5th Class

     Introduction   In the previous chapter we have studied about the fractions. In this chapter we will  study some operations on the fractions like addition, subtraction, multiplication, I and division on fractions.                

  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, more...

    Reciprocal of a Fraction     Reciprocal of a fraction is the fraction by which if the fraction is multiplied the product is 1. The reciprocal of a fraction has reversed numerator and denominator. For example,\[\frac{Q}{P}\]is the reciprocal of the fraction\[\frac{P}{Q}.\]     Find the reciprocal of \[\frac{11}{13}.\]   Solution: Reciprocal of \[\frac{11}{13}=\frac{13}{11}.\]  

    Equivalent Fractions     Two or more fractions are said to be equivalent fractions if they have the same value. In other word s when equivalent fractions are reduced into their simplest form, they give the same fraction. For example, \[\frac{10}{15},\frac{20}{30},\frac{30}{45},\frac{40}{60}...\] etc. are equivalent fractions.       Are the fractions\[\frac{24}{27}\]and\[\frac{8}{9}\]equivalent fractions?   Solution: The simplest form of \[\frac{24}{27}=\frac{8}{9}.\]Therefore, \[\frac{24}{27}\] and \[\frac{8}{9}\]are equivalent fractions.     How to Find Equivalent Fractions of a Given Fraction Multiply both the numerator and denominator of the given fraction by a common number.         Find three equivalent fractions of\[\frac{6}{7}.\]   Solution: (a)\[\frac{6}{7}=\frac{6\times 2}{7\times 2}=\frac{12}{14}\]         (b)\[\frac{6}{7}=\frac{6\times 3}{7\times 3}=\frac{18}{21}\] (c)\[\frac{6}{7}=\frac{6\times 4}{7\times 4}=\frac{24}{28}\] Thus \[\frac{12}{14},\frac{18}{21}\]and \[\frac{24}{28}\]are equivalent fractions of \[\frac{6}{7}.\]

    Lowest or Simplest Form of a Fraction                   When HCF of numerator and denominator of a fraction is 1, the fraction is in its simplest or lowest form. For example: The fraction \[\frac{5}{7}\]is in its simplest form as HCF of 5 and 7 is 1.     Is the fraction \[\frac{27}{72}\] in its lowest form?   Solution: HCF of 27 and 72 is 9. Therefore, the fraction \[\frac{27}{72}\] is not in its simplest form.       How to Reduce a Fraction into Lowest Form To reduce a fraction into its lowest form, numerator and denominator of the fraction is divided by their HCF. The resulting fraction is the reduced form of the given fraction.       Reduce the fraction more...

   Coversion of Fractions       Conversion of an Improper Fraction into a Mixed Fraction Divide the numerator by the denominator. The quotient represents the whole number, the remainder represents the numerator and the divisor represents the denominator for the fractional part in the mixed fraction.       Change \[\frac{189}{18}\]into a mixed fraction.   Solution: Divide 189 by 18       Thus remainder = 9, Quotient = 10, and divisor = 18 Therefore, the mixed fraction for \[\frac{189}{18}=10\frac{9}{18}.\]         Conversion of a Mined Fraction into an Improper Fraction The whole number is multiplied with the denominator of the fractional part and the product is added by numerator. The sum represents numerator for the improperfraction and denominator of the more...

  Fraction       Like Fraction The fractions which have the same denominator are called like fractions. For example, \[\frac{5}{7},\frac{9}{7},\frac{5}{7}\]are like fractions as they have the same denominator.     Write the like fraction of \[\frac{8}{21}\]whose numerator is 4.   Answer: According to the question numerator should be 4 and like fractions have same denominator thus the required fraction will be \[\frac{4}{21}.\]     Unlike Fraction The fractions which have different denominators are called unlike fractions. For example, \[\frac{58}{87},\frac{52}{75},\frac{45}{88}\]are unlike fractions as they have different denominators.     Represent the shaded part in the following figures into fractional form and check are they unlike fractions?     Fractional more...

    Introduction   Fraction is a number which is used to represent a part of a whole. It is in the form P of \[\frac{P}{Q}\]. Where P and Q are natural numbers. P is called numerator of the fractionand Q is called denominator. For example, \[\frac{5}{9}\] is a fraction, where 5 is numeratorand 9 is denominator of the fraction.       Represent the shaded part of the following figure as a fraction and write numerator and denominator of the fraction.     Explanation The above figure has been divided into 5 equal parts. Out of 5 parts 1 part is shaded. Therefore, fractional representation of the shaded part \[\frac{1}{5}\] and numerator = 1, and denominator = 5.

   Multiples                When two or more than two numbers are multiplied with each other, the resulting number is the multiple of all that numbers. For example, if A x B = C, C is multiple of both A and B.       Multiples of 5 = 5, 10, 15, 20, 25, ____ Multiples of 2 = 2, 4, 6, 8, 10, 12,____ Multiples of 10 = 10, 20, 30, 40, ____ Common Multiples The same multiples of two or more than two different numbers are called common multiples.     Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40,__ Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45,___ Common multiples of 4 and 5 = 20, 40, more...

    Common Factors     The same factors of two or more than two different numbers are called common factors.       Factors of 24 = 1, 2, 3,4, 6, 8, 12, 24 Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30. Here 1, 2, 3, and 6 are the common factors of 24 and 30.       Co-prime or Relatively Prime Numbers If two numbers have only one common factor, the numbers are called co-prime or relatively prime numbers.       Factors of 2 = 1, 2 Factors of 5 = 1, 5 Thus 2 and 5 have only one common factor 1, therefore, 2 and 5 are co- prime numbers.     more...