1 Revision Recall basics of fractions A fraction is a part of a whole like one half (1/ one third (1/3) two thirds (2/3) one quarter (1/4) etc Write the fraction represented by the shaded part in the following figure For example half of an apple is a fraction of an apple Shade the figure below to represent 2 The number above the vinculum (line) is called the Numerator and the number below the vinculum (line) is called the Denominator The fraction of 4 days in a week is since the total number of days in a week is 7 ¾ of 20 = 15 There are 28 pebbles in a bowl of them are brown in color ½ are red in color and the rest are white Find what fraction of pebbles is white in color There are 15 dozens of bananas in the shop Raju sold of them How many bananas didn t he sell? 3 dozens or 36 bananas 1
3 on a Number Line On a number line Proper fractions are represented between 0 and 1 Improper fractions are represented beyond 1 See below the table Represent on a number line See below the table To represent on the number line divide the gap between 0 and 1 into 5 equal parts and now represent on it 0 3 1 2 5 0 7 1 2 9 4 Types of The fraction in which the numerator is less than the denominator is called a proper fraction The fraction in which the numerator is greater than the denominator is called an improper fraction When the improper fraction is written as a combination of a whole and a part it is called a mixed fraction It is represented as: ( ) 4 6 25-24 1 Quotient = 4 Remainder = 1 Divisor = 6 ( ) Express the following as improper fractions: Express the following as mixed fractions: 2
5 Equivalent and Simplest Form of a Fraction Equivalent Equivalent fractions of a given fraction are formed by multiplying or dividing both numerator and denominator of the fraction by the same number fractions of are equivalent and Replace the blank in each of the following fractions with the correct number: 36 30 Simplest Form of a Fraction To reduce the given fraction to the simplest form we first find the HCF of numerator and denominator and then divide both of them by the HCF The simplest form of is Since HCF of 48 and 72 is 24 Reduce the following fractions into their simplest form: 6 Comparison of having the same denominators are called like fractions having different denominators are called unlike fractions In like fractions the fraction with the Since 3 < 7 and both are like fractions Since the numerators are same the Arrange the following fractions in ascending order: 3
biggest numerator is the largest and that with the smallest numerator is the smallest While comparing unlike fractions first convert them into like fractions by finding the LCM of denominators For unlike fractions whose numerators are same larger the denominator smaller is the fraction fraction with the smaller denominator is the larger one Since LCM of 5 and 7 is 35 and So we get 21 < 30 7 Addition of Addition of Like To add two or more like fractions add the numerators and put the answer over the common denominator The sum of since Find the sum of the following: and and Addition of Unlike To add two or more unlike fractions first change them into like fractions and then perform the addition Since the LCM of 6 and 5 is 30 So Thus Add: Anirudh uses of petrol per week to travel between home and office and 2 of petrol per week to get grocery every week from the market Find the total amount of petrol used by him in a week 4
8 Subtraction of Subtraction of Like To subtract two or more like fractions subtract the numerators in order and put the answer over the common denominator Difference of Since Solve Subtract the difference of from the sum of Subtraction of Unlike Solve: To subtract two or more unlike fractions first convert the fractions into like fractions by finding the LCM of their denominators and then then perform the subtraction Since the LCM of 5 and 9 is 45 So and In a park is occupied by grass bed is occupied by trees and the rest is used for path way Find what fraction of the park is used for pathway Thus 5