Passport-G4-Textbook-Maths-FY

Solved Solve these Steps Step 4: To add the like The fraction that The fraction that The fraction that fractions in step 3, add represents the their numerators and represents the shaded represents the shaded part of the write the sum on the given figure is same denominator. part of the given shaded part of the ____ + ____=____. figure is given figure is 1 + 2 = 1+ 2 = 3 . ____ + ____=____. 66 6 6 Step 5: Write the whole Like fraction Like fraction Like fraction representing the representing the as a like fraction of the representing the whole = 6 . whole = _______. whole = _______. sum in step 4. Then, to 6 So, the fraction So, the subtract the like fractions, that represents the subtract their numerators. So, the fraction unshaded part of fraction that Write the difference on that represents the the given figure is represents the the same denominator. unshaded part of the unshaded part of given figure is ____ − ____=____. the given figure is 6−3 =6−3 = 3. ____ − ____=_____. 66 6 6 Example 14: Add: a) 3 + 1 45 23 57 Solution: 88 b) + c) + a) 3 + 1 = 3 + 1 = 4 13 13 100 100 Example 15: 88 8 8 c) 48 – 26 Solution: b) 4 + 5 = 4 + 5 = 9 125 125 13 13 13 13 c) 23 + 57 = 23 + 57 = 80 100 100 100 100 Subtract: a) 8 – 4 b) 33 – 25 99 37 37 a) 8 – 4 = 4 99 9 33 25 = 33 − 25 = 8 b) – 37 37 37 37 48 26 48 − 26 22 c) – = = 125 125 125 125 Fractions - I 97 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 101 28-12-2017 15:11:16

Train My Brain Solve: b) 3 + 1 c) 11 − 3 a) 1 + 2 34 34 15 15 99 8.3 I Apply In some real-life situations, we use addition or subtraction of like fractions. Let us see a few examples. Example 16: The figure shows some parts of a ribbon coloured in blue and yellow. Find the total part of the ribbon coloured blue and yellow. What part of the ribbon is not coloured? Solution: Total number of parts of the ribbon = 9 Part of the ribbon coloured blue = 2 9 Part of the ribbon coloured yellow = 3 9 Total part of the ribbon coloured = 2 + 3 = 2 + 3 = 5 99 9 9 Part of the ribbon that is not coloured is 9 − 5 = 9 − 5 = 4 99 9 9 (Note: This is the same as writing the fraction of the ribbon not coloured from the figure. 4 parts of the 9 parts of the ribbon are not coloured) Example 17: Suman ate a quarter of a chocolate bar on one day and another quarter of Solution: the chocolate on the next day. How much chocolate did Suman eat in all? How much chocolate is remaining? Part of the chocolate eaten by Suman on the first day = 1 4 Part of the chocolate eaten by him on the next day = 1 4 Total chocolate eaten by Suman on both the days = 1 + 1 = 1+1 = 2 44 4 4 98 28-12-2017 15:11:16 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 102

He ate 2 chocolate in all. Remaining chocolate = 4 − 2 = 4 − 2 = 2 Example 18: 4 44 4 4 Solution: Manav painted two-tenths of a strip of chart in one hour and four-tenths of it 1st hour: in the next hour. What part of the strip did he paint in two hours? How much is left unpainted? Part of the strip of chart painted by Manav in one hour = 2 10 Part of the strip painted by him in the next hour = 4 10 2nd hour: Part of the strip painted by him in two hours = 2 + 4 = 2 +4 = 6 10 10 10 10 Part of the strip of chart left without painting = 10 – 6 = 4 10 10 10 8.3 [From the figure, the total part of the strip painted = 6 and the part of the 10 strip not painted = 4 .] 10 I Explore (H.O.T.S.) Let us see some more examples of addition and subtraction of like fractions. Example 19: Veena ate 5 of a pizza in the morning and 1 in the evening. What part of 88 the pizza is remaining? Solution: Part of the pizza eaten by Veena in the morning = 5 8 Part of the pizza eaten by Veena in the evening = 1 8 To find the remaining part of pizza, add the parts eaten and subtract the sum from the whole. Total part of the pizza eaten = 5 + 1 = 5 +1 = 6 88 8 8 Part of the pizza remaining = 1 – 6 = 8 – 6 = 2 8 88 8 Fractions - I 99 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 103 28-12-2017 15:11:17

Maths Munchies 213 Egyptians were the first to use fractions. But their method was very complicated. The Babylonians were the first people to come up with a more sensible way of representing fractions. By about 500 AD, the Indians had developed a system of writing called the Brahmi script, which had nine symbols and a zero. In 550 AD, an Indian mathematician named Aryabhata used continued fractions to solve more difficult problems. The Greeks used fractions in astronomy, architecture and music theory for describing musical intervals and the harmonic progression of string lengths. Connect the Dots English Fun The word fraction actually comes from the Latin ‘fractio’ which means ‘to break’. Social Studies Fun Do you know that an imaginary line running around the globe divides the Earth into two halves? This line is known as the equator. The distance from the equator to either of the poles is one-fourth of a circle round the Earth. 100 28-12-2017 15:11:17 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 104

Drill Time Concept 8.1: Equivalent Fractions 1) Shade the regions to show equivalent fractions. a) 1 and 2   2 4  b) 1 and 2  5 10  2) Write four equivalent fractions for each of the following fractions. a) 1 b) 4 c) 3 d) 4 2 7 10 11 Concept 8.2: Identify and Compare Like Fractions 3) Identify like and unlike fractions from the following. a) 2 , 2 , 1 , 5 , 2 , 7 , 6 , 2 b) 7 , 4 , 4 , 2 , 4 , 2 , 3 , 6 83286889 9 5 9 9 7 4 4 9 c) 6 , 5 , 5 , 4 , 8 , 7 , 9 , 2 d) 3 , 4 , 1 , 3 , 1 , 4 14 14 17 17 17 14 17 14 5 5 5 7 9 11 4) Arrange the following fractions in the ascending order. a) 3 , 1 , 7 , 4 b) 3 , 2 , 9 , 5 c) 1 , 3 , 4 , 2 d) 1 , 8 , 7 , 9 11 11 11 11 13 13 13 13 7777 14 14 14 14 5) Arrange the following fractions in descending order. d) 1 , 7 , 8 , 3 20 20 20 20 a) 1 , 8 , 7 , 4 b) 3 , 6 ,10 , 8 c) 7 , 9 , 2 ,13 9999 17 17 17 17 21 21 21 21 e) 1 + 2 13 13 Concept 8.3: Add and Subtract Like Fractions 6) Add: a) 2 + 5 b) 3 + 16 c) 9 + 4 d) 8 + 4 77 11 11 55 17 17 Fractions - I 101 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 105 28-12-2017 15:11:17

Drill Time 7) Subtract: a) 15 − 7 b) 9 − 5 c) 11 − 3 d) 7 − 4 e) 13 − 12 66 88 40 40 45 45 30 30 8) Word problems a) L eena paints three-sixths of a cardboard and Rani paints half of similar cardboard. Who has painted a smaller area? b) Colour each figure to represent the given fraction and compare them. 5 7 8 8 c) Ajit ate 1 of a cake in the morning and 2 of it in the evening. What part of the 55 cake is remaining? A Note to Parent Fractions play an important role in cooking. Ingredients of recipes use fractions. While cutting fruits and vegetables, help your child to understand fractions of a whole fruit or a vegetable. 102 28-12-2017 15:11:17 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 106

Chapter Fractions - II 9 I Will Learn About • finding fractions of a number. • problems based on finding fractions. • proper, improper and mixed fractions. • converting improper to mixed fractions and vice versa. Concept 9.1: Fraction of a Number I Think Jasleen’s father told her that he spends two-thirds of his salary per month and saves the rest. Jasleen calculated the amount her father saves from his salary of ` 25,000 per month. How do you think Jasleen could calculate her father’s savings per month? 9.1 I Recall In Class 3, we have learnt how to find the fraction of a collection. To find the fraction of a collection, we find the number of each type of object in the total collection. Let us answer these to recall the concept. a) A half of a dozen bananas = _______________ bananas b) A quarter of 16 books = _______________ books JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 107 103 28-12-2017 15:11:17

c) A third of 9 balloons = _______________ balloons d) A half of 20 apples = _______________ apples e) A quarter of 8 pencils = _______________ pencils 9.1 I Remember and Understand Let us now learn to find the fraction of a number. Suppose there are 20 shells in a bowl. Vani wants to take 1 of them. So, she divides the shells into 5 (the number in the denominator) 5 equal groups and takes 1 group (the number in the numerator). This gives 5 groups with 4 shells in each group. So, 1 of 20 is 4. To find the fraction of 5 a number, we multiply Vani’s sister Rani wants to take 3 of the shells. So, she divides the number by the fraction. 10 the shells into 10 (the number in the denominator) equal groups, and takes 3 groups (the number in the numerator) of them. This gives 2 shells in each group. Hence, Rani takes 6 shells. Therefore, 3 of 20 is 6. 10 We write 1 of 20 as 1 × 20 = 20 = 4. 5 55 Similarly, 3 of 20 = 3 × 20 = 6. 10 10 Example 1: Find the following: a) 2 of a metre (in cm) 1 5 b) 10 of a kilogram (in g) Solution: a) 2 of a metre = 2 × 1 m = 2 × 100 cm = 2 × 100 cm = 200 cm = 40 cm 5 55 55 b)  1 of a kilogram = 1 × 1 kg = 1 × 1000 g = 1000 g = 100 g 10 10 10 10 Example 2: Find the following: a) 2 of an hour (in minutes) b) 1 of a day (in hours) Solution: 3 4 a) 2 2 × 1 h = 2 × 60 min = 2 × 60 = 120 = 40 min of an hour = 3 3 3 33 b) 1 of a day = 1 × 1 day = 1 × 24 h = 1 × 24 h = 24 hrs = 6 h 4 44 4 104 28-12-2017 15:11:17 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 108

Train My Brain Find fractions of the given numbers. a) 5 of 36 b) 3 of 64 c) 7 of 88 6 8 11 9.1 I Apply Let us now see some real-life examples in which we find the fraction of a number. Example 3: Ravi has ` 120 with him. He gave two-thirds of it to his sister. How much money is left with Ravi? Solution: Amount Ravi has = ` 120 Amount Ravi gave his sister = 2 of ` 120 = 2 × ` 120 = 2 × ` 40 = ` 80 33 Difference in the amounts = ` 120 – ` 80 = ` 40 Therefore, ` 40 is left with Ravi. Example 4: Reema completed one-tenth of a distance of 2 kilometres. How much distance (in metres) has she covered? Solution: The total distance to be covered by Reema = 2 km We know that 1 km = 1000 m. So, 2 km = 2000 m. The distance covered by Reema = 1 of 2 kilometres = 1 x 2000 m = 200 m Example 5: 10 10 Therefore, Reema has covered 200 metres of the distance. A school auditorium has 2500 chairs. On the annual day, 4 of the auditorium 5 was occupied. How many chairs were occupied? Solution: Total number of chairs in the auditorium = 2500 4 Fraction of chairs occupied = 5 4 4×2500 10000 Number of chairs occupied = × 2500 = = 5 55 Therefore, 2000 chairs were occupied in the auditorium. Fractions - II 105 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 109 28-12-2017 15:11:18

9.1 I Explore (H.O.T.S.) Let us now see some more examples where we have to find the fraction of a number. Example 6: Venu paints three-sixths of a cardboard and Raj paints a third of it. If the cardboard has an area of 144 sq.cm, what area of the cardboard did each Solution: of them paint? Fraction of the cardboard painted by Venu = 3 6 Fraction of the cardboard painted by Raj = 1 3 Area of the cardboard = 144 sq. cm 3 Area of the cardboard painted by Venu = × 144 sq.cm 6 =3 × 144 sq.cm = 432 sq.cm = 72 sq.cm 66 Area of the cardboard painted by Raj = 1 × 144 sq.cm 3 =1× 144 sq.cm = 144 sq.cm = 48 sq.cm 33 Therefore, Venu painted 72 sq.cm of the cardboard and Raj painted 48 sq.cm of the cardboard. Example 7: Find if 2 of 154 and 4 of 49 are equal to each other or one of them is greater 11 7 than the other. Solution: To find if the fractions of the numbers are equal, we first find their values and compare them. 2 of 154 = 2 × 154 = 2 × 154 = 308 = 28 11 11 11 11 4 of 49 = 4 × 49 = 4 × 49 = 196 = 28 77 77 Therefore, 2 of 154 = 4 of 49. 11 7 106 28-12-2017 15:11:18 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 110

Concept 9.2: Conversions of Fractions I Think Jasleen knew about fractions in which the numerators were less than their denominators. She wondered if there could be some fractions in which the numerators are greater than their denominators. Do you know of such fractions? 9.2 I Recall In the previous chapter, we have learnt about addition and subtraction of like fractions. Recall that the sum of two like fractions is a like fraction. Let us answer these to recall the concept. a) 2 + 1 = ______ 41 5 5 b) 7 + 7 = ______ c) 1 + 5 = ______ d) 3 + 1 = _______ 11 11 22 e) 1 + 3 = ______ f) 2 + 1 = _______ 88 99 9.2 I Remember and Understand Consider 1 + 5 = 6 . Here, the sum of two like fractions is a like fraction with its numerator less 888 than its denominator. Such fractions are called proper fractions. Sometimes ,it is possible that we get the sum with its numerator greater than the denominator. For example, 7 + 5 = 12 . Here, the sum of two like fractions is a like fraction with its 88 8 Fractions - II 107 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 111 28-12-2017 15:11:18

numerator greater than its denominator. Such fractions are called improper fractions. Note: In some cases, the sum of the numerators of the like fractions may be equal to the denominator. Then, the fraction is said to be an improper fraction. For example, 3 + 4 = 7 , 3 + 5 = 8 and so on. Proper fractions – Fractions 7 7 78 8 8 having the numerators less than the denominators. Fractions such as 7 , 8 and so on can also be written as a whole, that is 1. 7 8 Improper fractions – Fractions having the numerators greater We can write 12 as the sum of like fractions as 8 + 4 . This than the denominators. 8 88 Mixed fractions – Fractions has a whole 8 and a proper fraction  4  . That is,  8   8  12 = 1 + 4 = 14 . Such fractions are called mixed having whole numbers and 8 88 proper fractions. fractions. A mixed fraction is also called a mixed number. For example, in the mixed fraction 12 3 , 12 is the whole and 3 is the proper fraction. 88 Example 8: List out proper fractions, improper fractions and mixed fractions from the following: 13 ,15 7 , 11 , 37 , 9 , 65 13 , 143 , 75 3 ,107 27 , 72 , 68 2 , 29 , 50 23 , 69 , 53 18 9 34 6 14 17 98 4 49 59 5 32 35 32 30 Solution: From the given fractions, Proper fractions: 13 , 11 , 9 , 29 18 34 14 32 Improper fractions: 37 , 143 , 72 , 69 , 53 6 98 59 32 30 Mixed fractions: 15 7 , 65 13 , 75 3 , 107 27 , 68 2 , 50 23 9 17 4 49 5 35 We usually write fractions as proper or mixed fractions. So, we need to learn to convert improper fractions to mixed fractions and mixed fractions to improper fractions. Conversion of improper fractions to mixed fractions Let us understand the conversion of improper fractions to mixed fractions by solving a few examples. Example 9: Convert 37 to its mixed fraction form. Solution: 6 To convert improper fractions into mixed fractions, follow these steps. 108 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 112 28-12-2017 15:11:18

Solved Solve these 37 Steps 6 143 72 69 53 98 59 32 30 Step 1: Divide the numerator 6 by the denominator. )6 37 − 36 1 Step 2: Write the quotient and Quotient = 6 the remainder. Remainder = 1 Step 3: Write the quotient as The mixed the whole. The remainder is fraction form of the numerator of the proper 37 is 6 1 . fraction and the divisor is its 66 denominator. This gives the required mixed fraction. Conversion of mixed fractions to improper fractions Let us understand the conversion of mixed fractions into improper fractions by solving a few examples. Example 10: Convert 15 7 into its improper fraction. 9 Solution: To convert mixed fractions into improper fractions, follow these steps. Solved Solve these 75 3 Steps 15 7 65 13 4 107 27 9 17 49 Step 1: Multiply the whole by the 15 × 9 = 135 denominator. Step 2: Add the numerator of the proper 135 + 7 = 142 fraction to the product in Step 1. Step 3: Write the sum as the denominator The improper of the proper fraction. fraction form of This given the required improper fraction. 15 7 is 142 9 9. Fractions - II 109 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 113 28-12-2017 15:11:18

Train My Brain Give five examples of proper, improper and mixed fractions. 9.2 I Apply Let us now see a few real-life examples involving conversions of fractions. Example 11: Rohan wants to arrange 60 books in his shelf. If only 13 books can be put in a rack, how many racks will be filled by the books? Give your answer as a mixed fraction and as an improper fraction. Solution: Number of books Rohan wants to arrange = 60 Number of books that can be arranged on each rack = 13 Number of racks that are filled = 60 ÷ 13 = 4 8 Example 12: 13 Solution: Improper fraction equivalent to 4 8 = 60 13 13 On a science fair day, a group of students prepared 12 1 litres of orange 2 juice. Express the number of litres of orange juice as an improper fraction. Number of litres of orange juice made = 12 1 2 Improper fraction equivalent to 12 1 = 12 × 2 +1 = 25 2 2 2 9.2 I Explore (H.O.T.S.) Conversion of fractions is done when we need to add and subtract fractions. In the previous chapter, we have already learnt addition and subtraction of like (proper) fractions. Let us see a few examples that involve addition and subtraction of improper and mixed fractions. Example 13: Add: a) 42 + 35 b) 50 23 + 16 Solution: 25 25 35 35 a) 42 + 35 25 25 T o add the given like improper fractions, we add their numerators and write the sum on the same denominator. 110 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 114 28-12-2017 15:11:18

Therefore, 42 + 35 = 42 + 35 = 77 25 25 25 25 W e usually write fractions as proper or mixed fractions. So, we convert the sum into a mixed fraction by dividing the numerator by the denominator. 77 = 3 2 (77 ÷ 25 gives the quotient as 3 and remainder as 2.) 25 25 Therefore, the sum of the given fractions is 3 2 . 25 b) 50 23 + 16 35 35 T o add the given fractions, we have to convert the mixed fraction into Example 14: improper fraction. Solution: So, 50 23 = (50×35)+23 =11777530 + 23 =1773 35 35 35 35 35 T hen add their numerators and write the sum as the numerator. Therefore, 50 23 + 16 = 1773 + 16 = 1773 + 16 = 1789 . 35 35 35 35 35 35 Convert the improper fraction into a mixed fraction. 1789 = 51 4 (1789 ÷ 35 gives the quotient as 51 and the remainder as 4.) 35 35 Therefore, the sum of the given fractions is 51 4 . 35 Subtract: a) 342 - 135 b) 34 17 - 37 25 25 42 42 a) 342 - 135 25 25 To subtract the given improper fractions, we subtract their numerators. We then write the difference as the numerator. Therefore, 342 - 135 = 342 −135 = 207 25 25 25 25 A s we usually write fractions as proper or mixed fractions, we convert the difference into a mixed fraction. 207 = 8 7 (207 ÷ 25 the quotient as 8 and the remainder as 7.) 25 25 Therefore, the difference of the given fractions is 8 7 . b) 34 17 - 37 25 42 42 T o subtract the given fractions, we first convert the mixed fraction into an improper fraction. Fractions - II 111 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 115 28-12-2017 15:11:18

So, 34 17 = 34 × 42 + 17 = 1445 42 42 42 T hen subtract their numerators and write the difference as the numerator. Therefore, 34 17 − 37 = 1445 − 37 = 1445 − 37 = 1408 42 42 42 42 42 42 Again convert the improper fraction into a mixed fraction. 11440485 = 33 22 (1408 ÷ 42 the quotient as 33 and the remainder as 22.) 4422 42 Therefore, the difference of the given fractions is 33 22 . 42 Maths Munchies 6 3+2 4=8+ 3+4 213 Add mixed fractions without conversion. 55 5 Step 1: Add the whole numbers. Step 2: Add the fractions. =87 =8 5+2 Step 3: If the sum is an improper fraction then convert it into a 55 mixed fraction. =8+ 5+2 Step 4: Add the whole number to the whole number and write 5 the remaining fraction. =8+ 5 + 2 55 = 8 +1+ 2 =9+ 2 =9 2 5 55 Connect the Dots Train My Brain Social Studies Fun About 3 of the Earth is covered with water, out of which 4 97 is salt water and is not suitable for drinking. 100 112 28-12-2017 15:11:19 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 116

English Fun Write your name. Write the number of letters in it. Write fractions to show the number of vowels present in your name. Drill Time Concept 9.1: Fraction of a Number 1) Find the following: a) 1 of 20 b) 3 of 24 c) 3 of 20 d) 4 of 12 e) 2 of 18 2 45 6 3 Concept 9.2: Conversions of Fractions 2) Convert the following improper fractions to mixed fractions. a) 35 b) 121 c) 93 d) 100 e) 115 4 12 12 26 20 3) Convert the following mixed fractions to improper fractions. a) 15 6 b) 23 2 c) 40 4 d) 125 9 e) 40 3 8 3 5 10 5 4) Word Problems a) A t Sudhir’s birthday party, there are 19 sandwiches to be shared equally among 13 children. What part of the sandwiches will each child get? Give your answer as a mixed fraction. b) I bought 2 1 litres of paint but used only 3 litres. How much paint is left with 22 me? Give your answer as an improper fraction. A Note to Parent Give different currency notes to your child. Ask them to find if some of them are half, one- fourth or three-fourths of some others of the given currency notes. For example, ` 50 is one-fifth of ` 250. Fractions - II 113 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 117 28-12-2017 15:11:19

Chapter Decimals 10 I Will Learn About • the term ‘decimal’ and its parts. • understanding decimal system. • expanding decimal numbers with place value charts. • converting fractions to decimals and vice versa. Concept 10.1: Conversion Involving Fractions I Think Jasleen and her friends participated in the long jump event in their Jasleen – 4.1m Ravi – 2.85m games period. Her sports teacher noted the distance they jumped on Rajiv – 3.05 m a piece of paper as shown here. Amit – 2.50m Jasleen wondered why the numbers had a point between them as in the case of writing money. Do you know what the point means? 10.1 I Recall Recall that in Class 3 we have learnt to measure the lengths, weights and volumes of objects. 114 28-12-2017 15:11:19 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 118

For example, a pencil is 12.5 cm long. 12. 5 cm A crayon is 5.4 cm long. 5.4 cm The weight of your mathematics textbook is 0.905 kg. A milk packet has 0.250 of milk, and so on. In all these values, we see numbers with a point between them. Have you read price tags on some items when you go shopping? ` 300.75 ` 439.08 They also have numbers with a point between them. Let us learn why a point is used in such numbers. 10.1 I Remember and Understand We know how to write fractions. In this figure, 3 portion is coloured and 7 portion is not coloured. 10 10 3 or 0.3 and the We can write the coloured portion of the figure as 10 portion that is not coloured as 7 or 0.7. 10 Numbers such as 0.3, 0.7, 3.0, 3.1, 4.7, 58.2 and so on are called decimal numbers or simply decimals. Tenths: The figure below is divided into ten equal parts. 1 111 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 Each column is of the same size. Then, each of the ten equal parts is 1 . It is read as one-tenth. Fractional form of each equal part is 1 . 10 10 Decimals 115 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 119 28-12-2017 15:11:19

Decimal form of each equal part is 0.1. A decimal number has two parts. We read numbers like 0.1, 0.2, 0.3 … as ‘zero point one’, ‘zero point two’, ‘zero point three’ and so on. Zero is written to 48 . 35 indicate the place of the whole number. Note: T he numbers in the decimal part are read as separate Whole or Decimal digits. integral part part (< 1) (= or > 0) Recall the place value chart of numbers. Decimal Point 100 × 10 10 × 10 1 × 10 1 Thousands Hundreds Tens Ones 6 2 5 5 3 2 2 6 5 2 We know that in this chart, as we move from right to left, the value of the digit increases 10 1 times. Also, as we move from left to right, the value of a digit becomes times. The place 10 value of the digit becomes one-tenth, read as a tenth. Its value is 0.1 read as ‘zero point one’. 2 is read as ‘two-tenths’, 7 is read as ‘seven–tenths’ and so on. 10 10 We can extend the place value chart to the right as follows: 1 × 1000 1 × 100 1 × 10 1 . 1 Thousands Hundreds Tens 10 Ones Decimal Tenths 2 7 . 2 14 4 . 3 3 01 3 . 6 5 . 7 The number 3015.7 is read as three thousand and fifteen point seven. Similarly, the other numbers are read as follows: Seven point two; twenty-four point three and one hundred and forty-three point six. The point placed in between the number is called the decimal point. The system of writing numbers using a decimal point is called the decimal system. 116 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 120 28-12-2017 15:11:19

[Note: ‘Deci’ means 10.] Tens Ones Decimal Tenths Hundredths Hundredths: 1 point Study this place value chart. 2 1 1 . 10 100 Thousands Hundreds 3 . 9 1 × 1000 1 × 100 1 × 10 2 8 6 When the number moves right from the tenths place, we get a new place, which is 1 of the tenths place. It is called the ‘hundredths’ place written as 1 and read 10 100 as one-hundredths. Its value is 0.01, read as ‘zero point zero one’. 2 is read as two-hundredths, 5 is read as five-hundredths and so on. 100 100 So, the number in the place value chart is read as ‘two thousand eight hundred and sixty-two point three nine’. Expansion of decimal numbers Using the place value chart, we can expand decimal numbers. Let us see a few examples. Example 1: Expand these decimals. a) 1430.8 b) 359.65 c) 90045.75 d) 654.08 Solution: To expand the given decimal numbers, first write them in the place value chart as shown. S. no Ten Thousands Hundreds Tens Ones Decimal Tenths Hundredths thousands 1 point 4 3 0 . 8 a) 0 3 5 9 65 0 4 5 . 75 b) 6 5 4 08 . c) 9 . d) Expansions: 1 a) 1430.8 = 1 × 1000 + 4 × 100 + 3 × 10 + 0 × 1 + 8 × 10 b) 359.65 = 3 × 100 + 5 × 10 + 9 × 1 + 6 × 1 + 5 × 1 10 100 Decimals 117 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 121 28-12-2017 15:11:19

c) 90045.75 = 9 × 10000 + 0 × 1000 + 0 × 100 + 4 × 10 + 5 × 1 + 7 × 1 + 5 × 1 10 100 Example 2: 1 1 d) 654.08 = 6 × 100 + 5 × 10 + 4 × 1 + 0 × + 8 × 10 100 Write these as decimals. Solution: a) 7 × 1000 + 2 × 100 + 6 × 10 + 3 × 1 + 9 × 1 + 3 × 1 10 100 b) 3 × 10000 + 0 × 1000 + 1 × 100 + 9 × 10 + 6 × 1 + 4 × 1 + 5 × 1 10 100 c) 2 × 1000 + 2 × 100 + 2 × 10 + 2 × 1 + 2 × 1 + 2 × 1 10 100 d) 5 × 100 + 0 × 10 + 0 × 1 + 0 × 1 + 5 × 1 10 100 First write the numbers in the place value chart as shown. S. no Ten Thousands Hundreds Tens Ones Decimal Tenths Hundredths thousands point a) 7 2 63 . 93 b) 3 0 1 96 . 45 c) 2 2 22 . 22 d) 5 00 . 05 Standard forms of the given decimals are: a) 7263.93 b) 30196.45 c) 2222.22 d) 500.05 Conversion of fractions to decimals Fractions can be written as decimals. Consider an example. Example 3: Express these fractions as decimals. Solution: a) 18 2 b) 43 5 c) 26 1 d) 4 9 10 10 10 10 To write the given fractions as decimals, follow these steps. Step 1: Write the integral part as it is. Step 2: Place a point to its right. Step 3: Write the numerator of the proper fraction part. a) 18 2 = 18.2 b) 43 5 = 43.5 10 10 c) 26 1 = 26.1 d) 4 9 = 4.9 10 10 118 28-12-2017 15:11:20 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 122

Example 4: Express these fractions as decimals. Solution: a) 25 b) 17 2 c) 43 d) 5 92 100 100 100 100 a) 25 = 25 hundredths = 0.25 100 b) 17 2 = 17 and 2 hundredths = 17.02 100 c) 43 = 43 hundredths = 0.43 100 d) 5 92 = 5 and 92 hundredths = 5.92 100 Shortcut method: Fractions having 10 or 100 as their denominators, can be expressed in their decimal form by following the steps given below. Step 1: Write the numerator. Step 2: Then count the number of zeros in the denominator. Step 3: Place the decimal point after the same number of digits from the right as the number of zeros. For example, the decimal form of 232 = 2.32 100 Note: F or the decimal equivalent of a proper fraction, place a 0 as the integral part of the decimal number. Conversion of decimals to fractions To convert a decimal into a fraction, follow these steps. Step 1: Write the number without the decimal. Step 2: Count the number of decimal places (that is, the number of places to the right of the decimal number). Step 3: Write the denominator with 1 followed by as many zeros as the decimal point. Example 5: Write these decimals as fractions. a) 2.3 b) 13.07 c) 105.43 d) 0.52 Solution: a) 2.3 = 23 b) 13.07 = 1307 10 100 c) 105.43 = 10543 d) 0.52 = 52 100 100 Decimals 119 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 123 28-12-2017 15:11:20

Alternate method: A decimal having an integral part can be written as a mixed fraction. So, 2.3 = 2 and 3 tenths = 2 3 10 13.07 = 13 and 7 hundredths = 13 7 100 105.43 = 105 and 43 hundredths = 105 43 100 Train My Brain Solve the following: a) Expand 35.098. b) Write 4.78 as a fraction. c) Express 37 as a decimal. 100 10.1 I Apply Let us see a few real-life examples of decimals. Example 6: The amount of money with Sneha and her friends are given in the table. Sneha ` 432.50 Anjali ` 233.20 Rohan ` 515.60 Jay ` 670.80 Write the amounts in words. Solution: To write the decimals in words, the integral part is read as usual. The decimal part is read as digits. Amount In words ` 432.50 four hundred and thirty-two and fifty paise rupee ` 233.20 two hundred and thirty-three and twenty paise rupee ` 515.60 five hundred and fifteen and sixty paise rupee ` 670.80 six hundred and seventy and eighty paise rupee 120 28-12-2017 15:11:20 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 124

Example 7: The weights of some children in grams are given in the table below: Name Weight in grams Solution: Rahul 23456 Anil 34340 Anjali 28930 Soham 25670 Convert these weights into kilograms. We know that 1 kg = 1000 g. To convert grams to kilograms, we divide it by 1000. So, the weights in kilograms are as follows. Name Weight in grams Weight in kilograms Rahul 23456 23456 1000 = 23.456 Anil 34340 34340 = 34.340 Anjali 28930 1000 28930 = 28.930 1000 Soham 25670 25670 = 25.670 1000 Example 8: Complete this table. S. No Fraction Read as Decimal Read as 0.7 Zero point seven a) 7 7 tenths 10 b) 47 100 c) 3 5 10 d) 0.34 e) 12 and 65 hundredths Decimals 121 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 125 28-12-2017 15:11:20

Solution: S. No. Fraction Read as Decimal Read as a) 7 tenths 0.7 Zero point seven b) 7 47 hundredths 0.47 Zero point four seven c) 10 3 and 5 tenths 3.5 Three point five d) 47 34 hundredths 0.34 Zero point three four e) 100 12 and 65 hundredths Twelve point six five 12.65 35 10 34 100 12 65 100 Example 9: Ajay and Vijay represented the coloured part of the figure given as follows: Ajay: 3 Vijay: 0.03 10 Solution: Whose representation is correct? The number of shaded parts as a fraction is 3 or 3 tenths. 10 As a decimal it is 0.3 and not 0.03. So, Ajay’s representation is correct. 10.1 I Explore (H.O.T.S.) Observe the following: 2 tenth=s =2 0.2 10 5 tenth=s =5 0.5 10 8 tenth=s =8 0.8 10 122 28-12-2017 15:11:20 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 126

10 tenth=s 1=0 1 10 1 hundredths = 1 = 0.01 9 33 hundredths = 33 = 0.33 100 9 hundredths = 100 = 0.09 100 57 hundredths = 57 =0.57 100 hundredths = 100 = 1 100 100 Example 10: Write the decimals that represent the shaded part. a) b) c) Decimals 123 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 127 28-12-2017 15:11:20

d) Solution: a) The fully shaded part represents a whole. So, the decimal that represents the given figure is 1.3. b) The required decimal is 0.6. c) 10 + 43 = 143 = 114.433 10 100 100 100 d) 100 + 100 + 29 = 22.2299 100 100 100 100 Example 11: Observe the pattern in these decimals and write the next three numbers in each. a) 0.12, 0.13, 0.14, _________, _________, _________ b) 2.00, 2.10, 2.20, _________, _________, _________ c) 8.5, 9.5, 10.5, _________, _________, _________ d) 23.31, 23.41, 23.51, _________, _________, _________ Solution: a) 0.12, 0.13, 0.14, 0.15, 0.16, 0.17 (increases by 1 hundredths) b) 2.00, 2.10, 2.20, 2.30, 2.40, 2.50 (increases by 1 tenths) c) 8.5, 9.5, 10.5, 11.5, 12.5, 13.5 (increases by ones) d) 23.31, 23.41, 23.51, 23.61, 23.71, 23.81 (increases by 1 tenths) 124 28-12-2017 15:11:21 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 128

Maths Munchies 213 Faster method to convert a fraction to decimal 1 Consider this example: Convert into its decimal form. 5 Step 1: Multiply the numerator and the denominator of the fraction with a number to get 10 as the denominator. Multiply the numerator and the denominator by 2 so that 5 × 2 = 10. Step 2: Write in the fraction form as per step 1. So, this will give us 1 × 2 = 2 . 5 2 10 Step 3: Write in the decimal form. So, 0.2 is the decimal form of 1 . 5 Connect the Dots Social Studies Fun The Earth takes 23 hours, 56 minutes and 4.09 seconds to complete a rotation. But, to make it easy to calculate time, we take this as 24 hours. English Fun A word contains ten letters, out of which three are vowels. Write the fraction of the number of consonants. Express this in decimal form. Decimals 125 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 129 28-12-2017 15:11:21

Drill Time Concept 10.1: Conversion involving Fractions 1) Convert the following into fractions: a) 2.56 b) 14.02 c) 105.89 d) 52.60 e) 8.01 e) 834 2) Convert the following into decimals: 100 a) 2 23 23 d) 73 e) 1.87 10 b) c) 10 100 1000 3) Write the following decimals in words: a) 73.5 b) 413.45 c) 0.73 d) 13.45 4) Word problem The measures of some objects are given in the table. Height of a flag pole 9.50 m Side of a dining table 1.20 m Distance between the two cities 325.75 km Height of a plant 127.80 cm Write these lengths in words. A Note to Parent Give your child a bill and make them write the decimal numbers in it. Then ask them to write the number as fractions and in words. Such an exercise will give them a good practice of decimals. 126 28-12-2017 15:11:21 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 130

Chapter Money 11 I Will Learn About • converting rupees to paise and vice versa. • problems involving conversion of money. • adding and subtracting money with column method. • multiplying and dividing money. Concept 11.1: Conversion of Rupees and Paise I Think Jasleen had some play money in the form of notes and coins. While playing, her friend gave her ` 10. Jasleen has to give paise for the amount her friend gave her. How many paise should Jasleen give her friend? 11.1 I Recall We have already learnt to identify currency and coins, conversion of rupees to paise and also that 1 ` = 100 p. Let us answer these to revise the concept of conversion of money. a) ` 62 = __________ paise b) 500 paise = ` __________ c) ` 28 = __________ paise d) 900 paise = ` __________ e) ` 76 = __________ paise f) 200 paise = ` __________ JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 131 127 28-12-2017 15:11:21

11.1 I Remember and Understand We already know that to change rupees into paise we multiply the rupees by 100. For example, as ` 1 = 100 paise, ` 3 = 3 × 100 paise = 300 paise To convert paise to rupee To convert an amount into paise we multiply the rupees given just add a decimal point in the amount by 100 and add the product to the number of two digits from the right. paise. Let us see a few examples involving conversion between rupee and paise. Example 1: Convert ` 132.28 into paise. Solution: ` 132.28 = ` 132 + 28 p = ` 132 × 100 p + 28 p = 13200 p + 28 p = 13228 p Note: An easy way to convert rupees into paise is to remove the symbol (` and p)and the dot (.) between the rupees and the paise and write the number together. So, ` 132.28 = 13228 p. An amount of more than 100 paise, can be expressed in rupees and paise. To convert paise into rupees and paise, divide the number by 100. Write the quotient as rupees and remainder as paise. Example 2: Convert 24365 paise into rupees and paise. Solution: 24365 p = 24300 p + 65 p = ` 243 + 65 p = ` 243.65 Note: An easy way to convert ‘paise’ into ‘rupees’ and paise is to just put a dot (.) after two digits (ones and tens places) from the right and express it as `. TTh Th H T O So, 24365 = ` 243.65 2 4 36 5 a) C onvert ` 477.95 to paise. Solve these c) Convert 44390 paise into b) Convert ` 892.95 into rupees. paise. 128 28-12-2017 15:11:21 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 132

Train My Brain a) Convert 67923 paise into rupees. b) Convert ` 890.03 into paise. c) Convert 2234 paise into rupees. 11.1 I Apply Now let us solve some examples involving conversion of money. Example 3: Sheeba has ` 223.57. How many paise does she have in all? Solution: Amount with Sheeba = ` 223.57 We know that, ` 1 = 100 paise. ` 223.57 = ` 223 + 57 p = 223 × 100 p + 57 p = (22300 + 57) p = 22357 p Hence, Sheeba has 22357 paise. Example 4: Anish has 2435 p and Beena has ` 23.75. Who has more money? Solution: Amount with Anish = 2435 p Amount with Beena = ` 23.75 To compare the money they have, both the amounts must be in the same units. So, we convert rupees to paise. ` 23.75 = ` 23 × 100 p + 75 p (Since ` 1 = 100 p.) = (2300 + 75) p = 2375 p Clearly, 2435 > 2375. Therefore, Anish has more money. Example 5: Ram has ` 374.50 and Chandu has ` 365.75 in their kiddy banks. Who has less amount and by how much? Solution: Amount with Ram = ` 374.50 Amount with Chandu = ` 365.75 Comparing the rupee part of the amounts, we get 365 < 374. So, ` 365.75 < ` 374.50. Therefore, Chandu has less money. Money 129 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 133 28-12-2017 15:11:21

The difference in their amounts = ` 374.50 – ` 365.75 = ` 8.75 Therefore, Chandu has ` 8.75 less than Ram. 11.1 I Explore (H.O.T.S.) Let us see a few more examples of conversion of money. Example 6: Complete the following by writing the number of different coins that can be used to pay ` 10 using different coins. 50 paise coins ` 10 1-rupee coins 2 - rupee coins 2-rupee coins and 1-rupee coins 5-rupee coins Solution: 20 50 paise coins ` 10 10 1-rupee coins 5 2-rupee coins 3 2-rupee coins and 4 1-rupee coins 2 5-rupee coins Example 7: Solution: Write two different ways in which you can pay ` 50. Combination 1: ` 50 = ` 20 + ` 20 + ` 10 Combination 2: ` 50 = ` 10 + ` 10 + ` 10 + ` 10 + ` 10 130 28-12-2017 15:11:21 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 134

Concept 11.2: Add and Subtract Money with Conversion I Think Jasleen went shopping with her elder sister. She bought some groceries for ` 110.50, vegetables for ` 105.50 and stationery for ` 40. They had ` 300. Do you know how much money was left with them after shopping? 11.2 I Recall Recollect that we can add or subtract money just as we add or subtract numbers. 1) T o find the total amount, we write one amount below the other. We see to it that the decimal points are exactly one below the other. We then add the amounts just as we add numbers. 2) T o find the difference in amounts, we write the smaller amount below the bigger one. We see to it that the decimal points are exactly one below the other. We then subtract the smaller amount from the bigger one. Answer the following to revise the concept of addition and subtraction of money. a) ` 22.10 – ` 11.10 = ___________ b) ` 15.30 + ` 31.45 = ___________ c) ` 82.45 – ` 42.30 = __________ d) ` 15.30 – ` 5.20 = __________ e) ` 32 + ` 7.20 = ___________ 11.2 I Remember and Understand To add or subtract a given amount of money, we follow the steps given below. Step 1: Express the given amounts in figures as decimal numbers. Step 2: Arrange the given amounts in a column. In column method, the rupees and paise should be written Place the decimal points exactly below one with the decimal points Step 3: another. exactly one below the other. Add or subtract the amounts as usual. Money 131 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 135 28-12-2017 15:11:22

Step 4: In the sum or difference so obtained, put the decimal point exactly below the other decimal points. Let us see some examples. b) ` 239.74 + ` 355.54 Example 8: Add: a) ` 547.38 + ` 130.83 Solution: a) ` p b) ` p 11 11 5 4 7.38 2 3 9.7 4 + 1 3 0.83 4 ` 6 7 8.21 + 3 5 5.5 8 ` 5 9 5.2 Example 9: Subtract: a) ` 53354 − ` 24765 b) ` 866.95 − ` 492.58 p Solution: b) ` a) ` 12 12 14 7⁄ 1⁄6 8⁄ 1⁄5 8 6 6.9 5 4⁄ 2⁄ 2⁄ 4⁄ 1⁄4 − 4 9 2.5 8 53354 −24765 ` 3 7 4.3 7 ` 2 8 5 8 9 Train My Brain Solve the following: b) ` 656.85 + ` 750.50 c) ` 500.00 – ` 393.67 a) ` 323.47 + ` 135.55 11.2 I Apply Let us now see a few real-life situations where addition and subtraction of money are used. Example 10: Anita saved ` 213.60, ` 105.30 and ` 305.45 in three months from her pocket money. How much did she save in all? Solution: Amount saved in the 1st month = ` 213.60 Amount saved in the 2nd month = + ` 105.30 Amount saved in the 3rd month = + ` 305.45 Therefore, the total amount saved in 3 months = ` 624.35 132 28-12-2017 15:11:22 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 136

Example 11: Mrs. Gupta had ` 5000 with her. She spent ` 3520.50 for buying different food items. How much money is left with her? Solution: Amount with Mrs. Gupta = ` 5000.00 Amount spent on food items = – ` 3520.50 Therefore, the amount left with Mrs. Gupta = ` 1479.50 11.2 I Explore (H.O.T.S.) Let us see solve a few more real-life examples involving addition and subtraction of money. Example 12: Tanya had ` 525 and her friend Arpan had ` 330. They bought a gift for their brother’s birthday costing ` 495.75. How much amount is left with Tanya and Arpan so that they can continue their shopping? Solution: Amount Tanya had = ` 525 Amount Arpan had = ` 330 Total amount = ` 525 + ` 330 = ` 855 `p Total amount = 855 . 00 The amount spent for the gift = – 495 . 75 359 . 25 Therefore, ` 359.25 is left with Tanya and Arpan. Example 13: The cost of three items are ` 125, ` 150 and ` 175. Suresh has only notes of ` 100. If he buys the three items, how many notes must he give the shopkeeper? Solution: Does he get any change? If yes, how much change does he get? Total cost of the three items = ` 125 + ` 150 + ` 175 = ` 450 The denomination of money Suresh has = ` 100 The nearest hundred, greater than the cost of the three items is ` 500. So, the number of notes that Suresh has to give the shopkeeper is 5. ` 450 < ` 500. So, Suresh gets change from the shopkeeper. The change he gets = ` 500 − ` 450 = ` 50 Money 133 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 137 28-12-2017 15:11:22

Concept 11.3: Multiply and Divide Money I Think Jasleen knows the cost of one dairy milk chocolate and the cost of five biscuit packets. She could quickly find the cost of 10 dairy milk chocolates and 1 biscuit packet. Can you do such quick calculations? 11.3 I Recall Remember that we use multiplication to find cost of many items from the cost of one. Similarly, we use division to find the cost of one item from the cost of many. Multiplying or dividing an amount by a number is similar to the usual multiplication and division of numbers. Answer the following to revise the multiplication and division of numbers. a) 2356 × 10 = __________ b) 72 × 3 = ____________ c) 200 ÷ 4 = ___________ d) 549 ÷ 3 = ___________ e) 621 × 2 = ___________ 11.3 I Remember and Understand Let us understand how to multiply or divide the given amounts of money. Multiplying money When 1 or more items are of the To multiply an amount of money by a number, we same price, multiply the amount follow these steps. by the number of items to get the total amount. Step 1: Write the amount in figures without the decimal point. To find out the price of one item, divide the total amount by the number of items. 134 28-12-2017 15:11:22 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 138

Step 2: Multiply it by the given number, as we multiply any two numbers. Step 3: In the product, place the decimal point ( if the amount is a decimal number) after the second digit from the right. Example 14: Multiply: a) ` 14105 by 7 b) ` 312. 97 by 34 c) ` 506. 75 by 125 Solution: a) 2 3 b) 22 c) 11 1 13 2 `14105 ` 312 . 97 33 2 × ×7 34 ` 506 . 75 `98735 × 125 1 11 111 1251 . 88 2533 . 75 + 9389 . 10 + 10135 . 00 ` 10640 . 98 + 50675 . 00 ` 63343 . 75 Dividing money To divide an amount by a number, we follow these steps. Step 1: Write the amount as the dividend and the number as the divisor. Step 2: Carry out the division just as we divide any two numbers. Step 3: Place the decimal point in the quotient, immediately after dividing the rupees, that is, digits before the decimal point in the dividend. Example 15: Divide: a) ` 23415 by 7 b) ` 481.65 by 13 c) ` 543.40 by 110 Solution: )a) 3345 )b) 37.05 )c) 4.94 7 23415 13 481.65 110 543.40 − 21↓ − 39↓ − 440↓ 24 91 1034 − 21 − 91 − 990 31 06 440 − 28 − 00 − 440 35 65 000 − 35 − 65 00 00 Money 135 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 139 28-12-2017 15:11:22

Train My Brain Solve the following: b) ` 86.34 × 11 c) ` 334.12 ÷ 14 a) `123.67 × 768 11.3 I Apply Let us solve a few real-life examples involving multiplication and division of money. Example 16: A textbook of class 4 costs ` 75.20. What is the 1 ` . p cost of 35 such textbooks? . Solution: Cost of one textbook = ` 75. 20 3 1 20 Cost of 35 such textbooks = ` 75. 20 × 35 + 2 2 21 35 Therefore, the cost of 35 textbooks is ` 2632. 75 `2 6 00 × 00 1 00 76 56 32 Example 17: 19 cakes cost ` 332.50. What is the cost of 1 cake? Solution: Cost of 19 cakes = ` 332.50 17.50 Cost of 1 cake = ` 332.50 ÷ 19 Therefore, the cost of 1 cake is ` 17. 50. )19 332.50 Train My Bra−1i9n↓ 142 − 133 95 − 95 00 11.3 I Explore (H.O.T.S.) Let us see a few more examples involving multiplication and division of money. Example 18: Multiply the sum of ` 2682 and ` 2296 by 10 . 136 28-12-2017 15:11:22 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 140

Solution: The sum of ` 2682 and ` 2296 is ` 2682 + ` 2296. ` ` 1 8 497 0 2682 ×1 0 +2296 `4 9 7 8 4978 Therefore, the sum multiplied by 10 = 4978 × 10 = ` 49780. Example 19: A bag has one bundle of ` 50 notes and one bundle of ` 20 notes. It also has two bundles of ` 10 notes and one bundle of ` 5 notes. What is the total amount of money in the bag? [Note: Each bundle consists of 100 notes.] Solution: Amount in the bundle of ` 50 = 100 × ` 50 (1 bundle) = ` 5000 Amount in the bundle of ` 20 = ` 20 × 100 (1 bundle) = ` 2000 Amount in two bundles of ` 10 = ` 10 × 200 (2 bundles) = ` 2000 Amount in the bundle of ` 5 = ` 5 × 100 (1 bundle) = ` 500 Total money = ` 5000 + ` 2000 + ` 2000 + ` 500 = ` 9500 Therefore, the total amount of money in the bag is ` 9500. Maths Munchies 213 To convert rupee to paise, add two zeros at the end of the number and shift the decimal point two places to the right. Connect the Dots English Fun Apart from Hindi and English, which language appears on the front side of a currency note? Fifteen other languages appear on the reverse side of an Indian rupee note. List the names of the other languages. Money 137 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 141 28-12-2017 15:11:23

Social Studies Fun The earliest metal coins came from China. Try to find out different coins with their values and their shapes. Drill Time Concept 11.1: Conversion of Rupees and Paise 1) Convert the following to paise. d) ` 537.58 e) ` 724.80 a) ` 632.18 b) ` 952.74 c) ` 231.48 2) Convert paise to rupees. a) 52865 b) 64287 c) 13495 d) 34567 e) 78654 3) Word problems a) Rehmat has ` 892.64. How many paise does he have in all? b) A ndrews has 56700 paise. How much money does he have in all? Express your answer in rupees. Concept 11.2: Add and Subtract Money with Conversion 4) Add: b) ` 3467.45 + ` 2356. 50 c) 25382 p + 65237 p a) ` 875.62 + ` 964.98 e) ` 279.50 + ` 642.90 d) ` 456.23 + ` 123.75 5) Subtract: b) 85732 p – 23784 p c) ` 578.14 – ` 345.89 a) ` 132.75 – ` 112.90 e) ` 784.50 – ` 234.25 d) ` 456.72 – ` 234.34 6) Word problems a) R osy has ` 451.20 and Chetan has ` 495.35 in their piggy banks. Who has more amount and by how much? b) S hane spent ` 213.60, ` 105.30 and ` 305.45 in three months. How much did he spend in all? 138 28-12-2017 15:11:23 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 142

Drill Time Concept 11.3: Multiply and Divide Money 7) Multiply: b) 27510 p × 2 c) ` 315.50 × 10 a) ` 152.45 × 5 e) ` 115.50 × 35 d) ` 113.50 × 15 8) Divide: b) 22347 p ÷ 9 c) ` 111.44 ÷ 7 a) ` 126.12 ÷ 3 e) ` 824.40 ÷ 8 d) ` 121.77 ÷ 7 9) Word problems a) A packet of chips costs ` 24.40. How much will 5 such packets cost? b) A football costs ` 159.99. What is the cost of 26 such footballs? A Note to Parent Show your child different currency notes like ` 10, ` 20, ` 100, and so on. Also show them some shopping bills to make them understand how addition and subtraction of money are useful in our day-to-day life. Money 139 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 143 28-12-2017 15:11:23

Chapter Measurements 12 I Will Learn About • relation between units of length, weight and capacity. • converting smaller units to larger units. • multiplying and dividing length, weight and capacity. Concept 12.1: Multiply and Divide Lengths, Weights and Capacities I Think Jasleen had some guests visiting her place. Jasleen’s mother asked her to pour juice from three bottles, each of 1.5 litres, into 15 glasses. What was the total quantity of juice and how much juice was poured in each glass? 12.1 I Recall Let us revise the basic concepts of measurements, their units and the different operations involving measurements. Length: kilometre, centimetre, millimetre Weight: kilogram, gram, milligram Capacity: litre, millilitre Solve the following problems based on addition and subtraction of lengths, weights and capacities. 140 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 144 28-12-2017 15:11:23

a) 560 m 65 cm – 230 m 55 cm = ___________ b) 250 g + 2 kg 500 g = ___________ c) 5 ℓ 250 mℓ + 4 ℓ 250 mℓ = ___________ d) 240 m 22 cm – 220 m 20 cm = ___________ e) 745 km 45 m – 434 km 15 m = ___________ 12.1 I Remember and Understand Let us understand the relation between the different units of length, weight and capacity in detail. Relation between units of length, weight and capacity Larger unit – Smaller unit Smaller unit – Larger unit Length 1m= 1 km 1000 1 km = 1000 m 1 m = 100 cm 1 cm = 1 m 100 1 cm = 10 mm 1 mm = 1 cm 10 1 g = 1000 mg 1 kg = 1000 g Weight 1 mg = 1 g 1 litre = 1000 mℓ Capacity 1000 1g= 1 kg 1000 1 mℓ = 1 ℓ 1000 1 kilolitre = 1000 litres 1ℓ= 1 kℓ 1000 Measurements 141 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 145 28-12-2017 15:11:23

Conversion of smaller units to larger units Let us understand conversions through a few examples. To convert measures from a Example 1: Convert the following: larger unit to a smaller unit, a) 5000 m to km we multiply. b) 8000 g to kg c) 2000 mℓ to ℓ To convert measures from a Solution: smaller unit to a larger unit, we divide. Solved Solve these a) C onversion of m into km 9000 m = ________________ km 5000 m = _____________ km 4000 g = ______________ kg 1000 m = 1 km 3000 mℓ = ______________ ℓ So, 5000 m = 5000 ÷ 1000 m = 5 km 5000 m = 5 km b) C onversion of g into kg 8000 g = _____________ kg 1000 g = 1 kg So, 8000 g = 8000 ÷ 1000 g = 8 kg c) Conversion of mℓ into ℓ 2000 mℓ = _____________ ℓ 1000 mℓ = 1 ℓ So, 2000 mℓ = 2000 ÷ 1000 mℓ = 2 ℓ Multiply and divide length, weight and capacity Interestingly, multiplication and division of lengths, weights and capacities are similar to that of usual numbers. Let us see a few examples. Example 2: Solve: a) 65 kg 345 g × 28 142 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 146 28-12-2017 15:11:23

b) 18 km 361 m × 19 c) 7 ℓ 260 mℓ × 37 Solution: a) 65 kg 345 g × 28 b) 18 km 361 m × 19 c) 7  260 m× 37 kg g km m ℓ mℓ 1 1 73 5 1 42 34 18 361 65 345 × 14 × 1 19 28 165 7 260 1 183 249 522 348 610 × 37 +1 3 0 6 859 1829 1 760 50 820 900 660 + + 217 800 268 620 Example 3: Solve: a) 15 kg 183 g ÷ 21 b) 3 km 84 m ÷ 12 c) 5 ℓ 882 mℓ ÷ 17 a) 15 kg 183 g ÷ 21 b) 3 km 84 m ÷ 12 c) 5 ℓ 882 mℓ ÷ 17 15 kg 183 g 3 km 84 m 5 ℓ 882 mℓ = 15 × 1000 g + 183 g = 3 × 1000 m + 84 m = 5 × 1000 mℓ + 882 mℓ = 15183 g = 3084 m = 5882 mℓ 346 723 257 )17 5882 )21 15183 )12 3084 − 51 − 14 7 − 24 048 068 078 − 068 − 042 − 060 0063 0084 0102 − 0102 − 0063 − 0084 0000 0000 0 15 kg183 g ÷ 21 = 723 g 3 km 84 m ÷ 12 = 257 m 5 ℓ 882 mℓ ÷ 17 = 346 mℓ Measurements 143 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 147 28-12-2017 15:11:23

Train My Brain Solve the following: b) 3 ℓ 150 mℓ × 24 c) 3 km 15 m ÷ 15 a) 52 kg 240 g × 15 12.1 I Apply Let us solve a few examples based on multiplication and division of length, weight and capacity. Example 4: The distance between two post offices A and B is 58 km 360 m. What is the total distance travelled in four round trips between A and B? Solution: The distance between two post offices A and B is 58 km 360 m. Four round trips = 4 times from A to B and 4 times from B to A = 8 times the distance between A and B Therefore, the total distance travelled in four round trips = 58 km 360 m × 8 = 466 km 880 m Example 5: Mrs. Rani has 2 kg of coffee powder. She wants to put it into smaller packets of 25 g each. How many packets will she need? Solution: Weight of coffee powder Mrs. Rani has = 2 kg 1 kg = 1000 g 2 kg = 2 × 1000 g = 2000 g Weight of one small packet = 25 g Therefore, the number of packets she needs = 2000 g ÷ 25 g = 80 Example 6: Rahul has a can of 6112 mℓ juice. If he pours it equally in 16 glasses, what is the quantity of juice in each glass? Solution: Quantity of juice in full can = 6112 mℓ Number of glasses into which the juice is poured = 16 Quantity of juice in each glass = 6112 mℓ ÷ 16 = 382 mℓ Therefore, each glass contains 382 ml of juice. 144 28-12-2017 15:11:24 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 148

12.1 I Explore (H.O.T.S.) Sometimes, we have to use more than one mathematical operation to measure things. Consider these examples. Example 7: 185 kg sugar costing ` 444 is packed in paper bags. Each bag can hold 5 kg of sugar. Find the number of bags needed to pack all the sugar. Also, find the cost of each bag. Solution: Weight of sugar = 185 kg Weight of sugar in the paper bag = 5 kg Number of paper bags needed = 185 kg ÷ 5 kg = 37 Therefore, 37 paper bags of 5 kg sugar each can be made. Cost of 37 bags of sugar = ` 444 Cost of each bag = ` 444 ÷ 37 = ` 12 Therefore, 185 kg sugar can be packed into 37 bags costing ` 12 each. Example 8: A container can hold 13 ℓ 625 mℓ of milk. What is the capacity of 15 such containers? Give your answer in mℓ. Solution: Capacity of one container = 13 ℓ 625 mℓ Capacity of 15 such containers = 13 ℓ 625 mℓ × 15 = 204 ℓ 375 mℓ 1 litre = 1000 mℓ 204 ℓ = 204 × 1000 mℓ = 204000 mℓ 204 ℓ 375 mℓ = 204000 mℓ+ 375 mℓ = 204375 mℓ Therefore, the capacity of 15 cans is 204375 mℓ. Example 9: The distance between two places is 4520 km. Ratan travelled a fourth of the distance by bus paying ` 12 per km. As the bus failed, he hired a car and travelled three-fourths of the distance by paying ` 20 per km. What amount did he spend on travelling? Solution: Total distance = 4520 km 1 of the distance = 1 × 4520 km = 1130 km 4 4 Distance travelled by bus = 1130 km Measurements 145 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 149 28-12-2017 15:11:24

Ratan travelled 1130 km by bus. Cost of ticket per km = ` 12 Cost of ticket for 1130 km = 1130 × ` 12 = ` 13560 Fraction of distance travelled by car = 3 4 Actual distance travelled by car = 3 × 4520 km 4 = 3 × 1130 km = 3390 km Cost of travelling by car per km = ` 20 Cost of travelling 3390 km = 3390 × ` 20 = ` 67800 Total amount spent by Ratan on travelling = ` 13560 + ` 67800 = ` 81360 Maths Munchies The metric system is an internationally accepted decimal system of measurement. 213 It consists of a basic set of units of measurement, now known as base units. Connect the Dots Social Studies Fun Did you know that every country uses a different group of standard measurements? For example, In India, distance is measured in kilometres and weight is measured in kilograms. However, in the United States of America, miles is used to measure distance and pound to measure weight. Science Fun A light year is the distance travelled by light in a year. It is used to measure the distances between the Earth and distant stars and galaxies. 146 28-12-2017 15:11:24 JSNR_BGM_9789387552753-Passport-G4-Textbook-Maths-FY_Text.pdf 150