fraction.

- Fraction is a part of a whole.
- Numerator of proper fraction is smaller than denominator.
- Numerator of improper fraction is greater than denominator.
- Unit fractions have the numerator 1.
- Like fractions have same denominator.
- Unlike fractions have different denominator.
- Equivalent fractions have same value.
- Reciprocal of a fraction has reversed numerator and denominator.
- Value of a proper fraction is less than 1.
- Value of an improper fraction is always greater than 1.
- Improper fraction is always greater than proper fraction.

**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)**

*play_arrow*Fractions and Operation on Fractions*play_arrow*Introduction*play_arrow*Fraction*play_arrow*Coversion of Fractions*play_arrow*Lowest or Simplest Form of a Fraction*play_arrow*Equivalent Fractions*play_arrow*Reciprocal of a Fraction*play_arrow*Comparison of Unit Fractions

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