Page 1 Subhash had learnt about fractions in Classes IV and V , so whenever possible he would try to use fractions. One occasion was when he forgot his lunch at home. His friend Farida invited him to share her lunch. She had five pooris in her lunch box. So, Subhash and Farida took two pooris each. Then Farida made two equal halves of the fifth poori and gave one-half to Subhash and took the other half herself. Thus, both Subhash and Farida had 2 full pooris and one-half poori. Where do you come across situations with fractions in your life? Subhash knew that one-half is written as 1 2 . While eating he further divided his half poori into two equal parts and asked Farida what fraction of the whole poori was that piece? (Fig 7.1) Without answering, Farida also divided her portion of the half puri into two equal parts and kept them beside Subhash’s shares. She said that these four equal parts together make Fig 7.2 Fig 7.1 7.1 Introduction Chapter 7 Chapter 7 Chapter 7 Chapter 7 Chapter 7 Fractions Fractions Fractions Fractions Fractions 2 pooris + half-poori–Subhash 2 pooris + half-poori–Farida 2020-21 Page 2 Subhash had learnt about fractions in Classes IV and V , so whenever possible he would try to use fractions. One occasion was when he forgot his lunch at home. His friend Farida invited him to share her lunch. She had five pooris in her lunch box. So, Subhash and Farida took two pooris each. Then Farida made two equal halves of the fifth poori and gave one-half to Subhash and took the other half herself. Thus, both Subhash and Farida had 2 full pooris and one-half poori. Where do you come across situations with fractions in your life? Subhash knew that one-half is written as 1 2 . While eating he further divided his half poori into two equal parts and asked Farida what fraction of the whole poori was that piece? (Fig 7.1) Without answering, Farida also divided her portion of the half puri into two equal parts and kept them beside Subhash’s shares. She said that these four equal parts together make Fig 7.2 Fig 7.1 7.1 Introduction Chapter 7 Chapter 7 Chapter 7 Chapter 7 Chapter 7 Fractions Fractions Fractions Fractions Fractions 2 pooris + half-poori–Subhash 2 pooris + half-poori–Farida 2020-21 MATHEMATICS 134 one whole (Fig 7.2). So, each equal part is one-fourth of one whole poori and 4 parts together will be 4 4 or 1 whole poori. When they ate, they discussed what they had learnt earlier. Three parts out of 4 equal parts is 3 4 . Similarly, 3 7 is obtained when we divide a whole into seven equal parts and take three parts (Fig 7.3). For 1 8 , we divide a whole into eight equal parts and take one part out of it (Fig 7.4). Farida said that we have learnt that a fraction is a number representing part of a whole. The whole may be a single object or a group of objects. Subhash observed that the parts have to be equal. 7.2 A Fraction Let us recapitulate the discussion. A fraction means a part of a group or of a region. 5 12 is a fraction. We read it as “five-twelfths”. What does “12” stand for? It is the number of equal parts into which the whole has been divided. What does “5” stand for? It is the number of equal parts which have been taken out. Here 5 is called the numerator and 12 is called the denominator. Name the numerator of 3 7 and the denominator of 4 15 . 2 3 Play this Game You can play this game with your friends. Take many copies of the grid as shown here. Consider any fraction, say 1 2 . Each one of you should shade 1 2 of the grid. Fig 7.4 Fig 7.3 2020-21 Page 3 Subhash had learnt about fractions in Classes IV and V , so whenever possible he would try to use fractions. One occasion was when he forgot his lunch at home. His friend Farida invited him to share her lunch. She had five pooris in her lunch box. So, Subhash and Farida took two pooris each. Then Farida made two equal halves of the fifth poori and gave one-half to Subhash and took the other half herself. Thus, both Subhash and Farida had 2 full pooris and one-half poori. Where do you come across situations with fractions in your life? Subhash knew that one-half is written as 1 2 . While eating he further divided his half poori into two equal parts and asked Farida what fraction of the whole poori was that piece? (Fig 7.1) Without answering, Farida also divided her portion of the half puri into two equal parts and kept them beside Subhash’s shares. She said that these four equal parts together make Fig 7.2 Fig 7.1 7.1 Introduction Chapter 7 Chapter 7 Chapter 7 Chapter 7 Chapter 7 Fractions Fractions Fractions Fractions Fractions 2 pooris + half-poori–Subhash 2 pooris + half-poori–Farida 2020-21 MATHEMATICS 134 one whole (Fig 7.2). So, each equal part is one-fourth of one whole poori and 4 parts together will be 4 4 or 1 whole poori. When they ate, they discussed what they had learnt earlier. Three parts out of 4 equal parts is 3 4 . Similarly, 3 7 is obtained when we divide a whole into seven equal parts and take three parts (Fig 7.3). For 1 8 , we divide a whole into eight equal parts and take one part out of it (Fig 7.4). Farida said that we have learnt that a fraction is a number representing part of a whole. The whole may be a single object or a group of objects. Subhash observed that the parts have to be equal. 7.2 A Fraction Let us recapitulate the discussion. A fraction means a part of a group or of a region. 5 12 is a fraction. We read it as “five-twelfths”. What does “12” stand for? It is the number of equal parts into which the whole has been divided. What does “5” stand for? It is the number of equal parts which have been taken out. Here 5 is called the numerator and 12 is called the denominator. Name the numerator of 3 7 and the denominator of 4 15 . 2 3 Play this Game You can play this game with your friends. Take many copies of the grid as shown here. Consider any fraction, say 1 2 . Each one of you should shade 1 2 of the grid. Fig 7.4 Fig 7.3 2020-21 Fractions and Fractions and Fractions and Fractions and Fractions and Integers Integers Integers Integers Integers Fractions and Fractions and Fractions and Fractions and Fractions and Integers Integers Integers Integers Integers FRACTIONS 135 1 6 1 3 3 4 EXERCISE 7.1 1. Write the fraction representing the shaded portion. 2. Colour the part according to the given fraction. 1 4 (v) (vi) (vii) (viii) (i) (ii) (iii) (iv) (ix) (x) 4 9 2020-21 Page 4 Subhash had learnt about fractions in Classes IV and V , so whenever possible he would try to use fractions. One occasion was when he forgot his lunch at home. His friend Farida invited him to share her lunch. She had five pooris in her lunch box. So, Subhash and Farida took two pooris each. Then Farida made two equal halves of the fifth poori and gave one-half to Subhash and took the other half herself. Thus, both Subhash and Farida had 2 full pooris and one-half poori. Where do you come across situations with fractions in your life? Subhash knew that one-half is written as 1 2 . While eating he further divided his half poori into two equal parts and asked Farida what fraction of the whole poori was that piece? (Fig 7.1) Without answering, Farida also divided her portion of the half puri into two equal parts and kept them beside Subhash’s shares. She said that these four equal parts together make Fig 7.2 Fig 7.1 7.1 Introduction Chapter 7 Chapter 7 Chapter 7 Chapter 7 Chapter 7 Fractions Fractions Fractions Fractions Fractions 2 pooris + half-poori–Subhash 2 pooris + half-poori–Farida 2020-21 MATHEMATICS 134 one whole (Fig 7.2). So, each equal part is one-fourth of one whole poori and 4 parts together will be 4 4 or 1 whole poori. When they ate, they discussed what they had learnt earlier. Three parts out of 4 equal parts is 3 4 . Similarly, 3 7 is obtained when we divide a whole into seven equal parts and take three parts (Fig 7.3). For 1 8 , we divide a whole into eight equal parts and take one part out of it (Fig 7.4). Farida said that we have learnt that a fraction is a number representing part of a whole. The whole may be a single object or a group of objects. Subhash observed that the parts have to be equal. 7.2 A Fraction Let us recapitulate the discussion. A fraction means a part of a group or of a region. 5 12 is a fraction. We read it as “five-twelfths”. What does “12” stand for? It is the number of equal parts into which the whole has been divided. What does “5” stand for? It is the number of equal parts which have been taken out. Here 5 is called the numerator and 12 is called the denominator. Name the numerator of 3 7 and the denominator of 4 15 . 2 3 Play this Game You can play this game with your friends. Take many copies of the grid as shown here. Consider any fraction, say 1 2 . Each one of you should shade 1 2 of the grid. Fig 7.4 Fig 7.3 2020-21 Fractions and Fractions and Fractions and Fractions and Fractions and Integers Integers Integers Integers Integers Fractions and Fractions and Fractions and Fractions and Fractions and Integers Integers Integers Integers Integers FRACTIONS 135 1 6 1 3 3 4 EXERCISE 7.1 1. Write the fraction representing the shaded portion. 2. Colour the part according to the given fraction. 1 4 (v) (vi) (vii) (viii) (i) (ii) (iii) (iv) (ix) (x) 4 9 2020-21 MATHEMATICS 136 3. Identify the error, if any . This is 1 2 This is 1 4 This is 3 4 4. What fraction of a day is 8 hours? 5. What fraction of an hour is 40 minutes? 6. Arya, Abhimanyu, and Vivek shared lunch. Arya has brought two sandwiches, one made of vegetable and one of jam. The other two boys forgot to bring their lunch. Arya agreed to share his sandwiches so that each person will have an equal share of each sandwich. (a) How can Arya divide his sandwiches so that each person has an equal share? (b) What part of a sandwich will each boy receive? 7. Kanchan dyes dresses. She had to dye 30 dresses. She has so far finished 20 dresses. What fraction of dresses has she finished? 8. Write the natural numbers from 2 to 12. What fraction of them are prime numbers? 9. Write the natural numbers from 102 to 1 13. What fraction of them are prime numbers? 10. What fraction of these circles have X’s in them? 11. Kristin received a CD player for her birthday. She bought 3 CDs and received 5 others as gifts. What fraction of her total CDs did she buy and what fraction did she receive as gifts? 7.3 Fraction on the Number Line Y ou have learnt to show whole numbers like 0,1,2... on a number line. W e can also show fractions on a number line. Let us draw a number line and try to mark 1 2 on it. We know that 1 2 is greater than 0 and less than 1, so it should lie between 0 and 1. Since we have to show 1 2 , we divide the gap between 0 and 1 into two equal parts and show 1 part as 1 2 (as shown in the Fig 7.5). 2020-21 Page 5 Subhash had learnt about fractions in Classes IV and V , so whenever possible he would try to use fractions. One occasion was when he forgot his lunch at home. His friend Farida invited him to share her lunch. She had five pooris in her lunch box. So, Subhash and Farida took two pooris each. Then Farida made two equal halves of the fifth poori and gave one-half to Subhash and took the other half herself. Thus, both Subhash and Farida had 2 full pooris and one-half poori. Where do you come across situations with fractions in your life? Subhash knew that one-half is written as 1 2 . While eating he further divided his half poori into two equal parts and asked Farida what fraction of the whole poori was that piece? (Fig 7.1) Without answering, Farida also divided her portion of the half puri into two equal parts and kept them beside Subhash’s shares. She said that these four equal parts together make Fig 7.2 Fig 7.1 7.1 Introduction Chapter 7 Chapter 7 Chapter 7 Chapter 7 Chapter 7 Fractions Fractions Fractions Fractions Fractions 2 pooris + half-poori–Subhash 2 pooris + half-poori–Farida 2020-21 MATHEMATICS 134 one whole (Fig 7.2). So, each equal part is one-fourth of one whole poori and 4 parts together will be 4 4 or 1 whole poori. When they ate, they discussed what they had learnt earlier. Three parts out of 4 equal parts is 3 4 . Similarly, 3 7 is obtained when we divide a whole into seven equal parts and take three parts (Fig 7.3). For 1 8 , we divide a whole into eight equal parts and take one part out of it (Fig 7.4). Farida said that we have learnt that a fraction is a number representing part of a whole. The whole may be a single object or a group of objects. Subhash observed that the parts have to be equal. 7.2 A Fraction Let us recapitulate the discussion. A fraction means a part of a group or of a region. 5 12 is a fraction. We read it as “five-twelfths”. What does “12” stand for? It is the number of equal parts into which the whole has been divided. What does “5” stand for? It is the number of equal parts which have been taken out. Here 5 is called the numerator and 12 is called the denominator. Name the numerator of 3 7 and the denominator of 4 15 . 2 3 Play this Game You can play this game with your friends. Take many copies of the grid as shown here. Consider any fraction, say 1 2 . Each one of you should shade 1 2 of the grid. Fig 7.4 Fig 7.3 2020-21 Fractions and Fractions and Fractions and Fractions and Fractions and Integers Integers Integers Integers Integers Fractions and Fractions and Fractions and Fractions and Fractions and Integers Integers Integers Integers Integers FRACTIONS 135 1 6 1 3 3 4 EXERCISE 7.1 1. Write the fraction representing the shaded portion. 2. Colour the part according to the given fraction. 1 4 (v) (vi) (vii) (viii) (i) (ii) (iii) (iv) (ix) (x) 4 9 2020-21 MATHEMATICS 136 3. Identify the error, if any . This is 1 2 This is 1 4 This is 3 4 4. What fraction of a day is 8 hours? 5. What fraction of an hour is 40 minutes? 6. Arya, Abhimanyu, and Vivek shared lunch. Arya has brought two sandwiches, one made of vegetable and one of jam. The other two boys forgot to bring their lunch. Arya agreed to share his sandwiches so that each person will have an equal share of each sandwich. (a) How can Arya divide his sandwiches so that each person has an equal share? (b) What part of a sandwich will each boy receive? 7. Kanchan dyes dresses. She had to dye 30 dresses. She has so far finished 20 dresses. What fraction of dresses has she finished? 8. Write the natural numbers from 2 to 12. What fraction of them are prime numbers? 9. Write the natural numbers from 102 to 1 13. What fraction of them are prime numbers? 10. What fraction of these circles have X’s in them? 11. Kristin received a CD player for her birthday. She bought 3 CDs and received 5 others as gifts. What fraction of her total CDs did she buy and what fraction did she receive as gifts? 7.3 Fraction on the Number Line Y ou have learnt to show whole numbers like 0,1,2... on a number line. W e can also show fractions on a number line. Let us draw a number line and try to mark 1 2 on it. We know that 1 2 is greater than 0 and less than 1, so it should lie between 0 and 1. Since we have to show 1 2 , we divide the gap between 0 and 1 into two equal parts and show 1 part as 1 2 (as shown in the Fig 7.5). 2020-21 Fractions and Fractions and Fractions and Fractions and Fractions and Integers Integers Integers Integers Integers Fractions and Fractions and Fractions and Fractions and Fractions and Integers Integers Integers Integers Integers FRACTIONS 137 Suppose we want to show 1 3 on a number line. Into how many equal parts should the length between 0 and 1 be divided? We divide the length between 0 and 1 into 3 equal parts and show one part as 1 3 (as shown in the Fig 7.6) Can we show 2 3 on this number line? 2 3 means 2 parts out of 3 parts as shown (Fig 7.7). Similarly, how would you show 0 3 and 3 3 on this number line? 0 3 is the point zero whereas since 3 3 is 1 whole, it can be shown by the point 1 (as shown in Fig 7.7) So if we have to show 3 7 on a number line, then, into how many equal parts should the length between 0 and 1 be divided? If P shows 3 7 then how many equal divisions lie between 0 and P? Where do 0 7 and 7 7 lie? Fig 7.7 × 1 3 0 1 Fig 7.6 1. Show 3 5 on a number line. 2. Show 1 10 0 10 5 10 , , and 10 10 on a number line. 3. Can you show any other fraction between 0 and 1? Write five more fractions that you can show and depict them on the number line. 4. How many fractions lie between 0 and 1? Think, discuss and write your answer? × 1 2 0 1 Fig 7.5 2020-21Read More

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