Revision Notes: Fractions | Mathematics Class 6 ICSE PDF Download

A fraction is a part of whole and is written as (a/b), where ‘a’ and ‘b’ are integers and 𝐛 ≠ 𝟎 
Ex: 2/3

• The upper term ‘a’ is called as “numerator” and lower term  ‘b’ is called the “denominator”. Thus  𝑭𝒓𝒂𝒄𝒕𝒊𝒐𝒏 = (𝐍𝐮𝐦𝐞𝐫𝐚𝐭𝐨𝐫/𝐃𝐞𝐦𝐨𝐦𝐢𝐧𝐚𝐭𝐨𝐫)
• Value of fraction = 1, if numerator = denominator 
• Value of fraction = 0, if numerator = 0; and denominator ≠ 0 
• Value of fraction is not defined if denominator = 0  
• Value of fraction remains unaltered  if it is multiplied and divided by same number 

Kinds of Fractions

• Simple Fraction: Fraction whose both terms integers. 
  Ex: 3/8, -7/3 
• Complex Fraction: Fraction whose one or both terms are fractional numbers. 
  Ex: 5/(8÷2) ; (9÷3)/(8÷2) 
• Decimal Fraction: Faction with denominator  10, 100, 1000, 10000.....
  Ex: 5/10, 56/100 
  Decimal Fraction = 3471/100 = 𝟑𝟒.𝟕𝟏  read as thirty four point seven one and 34 is the integral part and 0.71 is the decimal part. Adding or removing zeros at its extreme right will not change the value of fraction 
  Ex: 4.3 = 4.300; 3.6800 = 3.68
• Vulgar Fraction: Fraction  whose denominators are not 10, 100, 1000...
  Ex: 3/8, 4/2 
  Converting Decimal Fraction to Vulgar Fraction
  Remove decimal point and write resulting number as numerator and in denominator add as many zeros to right of one (1) as decimal places in given number
  Ex: 0.088 = 8/1000
  Reduce to simplest form 8/1000 = 11/125
• Proper Fraction: Fraction whose numnerator is less than or positive than its denominator. 
  Ex: 5/12, 135/245 
• Improper Fraction: Fraction whose numnerator is greater than its denominator. 
  Ex: 12/7, 335/245 
• Mixed Fraction: Fraction expressed as combination of an integer and a proper fraction.

Improper fraction expressed as Mixed fraction. 

• Ex: 49/12 can be written as 4(5/12) On dividing 49 by 12 we get 4 as quotient (Integer) as 5 as remainder (Numerator) and denominator is unaltered 

Mixed fraction expressed as Improper fraction.

• Ex∶ 5(7/8) can be written as 47/8; Numerator = (5 × 8) + 7 = 40 + 7 = 47 and Denominator is unaltered.

Fractions

• Equivalent Fractions: Fractions having same value are called equivalent fractions.
  Ex: 20/25 Dividing numnerator and denominator by 5 we get 4/5.
  28/35 on dividing by 7 we get 4/5. 
  Hence 20/25 and 28/35 are equivalent fractions 
• Like Fractions: Fractions having same denominators are called like fractions.
  Ex: 3/8, 5/4, 9/8 ...... 
• Unlike Fractions: Fractions with different denominators are called unlike fractions. 
  Ex: 2/6, 7/5, 9/3 ... 
• Bodmas: Bracket Of Division Multiplication Addition and Subtraction "of" between any two fractions is to be used as multiplication.  

Converting Unlike to like fractions: 

• Find LCM of denominators of all given fractions 
• Multiply each fraction’s numerator and denominator with same number such that denominator is equal to the LCM  
  
• Comparing Fractions: Convert the fractions into like fractions and then the fraction with the greater numerator is greater. 

Inserting Fraction between given fraction:

• Add numerator of the given fractions to get the required numerator
• Similarly add denominator to get the required denominator 

Fundamental Operations on Fractions

• Multiplication by an integer Keep denominator unchanged, multiply numerator by integer and simplify 
  Ex: 4 x (4/12) = 16/12 = 4/3
• Multiplication by fraction Multiply numerators together and denominators separately together and simplify 
  Ex:

Addition and Subtraction

• Fractions having same denominator 6(2/5) and 4(4/5)
  Convert into improper fraction 32/5 ± 24/5 
  Add / Sub the numerators of each fraction and denominator is retained. 
  (32 ± 24)/5  If the resultant is improper fraction convert to Mixed fraction 
• Fractions having different denominator 6(2/5) and 4(4/4)
  Convert into improper fraction 32/5 ± 20/4 
  Take L.C.M of numerators L.C.M (5, 4) = 20 which is the denominator Multiply each fraction with LCM  resultant are added/subtracted to numerator (32/5 x 20) ± (20/4 x 20) = (32×4) ± (20×5) = 128 ± 100

Division 

• Division in fraction Multiply fraction by the reciprocal of the divisor and simplify
  
• Division in decimal fraction Division by 10, 100,1000,…..shift decimal point to left as many digits as the number of zeros 
  Ex: 𝟒𝟑.𝟒 ÷ 𝟏𝟎𝟎 = 𝟎.𝟒𝟑𝟒 
• Division of decimal fraction by an integer is done like ordinary division and the decimal point is placed to quotient such that its number of digits after decimal point is equal to digits after decimal point in the dividend
  Ex: 𝟓.𝟔𝟒 ÷ 𝟐 = 𝟐.𝟖𝟐