2110032-Passport-G4-FoundationMax-Maths-FY

Steps Solved Solve these Step 4: Guess the quotient by 15 × 5 = 75 thinking of dividing 84 by 15 × 6 = 90 ) 15. 75 < 84 < 90 14 4874 Find the multiplication fact So, 75 is the required number − which has a number less than that is to be subtracted from or equal to the dividend and 84. the divisor. 156 − Write the factor other than 15 2340 ) the dividend and the divisor as the quotient. − 51 ↓ − 84 − 75 9 Step 5: Subtract and write 15 × 5 = 75 Dividend = _____ the difference. Repeat till all 15 × 6 = 90 Divisor = ______ the digits of the dividend are 90 = 90 brought down. So, 90 is the required number. Quotient = _____ 156 15 2340 Remainder = _____ ) − 51 ↓ 84 − 75 90 − 90 00 Quotient = 156 Remainder = 0 Step 6: Check if (Divisor × 15 × 156 + 0 = 2340 Quotient) + Remainder = 2340 + 0 = 2340 Dividend is true. If this is false, 2340 = 2340 (True) the division is incorrect. Let us see some properties of division. Properties of division 1) Dividing a number by 1 gives the same number as the quotient. For example: 15 ÷ 1 = 15; 1257 ÷ 1 = 1257; 1 ÷ 1 = 1; 0 ÷ 1 = 0 2) Dividing a number by itself gives the quotient as 1. Division 95 Merged File_PPS_Maths_G4_TB_Part 1.indb 95 2/1/2017 3:10:25 PM

For example: 15 ÷ 15 = 1; 1257 ÷ 1257 = 1; 1 ÷ 1 = 1 3) Division by zero is not possible and is not defined. For example: 10 ÷ 0; 1257 ÷ 0; 1 ÷ 0 are not defined Train My Brain Solve the following: a) 2868 ÷ 4 b) 7890 ÷ 12 c) 723 ÷ 15 7.1 I Apply Division of large numbers can be applied in many real-life situations. Consider these examples. Example 4: 4720 apples are to be packed in 8 baskets. If each basket 590 has the same number of apples, how many apples are 8 ) 4720 packed in each basket? − 40↓ Solution: Total number of apples = 4720 0 72 − 072 Number of baskets = 8 0000 The number of apples packed in each basket = 4720 ÷ 8 − 0000 Therefore, 590 apples are packed in each basket. 0000 Example 5: 2825 notebooks were distributed equally among 25 students. How many books did each student get? 1 1 3 25 2 8 2 5 ) Solution: Number of notebooks = 2825 − 2 5 ↓ Number of students = 25 0 3 2 0 2 5− Number of books each student got = 2825 ÷ 25 00 7 5 − 0 7 5 0 Therefore, each student got 113 notebooks. 0 0 0 96 Merged File_PPS_Maths_G4_TB_Part 1.indb 96 2/1/2017 3:10:28 PM

Example 6: 8308 people watched a hockey match. If 10 people watched from each cabin in the stadium, how many cabins were full? How many people were there in the remaining cabin? 83 0 10 8 3 0 8 ) Solution: Number of people = 8308 − 8 0 ↓ Number of people in each cabin = 10 3 0 3 0− Number of cabins = 8308 ÷ 10 = 830 0 0 8 Number of people in the remaining cabin = 8 (Remainder in the division of 8308 by 10). Therefore, 8 people were remaining in the cabin. 7.1 I Explore (H.O.T.S.) Let us see some more examples of situations where we use division of large numbers. Example 7: A school has 530 students in the primary section, 786 students in the middle school and 658 students in the high school section. If equal number of students are seated in 6 halls, how many students are seated in each hall? Solution: Number of students in the primary section = 530 Number of students in the middle school section = 786 329 ) Number of students in the high school section = 658 6 1974 − 18 Thus, the total number of students in the school 017 = (530 + 786 + 658) − 012 54 = 1974 − 54 1974 children are equally seated in 6 halls. 00 Therefore, the number of students in each hall = 1974 ÷ 6 = 329 students. Division 97 Merged File_PPS_Maths_G4_TB_Part 1.indb 97 2/1/2017 3:10:29 PM

Example 8: Divide the largest 4-digit number by the largest 2-digit number. Write the quotient and the remainder. 1 0 1 99 9 9 9 9 ) Solution: The largest 4-digit number is 9999. − 9 9 ↓ The largest 2-digit number is 99. 0 0 9 The required division is 9999 ÷ 99 − 0 0 0 9 9 Quotient = 101; Remainder = 0 − 9 9 0 0 Maths Munchies Divide by multiplication: 2 3 1 5255 ÷ 5 To make this easier, multiply both the numbers by 2 to make the divisor 10. Then 10510 ÷ 10 gives a quotient 1051 and remainder 0. Thus, 5255 ÷ 5 gives a quotient 1051 and remainder 0. Connect the Dots Science Fun There are more different kinds of living things than people on the Earth. All living things are divided into various groups. These divisions help scientists study these living things. Social Studies Fun India is a very large country. So, it becomes difficult to make laws for the entire country. To manage this large country, it is divided into 29 states and 7 union territories. 98 Merged File_PPS_Maths_G4_TB_Part 1.indb 98 2/1/2017 3:10:31 PM

A Note to Parent Collect the electricity bills of the past three months and show them to your child. Highlight the total amount and per unit cost of electricity. Explain how units of electricity are calculated. Now help your child calculate the number of units of electricity that were consumed in the past three months. Drill Time Concept 7.1: Divide Large Numbers 1) Divide 4-digit numbers by 1-digit numbers. a) 1347 ÷ 6 b) 4367 ÷ 5 c) 3865 ÷ 4 d) 5550 ÷ 5 2) Divide 4-digit and 3-digit numbers by 2-digit numbers. a) 3195 ÷ 10 b) 612 ÷ 10 c) 2676 ÷ 12 d) 267 ÷ 11 3) Word Problems a) A sum of ` 1809 is distributed equally among 9 women. How much money did each of them get? b) 10 boxes have 1560 pencils. How many pencils are there in a box? c) A school has 1254 students, who are equally grouped into 14 groups. How many students are there in each group? How many students are remaining? Division 99 Merged File_PPS_Maths_G4_TB_Part 1.indb 99 2/1/2017 3:10:31 PM

Fractions - I Fractions - I I Will Learn Concepts 8.1: Find Equivalent Fractions Using Pictures 8.2: Identify and Compare Like Fractions 8.3: Add and Subtract Like Fractions Merged File_PPS_Maths_G4_TB_Part 1.indb 100 2/1/2017 3:10:32 PM

Concept 8.1: Find Equivalent Fractions Using Pictures I Think Surbhi cuts 3 apples into 18 equal pieces. Ravi cuts an apple into 6 equal pieces. Did both of them cut the apples into equal pieces? To answer this question, we must know equivalent fractions. 8.1 I Recall In class 3, we have learnt that a fraction is a part of a whole. A whole can be a region or a collection. When a whole is divided into two equal parts, each of them is called ‘a half’. 1 ‘Half’ means 1 out of 2 equal parts. We write ‘half’ as . 2 Two halves make a whole. Numerator Numbers of the form are called fractions. Denominator The total number of equal parts into which a whole is divided is called the denominator. The number of such equal parts taken is called the numerator. Similarly, each of the 1 three equal parts of a whole is called a third. We write one-third as and, two-thirds 3 2 3 as . Three-thirds or make a whole. 3 3 1 Each of four equal parts of a whole is called a fourth or a quarter written as . 4 Two such equal parts are called two-fourths, and three equal parts are called three- 2 3 fourths, written as and respectively. Four quarters make a whole. 4 4 2 halves, 3 thirds, 4 fourths, 5 fifths, …, 10 tenths make a whole. So, we write a whole Fractions – I 101 Merged File_PPS_Maths_G4_TB_Part 1.indb 101 2/1/2017 3:10:34 PM

2 3 4 5 10 as , , , ,..., . 2 3 4 5 10 8.1 I Remember and Understand Let us now understand what equivalent fractions are. Suppose a bar of chocolate is cut as shown. Fractions that denote the same part of a whole are called equivalent 1 fractions. Ram eats of the chocolate. 5 Then the piece of chocolate he gets is 2 Raj eats of the chocolate. 10 Then the piece of chocolate he gets is We see that both the pieces of chocolates are of the same size. So, we say that the 1 1 fractions and 2 are equivalent. We write them as = 2 . 5 10 5 10 Example 1: Shade the regions to show equivalent fractions. 1 2 a) [ and ] 3 6 1 2 b) [ and ] 4 8 1 Solution: a) 3 102 Merged File_PPS_Maths_G4_TB_Part 1.indb 102 2/1/2017 3:10:37 PM

2 6 1 b) 4 2 8 Example 2: Find the figures that represent equivalent fractions. Also, mention the fractions. a) b) c) d) e) 1 Solution: The fraction represented by the shaded part of figure a) is . 2 2 The shaded part of figure b) represents . The shaded part of figure e) 4 1 represents . 2 So, the shaded part of figures a), b) and e) represent equivalent fractions. Train My Brain Answer the following: a) How many thirds make a whole? 1 3 b) Are and equivalent? 5 5 c) What is the value of 8 eighths? 8.1 I Apply Let us see a few examples of equivalent fractions. Fractions – I 103 Merged File_PPS_Maths_G4_TB_Part 1.indb 103 2/1/2017 3:10:39 PM

Example 3: Shade the second figure to give a fraction equivalent to the first. 2 Solution: The fraction denoted in the first figure is . This is half of the 4 given figure. So, to denote a fraction equivalent to the first, shade half of the the second figure as shown. Example 4: Venu paints four-sixths of a cardboard and Raj paints two-thirds of a similar sized cardboard. Who has painted a larger area? Solution: Fraction of the cardboard painted by Venu and Raj are as follows: Venu Raj It is clear that, both Venu and Raj have painted an equal area on each of the cardboards. 8.1 I Explore (H.O.T.S.) We have learnt how to find equivalent fractions using pictures. Let us see some more examples to find equivalent fractions. Example 5: Find two fractions equivalent to the given fractions. 2 33 a) b) 11 66 Solution: To find fractions equivalent to the given fractions, we either multiply or divide both the numerator and the denominator by the same number. a) 2 11 We see that 2 and 11 do not have any common factors. So, we cannot divide them to get an equivalent fraction of 2 . 11 104 Merged File_PPS_Maths_G4_TB_Part 1.indb 104 2/1/2017 3:10:40 PM

Therefore, we multiply both the numerator and the denominator by the same number, say 5. 2 2×5 10 = = 11 11×5 55 10 2 Thus, is a fraction equivalent to . 55 11 Likewise, we can multiply by any number of our choice to get more 2 fractions equivalent to 11 . 33 b) 66 We see that 33 and 66 have common factors 3, 11 and 33. So, dividing both the numerator and the denominator by 3, 11 or 33, we get fractions equivalent to the given fraction 33 . 66 33 ÷ 3 11 33 11÷ 3 33 ÷ 33 1 = , = or = 66 3 22 66 11 6 66 33 2 ÷ ÷ ÷ 11 3 1 33 Therefore, , and are the fractions equivalent to . 22 6 2 66 Example 6: Draw four similar rectangles. Divide them into 2, 4, 6 and 8 equal parts. 1 2 3 4 Then colour , , and parts of the rectangles respectively. 2 4 6 8 Compare these coloured parts and write the fractions using >, = or <. Solution: 1 2 2 4 Fractions – I 105 Merged File_PPS_Maths_G4_TB_Part 1.indb 105 2/1/2017 3:10:43 PM

3 6 4 8 From the coloured parts of these rectangles, we can see that all of 1 2 3 4 them are of the same size. So, all the fractions, , , and are 1 2 3 4 2 4 6 8 equivalent. Therefore, = = = . 2 4 6 8 Concept 8.2: Identify and Compare Like Fractions I Think Surbhi has a circular disc coloured in blue, green, red and white as shown. She wants to know if there is any special name for the fractions of different colours on the circular disc. Do you know any special name for such fractions? To find that, we must know about like fractions. 8.2 I Recall In class 3, we have learnt to represent shaded parts of a whole as fractions. Recall the same through the following example. 106 Merged File_PPS_Maths_G4_TB_Part 1.indb 106 2/1/2017 3:10:45 PM

Surbhi’s colourful circular disc is given here. Find the fraction represented by the following colours: a) Red b) Green c) Blue d) White 8.2 I Remember and Understand 1 2 3 Fractions such as , and , that have the same 8 8 8 denominator are called like fractions. 3 1 2 Fractions such as , and that have different 8 4 7 denominators are called unlike fractions. To understand like and unlike fractions, consider the following example. Fractions which have the Example 7: Identify the like and unlike fractions from the following. same denominators are called Like Fractions. 3 3 1 5 6 1 4 , , , , , , Fractions which have 7 5 7 7 7 4 11 different denominators are 3 1 5 6 Solution: , , and have the same called Unlike Fractions. 7 7 7 7 denominator. So, they are like fractions. 3 1 4 , and have different denominators. So, they are unlike fractions. 5 4 11 Example 8: Find the fraction of the parts not shaded in these figures. a) b) c) d) Which of them represent like fractions? Fractions – I 107 Merged File_PPS_Maths_G4_TB_Part 1.indb 107 2/1/2017 3:10:48 PM

Solution: a) Number of parts not shaded = 1 Total number of equal parts = 2 Number of parts not shaded 1 Fraction = Total number of equal parts = 2 b) Number of parts not shaded = 3 Total number of equal parts = 4 Number of parts not shaded 3 Fraction = = Total number of equal parts 4 c) Number of parts not shaded = 3 Total number of equal parts = 5 Number of parts not shaded 3 Fraction = = Total number of equal parts 5 d) Number of parts not shaded = 3 Total number of equal parts = 6 Number of parts not shaded 3 1 Fraction = = = Total number of equal parts 6 2 1 a) and d) are equal to . They represent like fractions. 2 Train My Brain Identify the like fractions from each of the following. a) 1 3 2 4 b) 5 6 2 8 6 7 1 c) 1 5 , 2 5 18 4 7 6 , , , , , , , , , , , , , , , 4 6 6 6 11 11 7 11 7 11 7 3 25 25 3 25 3 3 25 8.2 I Apply We can compare like fractions and tell which is greater or less than the others. To compare like fractions, we compare their numerators. The fraction with the greater numerator is greater. Let us understand this better through some examples. 108 Merged File_PPS_Maths_G4_TB_Part 1.indb 108 2/1/2017 3:10:49 PM

1 2 Example 9: Jai ate of the apple and Vijay ate of the apple. Who ate more? 3 3 Solution: Fraction of apple Jai ate = 1 3 2 Fraction of apple Vijay ate = 3 2 1 Since, 2 > 1, > 3 3 Clearly, Vijay ate more. Example 10: The equal parts of the circular disc shown in the figure are painted in different colours. Write the fraction of each colour on the disc. Compare the fractions and tell which colour is used more and which the least. Solution: Total number of equal parts on the disc is 16. Number of parts painted yellow is 3. Number of parts paintedyellow 3 Fraction = = Totalnumberofequal parts 16 The fraction of the disc that is painted white Number of parts paintedwhite 6 = Totalnumberofequal parts = 16 Train My Brain The fraction of the disc that is painted red Number of parts paintedred 4 = Totalnumberofequal parts = 16 The fraction of the disc that is painted blue Number of parts paintedblue 3 = Totalnumberofequal parts = 16 Comparing the numerators of these fractions, we get 3 < 4 < 6. Since, 6 3 16 is the greatest and 16 is the least, white is used the most and blue and yellow are the least. Fractions – I 109 Merged File_PPS_Maths_G4_TB_Part 1.indb 109 2/1/2017 3:10:51 PM

8.2 I Explore (H.O.T.S.) Let us see some more examples using comparison of like fractions. Example 11: Colour each figure to represent the given fraction and compare them. 2 3 5 5 Solution: 3 Clearly, the part of the figure represented by 5 is greater than that 2 3 2 represented by . Hence, is greater than . 5 5 5 Let us try to arrange some like fractions in ascending and descending orders. 1 6 2 5 4 Example 12: Arrange , , , and in the ascending and descending orders. 7 7 7 7 7 Solution: Comparing the numerators of the given like fractions, we have 1 < 2 < 4 < 5 < 6. 1 2 4 5 6 So, < < < < . 7 7 7 7 7 1 2 4 5 6 Therefore, the required ascending order is , , , , . 7 7 7 7 7 We know that, the descending order is just the reverse of the ascending order. 6 5 4 2 1 So, the required descending order is , , , , . 7 7 7 7 7 110 Merged File_PPS_Maths_G4_TB_Part 1.indb 110 2/1/2017 3:10:53 PM

Concept 8.3: Add and Subtract Like Fractions I Think Surbhi has a cardboard piece, equal parts of which are coloured in different colours. Some of the equal parts are not coloured. She wants to find the total part of the cardboard that has been coloured. And also, the part of the cardboard is that left uncoloured. How do you think Surbhi can find that? To answer this question, we must know how to add and subtract like fractions. 8.3 I Recall Recall that like fractions have the same denominators. To compare them, we compare their numerators. Let us answer the following to recall the concept of like fractions. Compare the following using >, < and =. a) 2 ____ 1 b) 4 ____ 8 c) 3 ____ 5 d) 7 ____ 3 e) 1 ____ 4 3 3 10 10 7 7 8 8 5 5 8.3 I Remember and Understand Let us understand addition and subtraction of like fractions through some examples. Example 13: In the given figures, find the fractions represented by the shaded parts While adding or subtracting like fractions, add or using addition. Then find the fractions subtract only their represented by the unshaded parts numerators. Write the sum using subtraction. or difference on the same denominator. Fractions – I 111 Merged File_PPS_Maths_G4_TB_Part 1.indb 111 2/1/2017 3:10:55 PM

a) b) c) Solution: Solved Solve these Steps Step 1: Count the Total number of Total number of Total number of total number of equal parts = 6 equal parts = equal parts = equal parts in the given figure. _____________ _____________ Step 2: Count the a) Number of parts a) Number of a) Number of number of parts of coloured pink parts coloured parts coloured each colour. = 1 yellow = ______ violet = _______ b) Number of parts coloured blue b) Number of b) Number of parts coloured parts coloured = 2 violet = _______ brown = ______ Step 3: Write the 1 2 Yellow: ________ Violet:________ fraction representing Pink: , Blue: 6 6 the number of parts Violet: ________ Brown:________ of each colour. Step 4: To add the The fraction that The fraction that The fraction that like fractions in represents the represents the represents the step 3, add their shaded part of the shaded part of shaded part of numerators and write given figure is the given figure is the given figure is the sum on the same 1 2 1 + 2 3 denominator. + = = ____ + ____=____ ____ + ____=____ 6 6 6 6 Step 5: Write the Like fraction Like fraction Like fraction whole as a like representing the representing the representing the fraction of the sum 6 whole = _______. whole = _______. in step 4. Then, to whole = . So, the So, the fraction So, the 6 subtract the like fraction that that represents fraction that fractions, subtract represents the the unshaded represents the their numerators. unshaded part of part of the given unshaded part of Write the difference the given figure is figure is the given figure is on the same 6 3 63− 3 denominator. 6 − 6 = 6 = 6 . ____ − ____=____. ____ − ____=_____. 112 Merged File_PPS_Maths_G4_TB_Part 1.indb 112 2/1/2017 3:10:56 PM

3 1 4 5 23 57 Example 14: Add: a) + b) + c) + 8 8 13 13 100 100 3 1 3+1 4 Solution: a) + = = 8 8 8 8 4 5 4+ 5 9 b) + = = 13 13 13 13 23 57 23 +57 80 c) + = = 100 100 100 100 8 4 33 25 48 26 Example 15: Subtract: a) – b) – c) – 9 9 37 37 125 125 8 4 4 Solution: a) – = 9 9 9 33 25 33 25− 8 b) – = = 37 37 37 37 48 26 48 26− 22 c) – = = 125 125 125 125 Train My Brain Solve: a) 1 + 2 b) 3 + 1 c) 11 − 3 9 9 34 34 15 15 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? Fractions – I 113 Merged File_PPS_Maths_G4_TB_Part 1.indb 113 2/1/2017 3:11:01 PM

Solution: Total number of parts of the ribbon = 9 2 Part of the ribbon coloured blue = 9 3 Part of the ribbon coloured yellow = 9 2 3 2 +3 5 Total part of the ribbon coloured = + = = 9 9 9 9 9 5 95− 4 Part of the ribbon that is not coloured is − = = 9 9 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 the chocolate on the next day. How much chocolate did Suman eat in all? How much chocolate is remaining? 1 Solution: Part of the chocolate eaten by Suman on one day = 4 1 Part of the chocolate eaten by him on the next day = 4 1 1 1+ 1 2 Total chocolate eaten by Suman on both the days = + = = 4 4 4 4 2 4 2 4 2− 2 He ate chocolate in all. Remaining chocolate = − = = 4 4 4 4 4 Example 18: Manav painted two-tenths of a strip of chart in one hour and four - tenths of it in the next hour. What part of the strip did he paint in two hours? How much is left unpainted? 2 Solution: Part of the strip of chart painted by Manav in one hour = 10 1 hour: st 4 Part of the strip painted by him in the next hour = 10 2 hour: nd 114 Merged File_PPS_Maths_G4_TB_Part 1.indb 114 2/1/2017 3:11:03 PM

2 4 2+4 6 Part of the strip painted by him in two hours = + = = 10 10 10 10 10 6 4 Part of the strip of chart left without painting = – = 10 10 10 6 [From the figure, total part of the strip painted = 10 and the part of the strip not painted = 4 ] 10 8.3 I Explore (H.O.T.S.) Let us see some more examples of addition and subtraction of like fractions. 5 1 Example 19: Veena ate of a pizza in the morning and in the evening. What 8 8 part of the pizza is remaining? 5 Solution: Part of the pizza eaten by Veena in the morning = 8 1 Part of the pizza eaten by Veena in the evening = 8 To find the remaining part of pizza, add the parts eaten and subtract the sum from the whole. 5 1 5+1 6 Total part of the pizza eaten = + = 8 = 8 8 8 8 6 6 Part of the pizza remaining = 1 – = – = 2 8 8 8 8 Fractions – I 115 Merged File_PPS_Maths_G4_TB_Part 1.indb 115 2/1/2017 3:11:06 PM

Maths Munchies Egyptians were the first to use fractions. But their way was very complicated. 2 3 1 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 from a way of writing called Brahmi, 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. 116 Merged File_PPS_Maths_G4_TB_Part 1.indb 116 2/1/2017 3:11:07 PM

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. Drill Time Concept 8.1: Find Equivalent Fractions using Pictures 1) Shade the regions to show equivalent fractions. a)  1 2  and   2 4  b)  1 2   and   5 10  2) Write four equivalent fractions for each of the following. 1 4 3 4 a) b) c) d) 2 7 10 11 Concept 8.2: Identify and Compare Like Fractions 3) Identify like and unlike fractions from the following. a) 2 3 15 6 7 6 9 b) 7 5 42 7 2 3 6 ,,,,,,, ,, ,,,,, 8 2 2 8 2 8 8 2 9 4 9 9 4 4 4 9 c) 6 5 54 8 7 9 2 d) 3 4 13 1 4 ,, ,, , , , , , , , , 14 14 17 17 17 14 17 14 5 5 5 7 9 11 Fractions – I 117 Merged File_PPS_Maths_G4_TB_Part 1.indb 117 2/1/2017 3:11:09 PM

Drill Time 4) Arrange the following fractions in the ascending order. 3 1 74 3 2 95 1 3 42 1 8 79 a) , , , b) , , , c) ,,, d) , , , 11 11 11 11 13 13 13 13 7 7 7 7 14 14 14 14 5) Arrange the following fractions in descending order. 1 8 74 3 6 10 8 7 9 213 1 7 8 3 a) ,, , b) , , , c) , , , d) , , , 9 9 9 9 17 17 17 17 21 21 21 21 20 20 20 20 Concept 8.3: Add and Subtract Like Fractions 6) Add: 2 5 3 16 9 4 8 4 1 2 a) + b) + c) + d) + e) + 7 7 11 11 5 5 17 17 13 13 7) Subtract: a) 15 7 b) 9 5 c) 11 − 3 d) 7 − 4 e) 13 12 − − − 6 6 8 8 40 40 45 45 30 30 8) Word problems a) Leena paints three-sixths of a cardboard and Rani paints a half of a similar cardboard. Who has painted a smaller area? b) Colour each figure to represent the given fraction and compare them. 5 7 8 8 1 2 c) Ajit ate of a cake in the morning and of it in the evening. What part of 5 the cake is remaining? 5 118 Merged File_PPS_Maths_G4_TB_Part 1.indb 118 2/1/2017 3:11:12 PM

Fractions - II Fractions - II Chapter I Will Learn Concepts 9.1: Find a Fraction of a Number 9.2: Conversions of Fractions Merged File_PPS_Maths_G4_TB_Part 1.indb 119 2/1/2017 3:11:13 PM

Concept 9.1: Find a Fraction of a Number I Think Surbhi’s father told her that he spends two-thirds of his salary per month and saves the rest. Surbhi calculated the amount her father saves from his salary of ` 25,000 per month. How do you think Surbhi could calculate her father’s savings per month? To answer this question, we must learn to find the fraction of a number. 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 banana = _______________ bananas b) A quarter of 16 books = _______________ books 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 1 bowl. Vani wants to take of them. So, she divides the shells into 5 (the number in 5 the denominator) equal groups and takes 1 group (the number in the numerator). 1 This gives 5 groups with 4 shells in each group. So, of 20 is 4. 5 120 Merged File_PPS_Maths_G4_TB_Part 1.indb 120 2/1/2017 3:11:14 PM

3 Vani’s sister Rani wants to take 10 of the shells. So, she divides the shells into 10 (the number in the denominator) equal groups, and takes 3 groups (the number in the Fraction of a number: numerator) of them. This gives 2 shells in each group. To find the fraction of a Hence, Rani takes 6 shells. Therefore, 3 of 20 is 6. number, we multiply the 1 1 20 10 We write of 20 as × 20 = = 4. number by the fraction. 5 5 5 3 3 × 20 Similarly, of 20 = = 6. 10 10 Example 1: Find the following: 2 1 a) of a metre (in cm) b) of a kilogram (in g) 5 10 2 2 2 2 × 100 200 Solution: a) of a metre = × 1 m = × 100 cm = cm = cm 5 5 5 5 5 = 40 cm 1 1 1 1000 b) of a kilogram = × 1 kg = × 1000 g = g = 100 g 10 10 10 10 Example 2: Find the following: 2 1 a) of an hour (in minutes) b) of a day (in hours) 3 3 2 2 2 2 × 60 120 Solution: a) of an hour = × 1 h = × 60 min = = = 40 min 3 3 3 3 3 1 1 1 24 b) of a day = × 1 day = × 24 h = 1 × 24 h = hrs = 6 h 4 4 4 4 Train My Brain Find fractions of the given numbers. 5 3 7 a) of 36 b) of 64 c) 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. Fractions – II 121 Merged File_PPS_Maths_G4_TB_Part 1.indb 121 2/1/2017 3:11:18 PM

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 2 120 Amount Ravi gave his sister = of ` 120 = 2 × ` = 2 × ` 40 = ` 80 3 3 Difference in the amounts = ` 120 – ` 80 = ` 40 Therefore, amount left with Ravi is ` 40. 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. 1 1 The distance covered by Reema = of 2 kilometres = x 2000 m 10 10 = 200 m Therefore, Reema has covered 200 metres of the distance. 1 4 Example 5: A school auditorium has 2500 chairs. On the annual day, 10 5 of the auditorium was occupied. How many chairs were occupied? Solution: Total number of chairs in the auditorium = 2500 1 Fraction of chairs occupied = 4 10 5 1 4 4 2500× Number of chairs occupied = × 2500 = 10 5 5 10000 = 5 Therefore, 2000 chairs in the auditorium were occupied. 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 of them paint? 122 Merged File_PPS_Maths_G4_TB_Part 1.indb 122 2/1/2017 3:11:19 PM

3 Solution: Fraction of the cardboard painted by Venu = 6 1 Fraction of the cardboard painted by Raj = 3 Area of the cardboard = 144 sq. cm 3 Area of the cardboard painted by Venu = × 144 sq.cm 6 3 144× 432 = sq.cm = sq.cm = 72 sq.cm 6 6 1 Area of the cardboard painted by Raj = × 144 sq.cm 3 1 144× 144 = sq.cm = sq.cm = 48 sq.cm 3 3 2 4 Example 7: Find if of 154 and of 49 are equal or one of them is greater than 11 7 the other. Solution: To find if the given fractions of numbers are equal, we first find their values and compare them. 2 2 2 154× 308 of 154 = × 154 = = = 28 11 11 11 11 4 4 4 49× 196 of 49 = × 49 = = = 28 7 7 7 7 2 4 Therefore, of 154 = of 49. 11 7 Concept 9.2: Conversions of Fractions I Think Surbhi 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? To answer this question, we must know about the types of fractions. Fractions – II 123 Merged File_PPS_Maths_G4_TB_Part 1.indb 123 2/1/2017 3:11:22 PM

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. 1 2 1 1 1 4 1 1 a) + = ______ b) + = ______ 10 5 10 5 10 7 10 7 c) 1 1 + 1 5 = ______ d) 1 3 + 1 1 = _______ 10 11 10 11 10 2 10 2 e) 1 1 + 1 3 = ______ f) 1 2 + 1 1 = _______ 10 8 10 8 10 9 10 9 9.2 I Remember and Understand 1 5 6 Consider + = . Here, the sum of two like fractions is a like fraction with its 8 8 8 numerator less 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. 7 5 12 For example, + = . Here, the sum of two 8 8 8 like fractions is a like fraction with its numerator greater than its denominator. Such fractions are Proper fractions - Fractions called improper fractions. having the numerators less than the denominators. Note: In some cases, the sum of the numerators Improper fractions - Fractions of the like fractions may be equal to the having the numerators greater denominator. Then, the fraction is said to be an than the denominators. Mixed fractions - Fractions improper fraction. For example, having whole numbers and 8 5 3 + = , + = and so on. improper fractions. 4 7 3 7 7 7 8 8 8 124 Merged File_PPS_Maths_G4_TB_Part 1.indb 124 2/1/2017 3:11:24 PM

7 8 Fractions such as , and so on can also be written as a whole, that is 1. 7 8 12 8 4  8  We can write as the sum of like fractions as + . This has a whole   and a 8 8 8  8  4 4 proper fraction  4  . That is, 12 = 1 + = 1 . Such fractions are called mixed fractions.    8  8 8 8 A mixed fraction is also called a mixed number. 3 3 For example, in the mixed fraction 12 , 12 is the whole and is the proper fraction. 8 8 Example 8: List out proper fractions, improper fractions and mixed fractions from the following: 13 7 11 37 9 13 143 3 27 72 2 29 23 69 53 ,15 , , , ,65 , ,75 ,107 , ,68 , ,50 , , 18 9 34 6 14 17 98 4 49 59 5 32 35 32 30 Solution: From the given fractions, 13 11 9 29 Proper fractions: , , , 18 34 14 32 37 143 72 69 53 Improper fractions: , , , , 6 98 59 32 30 7 13 3 27 2 23 Mixed fractions: 15 , 65 , 75 , 107 , 68 , 50 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 through some examples. Example 9: Convert 37 to its mixed fraction form. 6 Solution: To convert improper fractions into mixed fractions, follow these steps. Fractions – II 125 Merged File_PPS_Maths_G4_TB_Part 1.indb 125 2/1/2017 3:11:35 PM

Solved Solve these Steps 37 143 72 69 53 6 98 59 32 30 Step 1: Divide the 6 37 6( ) numerator by the denominator. − 36 1 Step 2: Write the quotient Quotient = 6 and the remainder. Remainder = 1 Step 3: Write the The mixed quotient as the whole. fraction form The remainder is the 37 1 numerator of the proper of 6 is 6 . 6 fraction and the divisor is its 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 through some examples. 7 Example 10: Convert 15 into its improper fraction. 9 Solution: To convert mixed fractions into improper fractions, follow these steps. Solved Solve these Steps 15 7 9 65 13 75 3 107 27 17 4 49 Step 1: Multiply the whole by the 15 × 9 = 135 denominator. Step 2: Add the numerator of the 135 + 7 = 142 proper fraction to the product in step 1. Step 3: Write the sum on the The improper denominator of the proper fraction. fraction form This given the required improper 15 7 142 fraction. of 9 is 9 . 126 Merged File_PPS_Maths_G4_TB_Part 1.indb 126 2/1/2017 3:11:39 PM

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 48 8 Number of racks that are filled = 60 ÷ 13 = 4 13 48 8 60 Improper fraction equivalent to 4 = 13 13 48 1 Example 12: On a science fair day, a group of students prepared 12 13 2 litres of orange juice. Express the number of litres of orange juice as an improper fraction. 1 Solution: Number of litres of orange juice made = 12 2 1 12 2+1× 25 Improper fraction equivalent to 12 = = 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 the addition and subtraction of like (proper) fractions. Let us see some examples of addition and subtraction of improper and mixed fractions. Example 13: Add: a) 42 + 35 b) 50 23 16 + 25 25 35 35 Fractions – II 127 Merged File_PPS_Maths_G4_TB_Part 1.indb 127 2/1/2017 3:11:41 PM

42 35 Solution: a) + 25 25 To add the given like improper fractions, we add their numerators and write the sum on the same denominator. 42 35 42 +35 77 Therefore, + = = 25 25 25 25 We 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 quotient 3 and remainder 2.) 25 25 2 Therefore, the sum of the given fractions is 3 25 . 23 16 b) 50 + 35 35 To add the given fractions, we have to convert the mixed fraction into improper fraction. 1750 + 23 23 (50 35)+23 1773× (50 35)+23 1773× (50 35)+23 1773× 1773 So,50 = = = = = = 35 35 35 35 35 35 35 35 Then add their numerators and write the sum on the same denominator. Train My Brain 23 16 1773 16 1773 + 16 1789 Therefore, 50 + = + = = . 35 35 35 35 35 35 Again convert the improper fraction into a mixed fraction. 1789 =51 4 (1789 ÷ 35 gives quotient 51 and remainder 4.) 35 35 Therefore, the sum of the given fractions is 51 4 . 35 Short cut method: 50 +  23 16   = 50 +  23 16  + +   35 35   35 35    + = 50 +   23 16    35  128 Merged File_PPS_Maths_G4_TB_Part 1.indb 128 2/1/2017 3:11:43 PM

= 50 +   39    35  = 50 1+ 4 35 4 = 51 35 342 135 17 37 Example 14: Subtract: a) - b) 34 - 25 25 42 42 342 135 Solution: a) - 25 25 To subtract the given like improper fractions, we subtract their numerators. We then write the difference on the same denominator. 342 135 342 - 135 207 Therefore, - = = 25 25 25 25 As we usually write fractions as proper or mixed fractions, we convert the difference into a mixed fraction. 207 = 8 7 (207 ÷ 25 gives quotient 8 and remainder 7). 25 25 7 Therefore, the difference of the given fractions is 8 25 . 17 37 b) 34 - 42 42 To subtract the given fractions, we first convert the mixed fraction into an improper fraction. 17 34 42× + 17 1445 So, 34 = = 42 42 42 Then subtract their numerators and write the difference on the same denominator. 17 37 1445 37 1445 37− 1408 Therefore, 34 − = − = = 42 42 42 42 42 42 Again convert the improper fraction into a mixed fraction. 1408 22 1445 42 = 33 42 (1408 ÷ 42 gives quotient 33 and remainder 22). 42 Therefore, the difference of the given fractions is 33 22 . 42 Fractions – II 129 Merged File_PPS_Maths_G4_TB_Part 1.indb 129 2/1/2017 3:11:46 PM

Maths Munchies Add mixed fractions without conversion. 2 3 1 3 4 3+4 Step 1: Write the mixed fractions one below the other. 6 +2 =8+ 5 5 5 Step 2: Add the whole numbers. 7 5+2 =8 =8 Step 3: Add the fractions. 5 5+2 5 Step 4: If the sum is an improper fraction then convert =8+ 5 5 2 it into a mixed fraction. =8+ + Step 5: Add the whole number to the whole number 5 5 2 2 2 and write the remaining fraction. =8+1+ =9+ =9 5 5 5 Connect the Dots Social Studies Fun Fresh Water th About 3 of the Earth is covered with 4 97 th water. Of this water, part is salt 100 water and is not suitable for drinking. Salt Water English Fun Write your name. Write the number of letters in it. Write fractions to show the number of letters in half of your name and one-fourth of your name. A Note to Parent Give different currency notes to your child. Ask him or her 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. 130 Merged File_PPS_Maths_G4_TB_Part 1.indb 130 2/1/2017 3:11:47 PM

Drill Time Concept 9.1: Find a Fraction of a Number 1) Find the following: 1 3 3 4 2 a) of 20 b) of 24 c) of 20 d) of 12 e) of 18 2 4 5 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: 6 3 5 10 3 a) 15 b) 23 c) 40 d) 125 e) 40 8 2 4 9 5 4) Word Problems a) At 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. 4 4 1 3 b) I bought 2 litres of paint but used only litres. How much paint is left with 6 2 6 2 me? Give your answer as an improper fraction. Fractions – II 131 Merged File_PPS_Maths_G4_TB_Part 1.indb 131 2/1/2017 3:11:49 PM

Decimals Decimals I Will Learn Concept 10.1: Conversion between Fractions and Decimals Merged File_PPS_Maths_G4_TB_Part 1.indb 132 2/1/2017 3:11:50 PM

Concept 10.1: Conversion between Fractions and Decimals I Think Surbhi and her friends participated in the long jump event in their games period. Her sports teacher noted the distance they jumped on a piece of paper as shown here. Surbhi – 4.1m Ravi – 2.85m Surbhi wondered why the numbers had a point between them Rajiv – 3.05 m as in the case of writing money. Amit – 2.50m Do you know what the point means? To answer this, we must learn about decimal numbers. 10.1 I Recall Recall that in class 3 we have learnt to measure the lengths, weights and volumes of objects. For example, a pencil is 12.5 cm long. A crayon is 5.4 cm long. 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? Decimals 133 Merged File_PPS_Maths_G4_TB_Part 1.indb 133 2/1/2017 3:11:52 PM

They too have numbers with a point between them. Let us learn why a point is used in such numbers. 10.1 I Remember and Understand 3 We know how to write fractions. In this figure, portion is coloured 7 10 and portion is not coloured. 10 3 We can write the coloured portion of the figure as 10 or 0.3 and the portion that is not coloured as 7 or 0.7. 10 The adjacent box is the label on a 500 m milk Nutritional facts (per 100 m) packet. Milk fat – 3.0 g All the values on it have a point in them. Proteins – 3.1 g Numbers such as 0.3, 0.7, 3.0, 3.1, 4.7, 58.2 and Carbohydrates – 4.7 g so on are called decimal numbers or simply Sugar – 10.0 g decimals. Minerals – 0.7 g Tenths: The figure below is divided into ten equal Energy – 58.2 kcal parts. 1 1 1 1 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 1 ten equal parts is . It is read as one-tenth. A decimal number has 10 1 two parts. Fractional form of each equal part is . 10 48 . 35 Decimal form of each equal part is 0.1. We read numbers like 0.1, 0.2, 0.3,….as ‘zero point Whole or Decimal one’, ‘zero point two’, ‘zero point three’ and so on. integral part part (< 1) Zero is written to indicate the place of the whole (= or > 1) number. Decimal point Note: The numbers in the decimal part are read as separate digits. 134 Merged File_PPS_Maths_G4_TB_Part 1.indb 134 2/1/2017 3:11:54 PM

Recall the place value chart of numbers. 100 × 10 10 × 10 1 × 10 1 Thousands Hundreds Tens Ones 2 5 6 3 2 5 6 2 5 2 We know that in this chart, as we move from right to left, the value of the digit increases 10 times. Also, as we move from left to right, the value of a digit becomes 1 times. The place value of the digit becomes one-tenth, read as a tenth. Its 10 2 7 value is 0.1 read as ‘zero point one’. is read as ‘two-tenths’, is read as 10 10 ‘seven – tenths’ and so on. We can extend the place value chart to the right as follows: 1 1 × 1000 1 × 100 1 × 10 1 . 10 Thousands Hundreds Tens Ones Decimal Tenths 7 . 2 2 4 . 3 1 4 3 . 6 3 0 1 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. [Note: ‘Deci’ means 10.] Decimals 135 Merged File_PPS_Maths_G4_TB_Part 1.indb 135 2/1/2017 3:11:55 PM

Hundredths: Study this place value chart. Decimal Thousands Hundreds Tens Ones Tenths Hundredths point 1 1 1 × 1000 1 × 100 1 × 10 1 . 10 100 2 8 6 2 . 3 9 When the number moves right from the tenths place, we get a new place, which is 1 1 10 of the tenths place. It is called the ‘hundredths’ place written as 100 and read as one-hundredths. Its value is 0.01, read as ‘zero point zero one’. 2 5 100 is read as two-hundredths, 100 is read as five-hundredths and so on. 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. Ten Decimal S. no Thousands Hundreds Tens Ones Tenths Hundredths thousands point a) 1 4 3 0 . 8 b) 3 5 9 . 6 5 c) 9 0 0 4 5 . 7 5 d) 6 5 4 . 0 8 Expansions: a) 1430.8 = 1 × 1000 + 4 × 100 + 3 × 10 + 0 × 1 + 8 × 1 10 1 1 b) 359.65 = 3 × 100 + 5 × 10 + 9 × 1 + 6 × + 5 × 10 100 136 Merged File_PPS_Maths_G4_TB_Part 1.indb 136 2/1/2017 3:11:56 PM

1 1 c) 90045.75 = 9 × 10000 + 0 × 1000 + 0 × 100 + 4 × 10 + 5 × 1 + 7 × 10 + 5 × 100 1 1 d) 654.08 = 6 × 100 + 5 × 10 + 4 × 1 + 0 × + 8 × 10 100 Example 2: Write these as decimals. 1 1 a) 7 × 1000 + 2 × 100 + 6 × 10 + 3 × 1 + 9 × + 3 × 10 100 1 1 b) 3 × 10000 + 0 × 1000 + 1 × 100 + 9 × 10 + 6 × 1 + 4 × 10 + 5 × 100 1 1 c) 2 × 1000 + 2 × 100 + 2 × 10 + 2 × 1 + 2 × 10 + 2 × 100 1 1 d) 5 × 100 + 0 × 10 + 0 × 1 + 0 × + 5 × 10 100 Solution: First fill the numbers in the place value chart as shown. Ten Decimal S. no Thousands Hundreds Tens Ones Tenths Hundredths thousands point a) 7 2 6 3 . 9 3 b) 3 0 1 9 6 . 4 5 c) 2 2 2 2 . 2 2 d) 5 0 0 . 0 5 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. 2 5 1 9 a) 18 b) 43 c) 26 d) 4 10 10 10 10 Solution: 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. 2 5 a) 18 = 18.2 b) 43 = 43.5 10 10 Decimals 137 Merged File_PPS_Maths_G4_TB_Part 1.indb 137 2/1/2017 3:11:59 PM

1 9 c) 26 = 26.1 d) 4 = 4.9 10 10 Example 4: Express these fractions as decimals. 25 2 43 92 a) b) 17 c) d) 5 100 100 100 100 25 Solution: a) = 25 hundredths = 0.25 100 2 b) 17 100 = 17 and 2 hundredths = 17.02 43 c) = 43 hundredths = 0.43 100 d) 5 92 = 5 and 92 hundredths = 5.92 100 Shortcut method: To write fractions with denominators 10 or 100 as decimals, follow these steps: 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. 232 For example, the decimal form of =2.32 100 Note: For 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. 138 Merged File_PPS_Maths_G4_TB_Part 1.indb 138 2/1/2017 3:12:02 PM

Example 5: Write these decimals as fractions. a) 2.3 b) 13.07 c) 105.43 d) 0.52 23 1307 Solution: a) 2.3 = 10 b) 13.07 = 100 10543 52 c) 105.43 = d) 0.52 = 100 100 Alternate method: Decimals having integral part can be written as mixed fractions. 3 So, 2.3 = 2 and 3 tenths = 2 10 7 13.07 = 13 and 7 hundredths = 13 100 43 105.43 = 105 and 43 hundredths = 105 100 Train My Brain Solve the following: a) Expand 35.098. b) Write 4.78 as a fraction. 37 c) Express 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. Decimals 139 Merged File_PPS_Maths_G4_TB_Part 1.indb 139 2/1/2017 3:12:05 PM

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 Rupees Four hundred and thirty-two and fifty paise ` 233.20 Rupees Two hundred and thirty-three and twenty paise ` 515.60 Rupees Five hundred and fifteen and sixty paise ` 670.80 Rupees Six hundred and seventy and eighty paise Example 7: The weights of some children in grams are given in the table below: Name Weight in grams Rahul 23456 Anil 34340 Anjali 28930 Soham 25670 Convert these weights into kilograms. Solution: 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 = 23.456 1000 Anil 34340 34340 = 34.340 1000 Anjali 28930 28930 = 28.930 1000 Soham 25670 25670 = 25.670 1000 140 Merged File_PPS_Maths_G4_TB_Part 1.indb 140 2/1/2017 3:12:05 PM

Example 8: Complete this table. S. No Fraction Read as Decimal Read as 7 a) 7 tenths 0.7 Zero point seven 10 47 b) 100 5 c) 3 10 d) 0.34 e) 12 and 65 hundredths Solution: S. No. Fraction Read as Decimal Read as 7 a) 7 tenths 0.7 Zero point seven 10 47 Zero point four b) 47 hundredths 0.47 100 seven c) 3 5 3 and 5 tenths 3.5 Three point five 10 34 Zero point three d) 34 hundredths 0.34 100 four e) 12 65 12 and 65 hundredths 12.65 Twelve point six five 100 Example 9: Ajay and Vijay represented the coloured part of the figure given as follows: 3 Vijay: 0.03 Ajay: 10 Whose representation is correct? Decimals 141 Merged File_PPS_Maths_G4_TB_Part 1.indb 141 2/1/2017 3:12:07 PM

3 Solution: The number of shaded parts as a fraction is or 3 tenths. As a decimal 10 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 tenths = 2 = 0.2 10 5 5 tenths = = 05 . 10 8 8 tenths = = 08. 10 10 10 tenths = =1 10 1 hundredths 9 hundredths 33 hundredths 1 9 33 = = 0.01 = = 0.09 = = 0.33 100 100 100 142 Merged File_PPS_Maths_G4_TB_Part 1.indb 142 2/1/2017 3:12:10 PM

57 hundredths 100 hundredths 57 100 = = 0.57 = =1 100 100 Example 10: Write the decimals that represent the shaded part. a) b) c) d) Decimals 143 Merged File_PPS_Maths_G4_TB_Part 1.indb 143 2/1/2017 3:12:12 PM

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. 10 43 143 43 c) + = =1 1.43 10 100 100 100 100 100 29 29 d) + + =2 2.29 100 100 100 100 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 ones by 1) d) 23.31, 23.41, 23.51, 23.61, 23.71, 23.81 (increases by 1 tenths) Maths Munchies Faster method to convert a fraction to decimal 2 3 1 6 1 Consider this example: Convert into its decimal form. 10 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 the step 1. 6 1 6 2 6 2 So, this will give us × = . 10 5 10 2 10 10 Step 3: Write in the decimal form. 6 1 So, 0.2 is the decimal form of . 10 5 144 Merged File_PPS_Maths_G4_TB_Part 1.indb 144 2/1/2017 3:12:13 PM