1. Revision Description Reflect and Review Teasers Answers Recall basics of fractions To convert into mixed fraction: improper fraction.

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1 4 1 Revision Reflect and Recall basics of fractions To convert into mixed fraction: Here is an improper fraction So on dividing 23 by 6 we get Quotient = 3 and Remainder = 5 Thus the mixed fraction form is Convert to improper fraction Rocky answered only 9 questions out of 15 in the English exam What fraction of questions did he not answer? To evaluate of 150 Here on dividing 150 by 15 we get 10 and on multiplying this with 4 we get 40 of 150 = = 40 2 Equivalent fractions Reflect and Finding Equivalent Equivalent fractions for are Find two equivalent fractions of Fill in the boxes to 1; 128 1

2 a given fraction can be found either by multiplying both the numerator and denominator by the same number or by dividing both the numerator and denominator by the same number equivalent fractions since and form equivalent fractions: Checking for Equivalent Check whether and are Yes To check whether two fractions are equivalent or not we can use cross multiplication ie multiply the numerator of the first fraction by the denominator of the second and the denominator of the first fraction by the numerator of the second If both the products are equal then the given fractions are equivalent otherwise they are not equivalent and are not equivalent fractions since 7 8 = 56 and 12 5 = 60 and equivalent or not 3 Lowest Form of a Fraction A fraction is said to be in its lowest form if the only common factor of the numerator and the denominator is 1 Reducing a given fraction to its lowest Reflect and since HCF of 48 and 108 is 12 Reduce the following to its lowest form: 2

3 form can be done using either the two given methods: Method 1: A fraction can be reduced to its lowest form by dividing both the numerator and the denominator by a common factor Repeat the process till the numerator and the denominator have no common factor except 1 Method 2: Find the HCF of the numerator and the denominator and divide both of them by their HCF The fraction will get reduced to the lowest form in one step 4 Comparison of Comparison of Like Between Reflect and smallest is the Arrange Like fractions have same denominator So we can easily compare them by comparing the numerators When the denominators are same the fraction with the smallest numerator is the smallest in ascending order 3

4 Comparison of Unlike Arrange Case 1: with the same numerator Between the smallest is When the numerators are same the fraction with the largest denominator is the smallest in ascending order Arrange descending order in Case 2: with different numerators - Convert these type of unlike fractions into like fractions by making the denominators same are in ascending order Since they are all unlike fractions the LCM of denominators 8 3 and 4 is 24 So and 5 Addition of Reflect and Addition of Like To add two or more like fractions add the numerators and put the answer over the same denominator The sum of since Find the sum of the following: and and 4

5 Addition of Unlike Solve To add two or more unlike fractions first change them into like fractions and then add Since the LCM of 5 and 7 is 35 So Raghu Neel and Monti decided to fill the tank with water Raghu filled the tank Neel filled the tank and Monti filled th of th of th Yes And of the tank Could three of them together fill the tank completely or not? Addition of Mixed Solve: 16 Method 1: First add the whole numbers and then add the fractions Method 2: Convert the mixed fractions into improper fractions and then add Since = 5 and Anupam bought 1 ½ kg of sugar and 3 ¼ kg of flour and kg of butter to bake her cake Find the total weight of ingredients used by her to bake the cake 6 kg 6 Subtraction of Subtraction of Like To subtract two or more like fractions subtract the numerators in order and put the answer over the same denominator Reflect and The difference of since Solve: Subtract from 5

6 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 subtract Since the LCM of 5 and 9 is 45 So and Neetu completed reading ½ of the book last week and she completed reading of the remaining in the first two days of this week Find what fraction of the book is left for her to finish Subtraction of Mixed Solve: First convert the mixed fractions into improper fractions with the same denominator and then subtract Since Meenakshi bought 15 L of oil in her monthly grocery and by the end of the month she was left with 8 ¾ L of oil How much did she consume in the whole month? 6 L 7 Multiplication of Multiplication of a Fraction by a Whole Number Reflect and Simplify the following: 216 Step 1: Write the whole number as a fraction with 1 as the denominator Step 2: Cancel out the common factors in the numerator and the denominator since 135 can be written as and be simplified as 6

7 Step 3: Multiply the numerators and multiply the denominators to obtain the final product Multiplication of a Fraction by Another Fraction Step 1: Multiply the numerators and the denominators respectively Step 2: Simplify to reduce it to the lowest form Here on cancelling the common factors we get which gives the product as Solve: Subhash s mother packed him with th of the cake made by her for his lunch Subash shared ¼ of it with his friend What part of the cake did Subhash s friend get? 3 th of the cake Multiplication of a Fraction by a Mixed Fraction The cost of 1 kg of rice is 45 ½ What is the cost of 5 ½ kg of rice? 250 ¼ Step 1: Change the mixed fraction into improper fraction and cancel out the common factors in the numerator and the denominator Since improper fraction form of is and cancelling the common factors Solve: Step 2: Multiply the numerators and the denominators respectively we get Step 3: Simplify to get a mixed fraction 7

8 8 Multiplicative Inverse Reflect and Two numbers are said to be multiplicative inverse of each other if their product is 1 The multiplicative inverse of 4 is ¼ since 4 ¼ = 1 Write the multiplicative inverse of the following: 1 9 Division of Division of a Whole Number by a Fraction Step 1: First we find the multiplicative inverse of the divisor Step 2: Then we multiply the dividend with the multiplicative inverse of the divisor and write the answer in the lowest form Division of a Fraction by a Whole Number While dividing a fraction by a whole number we need to write the whole number as a fraction with denominator 1 and follow the same steps as above Reflect and Since its multiplicative inverse is Since and and multiplicative inverse of 187 is Solve: Amrit ordered 8 pizzas for his birthday party and he distributed them equally among his friends and himself such that each of them could get ½ of a pizza Find how many friends had pizza Solve: 27 The weight of 25 bags of rice is 175 kg 500 g Find the weight of each bag of rice kg Division of a Fraction by Another Fraction Same as the division of whole number by a fraction Since the multiplicative inverse of is Divide the following: ¾ 8