51704171_BGM_Traveller G4 Mathematics Textbook FY_Text

Time8Chapter I Will Learn About • conversion of days, hours and minutes. • expressing the time in a.m. and p.m. • the 24-hour clock with respect to the 12-hour clock. 8.1 Conversion of Units of Time I Think Surbhi was going to school. When she started from home, the time shown by the clock was . Surbhi was easily able to read it as 8 o’clock. When she reached the school, the time shown by the school clock was . Surbhi found it difficult to read the time from the clock. Can you tell what time it is? I Recall There are 24 hours in a day. In a clock, the shorter hand is the hour hand and it completes one turn in 12 hours. The longer hand is the minute hand and it completes one turn in one hour. 97

Let us recall how to write the time from the given clocks. d) a) b) c) I Remember and Understand Observe this clock. The long hand is called the minute hand. The short hand is called the hour hand. It has numbers from 1 to 12 on its face. Between any two consecutive numbers on the clock, there are four small divisions. They divide the space between the two numbers into five equal parts. Each division between two consecutive numbers indicates a minute. Thus, the sixty divisions together make 60 minutes or 1 hour. Example 1: Let us read the time shown by these clocks. One has been done for you. a) b) c) The hour hand has crossed The hour hand has crossed The hour hand has crossed 10. _________________________. _________________________. The minute hand is on the The minute hand is on the The minute hand is on the third division after 2. So, the _________________________. _________________________. minutes is (2 × 5 + 3) = 13 minutes. So, the minutes is So, the minutes is _________________________. _________________________. Therefore, the time shown is 10:13. The time is ________. The time is ________. 98

We have learnt to read and write time in the 12-hour clock. Now, let us learn to write time in the 24-hour clock. In the 12-hour clock time: • The hour hand of the clock goes around the clock face (dial) twice in 24 hours. • To identify morning or evening, we write a.m. or p.m. along with the time. In the 24-hour clock time: • The time is expressed as a 4-digit number (in the form hhmm). 12-hour clock time 24-hour clock time Read as in 24-hour clock 6:24 a.m. 06:24 Six twenty-four hours 11:47 a.m. 11:47 3:31 p.m. 15:31 Eleven forty-seven hours 8:35 p.m. 20:35 Fifteen thirty-one hours Twenty thirty-five hours • Here, the first two digits from the left tell us the hours. The next two digits tell us the minutes. • 12 o’clock midnight is written as 00:00. 12 o’clock noon is written as 12:00. • The time before noon is written in a 12-hour clock but without a.m. For example, 5:34 a.m. is written as 05:34. • The time post noon is written by adding 12 to the number of hours. • For example, 5:37 p.m. is written as To convert the time from 24-hour 17:37, 6:19 p.m. is written as 18:19 and clock to 12-hour clock, we subtract so on. 12 from the number of hours and write p.m. after the difference. • When the hours is 12 and the minutes are more than 00, the time is past noon. To convert time from 12-hour clock In such cases, we do not subtract 12 to 24-hour clock for the time after from hours. We write the time as 12:22. 12 noon, we add 12 to the number of hours and omit writing p.m. Do you know? • Railways/Airlines/Armed forces use the 24-hour clock to keep time. • The 24-hour clock is used in digital watches. Example 2: Convert the given 24-hour clock time to 12-hour clock time. a) 14:23 b) 05:51 c) 09:17 d) 22:04 e) 18:00 f) 19:36 g) 23:55 h) 00:33 i) 00:45 j) 03:12 Time 99

Solution: a) (14 – 12):23 = 2:23 p.m. b) 5:51 a.m. c) 9:17 a.m. d) (22 – 12):04 = 10:04 p.m. e) (18 – 12):00 = 6 p.m. f) (19 – 12):36 = 7:36 p.m. g) (23 – 12):55 = 11:55 p.m. h) (00 + 12):33 = 12:33 a.m. i) (00 + 12):45 = 12:45 a.m. j) 3:12 a.m. Example 3: Draw the hands of a clock to show the given time. a) 13:17 b) 6:53 c) 19:12 d) 22:35 Solution: To draw the hands of a clock, first note the minutes. If the minutes are between 1 and 30, draw the hour hand between the given hour and the next. But care should be taken to draw it closer to the given hour. If the minutes are between 30 and 60, draw the hour hand closer to the next hour. Then, draw the minute hand on the number that shows the given minutes. a) b) c) d) We have learnt how to read and show time, exact to minutes and hours. Let us now learn to convert days, hours and minutes. Example 4: Convert: a) 2 days into hours b) 11 hours into minutes c) 360 minutes into hours d) 96 hours into days Solution: Solved Solve these a) To convert days into hours, multiply by 24. 5 days = _______________ hours 2 days = ____________ hours 1 day = 24 hours Therefore, 2 days = 2 × 24 hours = 48 hours 100

Solved Solve these 9 hours = ___________ minutes b) T o convert hours into minutes, multiply by 60. 11 hours = ___________ minutes 1 hour = 60 minutes Therefore, 11 hours = 11 × 60 minutes = 660 minutes c) T o convert minutes into hours, divide by 180 minutes = ___________ hours 60. 360 minutes = ___________ hours 60 minutes = 1 hour Therefore, 360 minutes = 360 ÷ 60 hours = 6 hours d) To convert hours into days, divide by 24. 120 hours = ___________ days 96 hours = ___________ days 24 hours = 1 day Therefore, 96 hours = 96 ÷ 24 days = 4 days (96 = 4 × 24) ? Train My Brain Draw the hands of a clock to show the time given: a) 6:12 b) 11:43 c) 3:32 I Apply Let us now understand the addition and subtraction of time. While adding time, we add the minutes (smaller units) first and then the hours (larger units). Let us see an example. Example 5: Add: 2 hours 15 minutes and 3 hours 35 minutes Time 101

Solution: Steps Solved Solve these Step 1: Write both the numbers one below the other. Hours Minutes Hours Minutes Step 2: Add the minutes first and 2 15 1 20 then the hours. +3 35 +3 10 Hours Minutes 2 15 +3 35 Hours Minutes 5 50 2 25 The sum is 5 hours 50 +2 20 minutes. While subtracting, we subtract the minutes first (smaller units) and then the hours (larger units). Example 6: Subtract: 1 hour 35 minutes from 3 hours 40 minutes Solution: Steps Solved Solve these Step 1: Write both the numbers Hours Minutes Hours Minutes one below the other, such that the smaller number is 3 40 4 30 subtracted from the larger. –1 35 –1 20 Step 2: Subtract the minutes Hours Minutes first and then the hours. 3 40 Hours Minutes –1 35 3 55 2 05 –2 40 The difference is 2 hours 5 minutes. The time between two given times is called the length of time or time duration or time interval. It is given by the difference between the end time and start time. Example 7: Find the duration of time from the given start time and end time. a) Start Time = 14:00; End Time = 17:45 b) Start Time = 6:30 p.m.; End Time = 9:45 p.m. Solution: a) Start Time = 14:00; End Time = 17:45 102

Time from 14:00 to 17:00 = (17 – 14) hours = 3 hours Time from 17:00 to 17:45 = 17:45 – 17:00 = 45 minutes Total time duration = 3 hours + 45 minutes = 3 hours 45 minutes. b) Start Time = 6:30 p.m.; End Time = 9:45 p.m. Time from 6:30 p.m. to 7:00 p.m. = 7:00 – 6: 30 = 30 minutes Time from 7:00 p.m. to 9:00 p.m. = 9:00 – 7:00 = 2 hours Time from 9:00 p.m. to 9:45 p.m. = 9:45 – 9:00 = 45 minutes Total time = 30 minutes + 2 hours + 45 minutes = 2 hours 75 minutes. = 3 hours 15 minutes I Explore (H.O.T.S.) Let us see a few real-life examples involving duration of time. Example 8: The clocks given show the start time and end time of a Maths class respectively. How long was the Maths class? Solution: The start time is 9:00 and the end time is 9:45. So, the time between is the length of the Maths class = 9:45 – 9:00 = 45 minutes Therefore, the length of the Maths class was 45 minutes. Example 9: Anil took a flight from Delhi at 10:10 p.m. and reached Hyderabad in 2 hours 5 minutes. At what time did the flight reach Hyderabad? Solution: Start time of the flight = 10:10 p.m. Duration of travel = 2 hours 5 minutes End time = Start time + Duration of travel = 10:10 p.m. + 2 hours 5 minutes = 12:15 a.m. (After 12 midnight, the time is taken as a.m.) Time 103

Example 10: A movie began at 5:35 p.m. Lucky switched on the TV at 18:23. For how much time did Lucky miss the movie? Solution: Start time of the movie = 5:35 p.m. Time when Lucky switched on the TV = 18:23 = (18 – 12):23 = 6:23 p.m. Time from 5:35 p.m. to 6 p.m. = 25 minutes Time from 6 p.m. to 6:23 p.m. = 23 minutes Total time = 25 minutes + 23 minutes = 48 minutes. Therefore, Lucky missed 48 minutes of the movie. Maths Munchies One hour is divided into sixty minutes and one minute is divide into sixty seconds. The number 60 was probably chosen for its mathematical convenience. It is exactly divisible by many smaller numbers: 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30. Connect the Dots Social Studies Fun The Earth’s rotation about its axis takes 24 hours. Science Fun A sundial is a tool that uses the position of the Sun to measure time, typically involving a shadow cast across a marked surface. 104

Drill Time 8.1 Conversion of Units of Time 1) Read the time on the clocks and write them in 12-hour and 24-hour formats. a) b) c) Evening Afternoon Morning d) e) f) Afternoon Evening Night 2) Convert: a) 240 minutes into hours b) 360 hours into days c) 5 hours into minutes d) 10 days into hours 3) Add: a) 3 hours 40 minutes and 1 hour 13 minutes b) 1 hour 26 minutes and 2 hours 22 minutes c) 2 hours 30 minutes and 2 hours 28 minutes Time 105

4) Subtract: a) 1 hour 20 minutes from 3 hours 55 minutes b) 3 hours 30 minutes from 4 hours 40 minutes c) 2 hours 40 minutes from 6 hours 49 minutes 5) Find the duration of time from the given start time and end time. a) Start Time = 12:00 and End Time = 14:15 b) Start Time = 3:00 p.m. and End Time = 5:00 p.m. c) Start Time = 3:15 p.m. and End Time = 7:20 p.m. d) Start Time = 7:20 a.m. and End Time = 10:41 a.m. e) Start Time = 15:56 and End Time = 17:57 A Note to Parent Encourage your child to make a note of the time when you go out with him or her. Also ask him or her to make a note of the time when you return. Ask your child to calculate the duration for which you went out based on the time he or she noted. 106

CHAPTER Fractions9 9Chapter Fractions 1 4 I Will Learn About • fractions as a part of a whole and its representation. • fractions of a collection. • like, unlike, unit and equivalent fractions. • addition and subtraction of like fractions. 9.1 Introduction to Fractions I Think Surbhi and her three friends, Joseph, Salma and Rehan, went on a picnic. Rehan brought only one apple with him. He wanted to share it equally with everyone. What part of the apple does each of them get? I Recall Look at the rectangle given in the next page. We can divide the whole rectangle into many equal parts as shown. 107

1 part: 2 equal parts: 3 equal parts: 4 equal parts: 5 equal parts: and so on. I Remember and Understand Let us understand the concept of parts of a whole. Suppose we want to share an apple with our friends. First, we count their number. Then, we cut the apple into as many equal pieces as the number of persons. Thus, each person gets an equal part of the apple after division. Fraction as a part of a whole A complete or full object is called a whole. Observe the following parts of a chocolate bar: Whole 2 equal parts 3 equal parts 4 equal parts 108

We can divide a whole into equal parts as shown. Each such division has a different name. To understand this better, let us do an activity. Activity: Halves Take a square piece of paper. Fold it into two equal parts as shown. Each equal part is called a ‘half’. ‘Half’ means 1 out of 2 equal parts. Putting these 2 equal parts together makes the complete piece of paper. We write ‘1 out of 2 equal parts’ as 1 . 2 In 1 , 1 is the number of parts taken and 2 is the total number of equal parts the whole 2 is divided into. Note: 1 and 1 make a whole. 2 2 Thirds In figure (a), observe that the three parts are not equal. We can also divide a whole into three equal parts as shown in figures (b) and (c). 11 1 33 3 Three unequal parts Three equal parts Fig. (a) Fig. (b) Fig (c) The shaded grey part in figure (c) is one out of three equal parts. So, each equal part is called a third or one-third. Two out of three equal parts of figure (c) are not shaded. We call it two-thirds (short form of 2 one-thirds). We write one-third as 1 and two-thirds as 2 . 3 3 Note: 1 , 1 and 1 or 1 and 2 make a whole. 3 3 3 3 3 Fractions 109

Fourths Similarly, fold a square piece of paper into four equal parts. Each of them is called a fourth or a quarter. In figure (d), the four parts are not equal. In figure (e), each equal part is called a fourth or a quarter and is written as 1 . 4 1 4 1 4 1 4 1 4 Four parts Four equal parts Fig (d) Fig (e) Two out of four equal parts are called two-fourths and three out of four equal parts are called three-fourths, written as 2 and 3 respectively. 4 4 Note: Each of 1 and 3 ; 1 1 1 and 1 or 1 1 and 2 make a whole. 4 4 4, 4, 4 4 4, 4 4 The total number of equal parts a whole is divided into is called the denominator. The number of such equal parts taken is called the numerator. A fraction is a part of a whole. Numbers of the form Numerator are For example, 1 , 1 , 1 , 2 and so on are fractions. 2 3 4 3 Denominator Let us now see a few examples. called fractions. Example 1: Identify the numerator and denominator in each of the following fractions: a) 1 b) 1 c) 1 2 3 4 110

Solution: S. No Fractions Numerator Denominator a) 1 1 2 2 1 1 3 b) 3 1 1 4 c) 4 Example 2: Identify the fraction for the shaded parts in the figures given. a) b) Solution: Steps Solved Solve this Total number of equal parts Step 1: Count the number of Total number of = _______ equal parts the figure is divided equal parts = 8 into (Denominator). Number of parts shaded = Step 2: Count the number of Number of parts ______ shaded parts (Numerator). shaded = 5 Step 3: Write the fractions. Fraction = Fraction = 5 Numerator 8 Denominator Fraction of a collection Finding a half We can find different fractions of a collection. Suppose there are 10 pens in a box. To find a half of them, we divide them into two equal parts. Each equal part is a half. Fractions 111

Each equal part has 5 pens, as 10 ÷ 2 = 5. So, 1 of 10 pens is 5 pens. 2 Finding a third One-third is 1 out of 3 equal parts.In the given figure, there are12 bananas. To find a third, we divide them into three equal parts. Each equal part is a third. Each equal part has 4 bananas, as 12 ÷ 3 = 4. So, 1 of 12 bananas is 4 bananas. 3 1 3 1 3 1 3 Finding a fourth (or a quarter) One-fourth is 1 out of 4 equal parts. In this figure, there are 8 books. To find a fourth, we divide the number of books into 4 equal parts. 112

1 1 1 1 4 44 4 Each equal part has 2 books, as 8 ÷ 4 = 2. So, 1 of 8 books is 2 books. 4 Let us see a few examples to find the fraction of a collection. Example 3: Write the fraction of the coloured shapes in each of the following. Shapes Fractions a) b) c) Solution: The fractions of the coloured parts of the given shapes are – a) b) Shapes Fractions c) 2 6 3 6 5 8 Example 4: Colour the given shapes to represent the given fractions. Shapes Fractions a) 1 5 b) 2 7 c) 3 4 Fractions 113

Solution: We can colour the shapes to represent the fractions as – Shapes Fractions a) 1 5 b) 2 7 c) 3 4 ? Train My Brain What fraction of the collection are: a) Chocolate cupcakes b) Strawberry cupcakes c) Blueberry cupcakes I Apply We have learnt to identify the fraction of a whole using the shaded parts. We can learn to shade a figure to represent a given fraction. Let us see some examples. Example 5: Shade a square to represent these fractions: 12 3 1 a) 4 b) 3 c) 5 d) 2 Solution: Follow these steps for shading a required shape to represent the given fractions. 114

Steps Solved Solve these 1 2 Step 1: Identify the 1 23 denominator and 4 35 Denominator the numerator. = Denominator Denominator Denominator Step 2: Draw the =4 == Numerator required shape. = Numerator = 1 Numerator Numerator == Divide it into as many equal parts as the denominator. Step 3: Shade the number of equal parts as the numerator. This shaded part represents the given fraction. Let us now learn to use fractions in real-life situations. Example 6: A set of 48 pens have 13 blue, 15 red and 11 black ink pens. The remaining are green ink pens. What fraction of the pens is green? Solution: Total number of pens = 48 Total number of blue, red and black ink pens = 13 + 15 + 11 = 39 Number of green ink pens = 48 – 39 = 9 Fraction of green ink pens = Number of green ink pens = 9 Total number of pens 48 Example 7: There is a bunch of balloons with three different colours. Write the fraction of balloons of each colour. Solution: Total number of balloons = 15 Number of green balloons = 2 2 Therefore, fraction of green balloons = 15 Number of yellow balloons = 3 Fractions 115

3 Therefore, fraction of yellow balloons = 15 Number of red balloons = 10 10 Therefore, fraction of red balloons = 15 I Explore (H.O.T.S.) Let us see some examples of real-life situations involving fractions. Example 8: Answer the following questions: a) How many one-sixths are there in a whole? Represent it in a circle. b) H ow many one-fifths are there in a whole? Represent it in a pentagon (a shape with five sides). c) How many halves make a whole? Represent it in a rectangle. Solution: a) There are 6 one-sixths in a whole. b) There are 5 one-fifths in a whole. c) 2 halves make a whole. 11 66 11 55 1 1 11 11 6 6 55 22 1 1 1 Train My Brain 6 6 5 In some real-life situations, we need to find a fraction of some goods such as fruits, vegetables, milk, oil and so on. Let us now see some such examples. Example 9: One kilogram of apples costs ` 16 and one kilogram of papaya costs ` 20. If Rita buys 1 kg of apples and 1 kg of papaya, how much did she spend? 2 4 Solution: Cost of 1 kg apples = ` 16 Cost of 1 kg apples = 1 of ` 16 = ` 16 ÷ 2 =` 8 2 2 116

(To find a half, we divide by 2.) Cost of 1 kg papaya = ` 20 Cost of 1 kg papaya = 1 of ` 20 = ` 20 ÷ 4= `5 4 4 (To find a fourth, we divide by 4.) Therefore, the money spent by Rita = ` 8 + ` 5 = ` 13 Example 10: Sujay completed 2 of his Maths homework. If he had to solve 25 5 Solution: problems, how many did he complete? Fraction of homework completed by Sujay = 2 5 Total number of problems to be solved = 25 Number of problems Sujay solved = 2 of 25 = (25 ÷ 5) × 2 =5× 2 = 10 5 Therefore, Sujay has solved 10 problems. 9.2 Like, Unlike and Equivalent Fractions I Think Surbhi cuts 3 cakes into 18 equal pieces. Zeenal cuts a cake into 6 equal pieces. Did both of them cut the cakes into equal number of pieces? I Recall Let us recall the concept of fractions by finding the fraction of the parts not shaded in these figures. a) = ____________ b) = ____________ c) = ___________ d) = ____________ Fractions 117

I Remember and Understand In the previous concept, we have learnt about fractions. Now let us learn the different types of fractions. Like fractions: Fractions such as 1 , 2 and 3 , that have the same denominator are 88 8 called like fractions. Unlike fractions: Fractions such as 1 , 2 and 3 that have different denominators are 84 7 called unlike fractions. To understand like and unlike fractions, consider the following example. Example 11: Identify the like and unlike fractions from the following. 3 , 3 , 1 5 6 1 4 Fractions with numerator Solution: 7 5 7, 7, 7, 4, 11 ‘1’ are called unit 3 1 5 6 fractions. For example, 7 7 7 7 , , and have the same denominator. 1 , 1 , 1 and so on. 234 Therefore, they are like fractions. 3 , 1 and 4 3 or 1 or 5 or 6 5 4 11 along with 7 7 7 7 have different denominators. Therefore, they are unlike fractions. Add and subtract like fractions While adding or subtracting like fractions, add or subtract only their numerators. Write the sum or difference with the same denominator. Let us understand this through some examples. 31 45 84 33 25 Example 12: Solve: a) 8 + 8 b) 13 + 13 c) 9 – 9 d) 37 – 37 Solution: a) 3 + 1 = 3+ 1 = 4 8 8 8 8 b) 4 + 5 = 4+5 = 9 13 13 13 13 84 4 c) 9 – 9 = 9 d) 33 – 25 = 33 − 25 = 8 37 37 37 37 118

Equivalent fractions Fractions that denote the same part of a whole are called equivalent fractions. Let us now understand what equivalent fractions are. Suppose a bar of chocolate is cut as shown. 1 Ram eats 5 of the chocolate. Then the piece of chocolate that he eats is: Raj eats 2 of the chocolate. 10 Then the piece of chocolate that he eats is: We see that both the pieces of chocolate are of the same size. So, we say that the fractions 1 and 2 are equivalent. We write them as 1 = 2 . 5 10 5 10 Example 13: Shade the regions to show equivalent fractions. a) 12 [ 3 and 6 ] b) 12 [ 4 and 8 ] Solution: a) 1 2 3 6 Fractions 119

12 b) 4 8 Example 14: Find the figures that represent equivalent fractions. Also, mention the fractions. a) b) c) d) Solution: The fraction represented by the shaded part of figure a) is 1 . 2 2 The shaded part of figure b) represents 4 . The shaded part of figure d) represents 1 . 2 So, the shaded parts of figures a), b) and d) represent equivalent fractions. Methods to find equivalent fractions There are two methods to find equivalent fractions. Let us learn them through a few examples. Example 15: Find two fractions equivalent to the given fractions. 2 12 a) 11 b) 16 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 W e see that 2 and 11 do not have any common factors. So, we cannot divide them to get an equivalent fraction of 121. T herefore, we multiply both the numerator and the denominator by the same number, say 5. 2 2×5 = 10 11= 11× 5 55 Therefore, 10 is a fraction equivalent to 121. 55 120

S imilarly, we multiply both the numerator and the denominator by the same number, say 2. 2×2 = 4 11×2 22 Therefore, 4 is a fraction equivalent to 121. 22 b) 12 16 W e see that 12 and 16 have common factors 2 and 4. So, dividing both the numerator and the denominator by 2 and 4, we get fractions equivalent to the given fraction 12 . 16 12 ÷ 2 = 6; 12 ÷ 4 = 3 16 ÷ 2 8 16 ÷ 4 4 Therefore, 6 and 3 are the fractions equivalent to 12 . 8 4 16 ? Train My Brain Identify the like fractions from each of the following. a) 1 , 3 , 2 , 4 b) 151,161, 72 ,181, 6 ,171, 71 c) 1, 5 , 2 , 3 , 18 , 3, 3, 6 4 6 6 6 7 3 25 25 5 25 4 7 25 I Apply Let us see some word problems involving like, unlike and equivalent fractions. Example 16: 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. Fractions 121

Example 17: Colour each figure to represent the given fraction and compare them. 3 2 5 5 Solution: Clearly, the part of the figure represented by 3 is greater than that 5 represented by 2 3 is greater than 2 . 5 . Therefore, 5 5 162 5 4 Example 18: Arrange 7 , 7 , 7 , 7 and 7 in the ascending and descending orders. Solution: Comparing the numerators of the given like fractions, we have 1 < 2 < 4 < 5 < 6. 12 4 56 So, 7 < 7 < 7 < 7 < 7. Therefore, the required ascending order is 1 2 , 4, 5 6 7, 7 7 7, 7. We know that, the descending order is just the reverse of the ascending order. 65421 Therefore, the required descending order is 7 , 7 , 7 , 7 , 7 . Example 19: 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 2 Part of the ribbon coloured blue = 9 3 Part of the ribbon coloured yellow = 9 Total part of the ribbon coloured = 2 + 3 = 2+3 = 5 9 9 9 9 Part of the ribbon that is not coloured is 9 − 5 = 9−5 = 4 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.) 122

I Explore (H.O.T.S.) Consider the following examples. Example 20: Draw four similar rectangles. Divide them into 2, 4, 6 and 8 equal parts. 123 5 Then colour 2 , 4 , 6 and 8 parts of the rectangles respectively. Compare these coloured parts and write the fractions using >, = or <. Solution: 1 2 2 4 3 6 5 8 From the coloured parts of these rectangles, we can see that all of them except 5 are of the same size. So, the fractions, 1 , 2 and 3 are 8 2 4 6 equivalent. Therefore, 1 = 2 = 3 . 2 4 6 51 Example 21: Veena ate 8 of a pizza in the morning and 8 in the evening. What part of the pizza is remaining? Fractions 123

Solution: 5 Part of the pizza eaten by Veena in the morning = 8 1 Part of the pizza eaten by Veena in the evening = 8 T o 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 Part of the pizza remaining = 1 – 6 = 8 – 6 = 2 8 8 8 8 Therefore, 2 part of the pizza is remaining. 8 Maths Munchies Egyptians have a different way to represent fractions. To represent 1 as numerator, they use a mouth picture which literally means ‘part’. So, the fraction one-fifth will be shown as given in the image. On the other hand, fractions were only written in words in Ancient Rome. 1 was called unica 6 was called semis 12 12 1 1 was called scripulum 24 was called semunica 144 Connect the Dots Science Fun Around 7 out of 10 parts of air is nitrogen. Oxygen is at the second position. 2 out of 10 parts of air is oxygen. 124

English Fun Think of at least two words that rhyme with each ‘numerator’ and ‘denominator’. Drill Time 9.1 Introduction to Fractions 1) Find the numerator and the denominator in each of these fractions. 2 b) 1 24 5 a) 5 7 c) 3 d) 9 e) 7 2) Identify the fractions of the shaded parts in these figures. a) b) c) d) e) 3) Find the fraction of the coloured parts in each of these figures. a) b) c) d) e) 4) Find 1 and 1 of the following collection. 2 4 Fractions 125

9.2 Like, Unlike and Equivalent Fractions 5) Write four equivalent fractions for each of the following. a) 1 b) 4 c) 3 d) 4 2 7 10 11 6) Shade the regions to represent equivalent fractions. a)  1 and 2   5 10  b)  1 and 2   2 4  7) Word problems 1 6 a) Zoya has 24 notebooks. 1 of them are unruled and of them are four-ruled. 2 How many books are (a) unruled and (b) four-ruled? b) A circular disc is divided into 12 equal parts. Venu shaded 1 of the disc pink 4 1 and 3 of the disc green. How many parts of the disc are shaded? How many parts are not shaded? 8) 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 83286 889 9 5 9 9 7 4 4 9 c) 6 ,154 ,5 ,147 ,187 ,174 ,197 ,124 d) 3 , 4 , 1 , 3 , 1 ,141 14 17 5 5 5 7 9 9) Arrange the following fractions in ascending order. a) 131, 111, 7, 141 b) 3 ,123 ,9 ,153 c) 1 , 3 , 4 , 2 d) 1 ,184 ,174 ,194 11 13 13 7 7 7 7 14 126

10) Arrange the following fractions in descending order. a) 1 , 8 , 7 , 4 b) 3 ,167 ,10 ,187 c) 271, 291, 221,1231 d) 1 , 7 , 8 , 3 9 9 9 9 17 17 20 20 20 20 11) Add: a) 2 + 5 b) 3+ 16 c) 9+ 4 d) 8 +4 e) 1 +2 7 7 11 11 5 5 17 17 13 13 12) 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 13) Word problems a) Colour each figure to represent the given fraction and compare them. 57 88 b) Akansha ate 1 of a cake in the morning and 2 of it in the evening. What 5 5 part of the cake is remaining? A Note to Parent Fractions are present all around us. The easiest way to make a child relate to fractions is through food items. Cut fruits such as apples and oranges in different equal parts and use them to help your child understand fractions. Fractions 127

CHAPTER 11 Money10Chapter I Will Learn About • conversion between Rupees and Paise. 10.1 Conversion between Rupees and Paise I Think Surbhi had some play money in the form of notes and coins. While playing, her friend gave her ` 10. Surbhi has to give paise for the amount her friend gave her. How many paise should Surbhi give her friend? I Recall Let us recall what we have learnt about money in the previous class. Observe the rates (per kg) of vegetables in the box given. Ramesh buys a few of them in different quantities. Write the rates and the amount to complete the bill for the vegetables he bought. 128

Pumpkin Potato Cabbage ` 99 ` 15 ` 100 Green peas ` 120 Onion Chillies Carrot ` 30 ` 68 ` 60 Tomato Brinjal Broccoli Amount ` 24.50 ` 60 ` 100 `p S.No Vegetables Bill Rate per item 1 Pumpkin Quantity 2 Tomato (in kg) 3 Carrot 4 Broccoli 1 5 Brinjal 1 2 2 2 Total I Remember and Understand We already know that ` 1 = 100 paise. To convert rupees into paise, we multiply the rupees by 100. For example, ` 3 = 3 × 100 paise = 300 paise. To convert an amount in ‘rupees’ and ‘paise’ into ‘paise’, we multiply the rupees by 100 and add the product to the number of paise. Let us see a few examples involving the conversion between rupees and paise. Example 1: Convert ` 132.28 into paise. Money can be added or Solution: ` 132.28 = ` 132 + 28 p subtracted easily using the = ` 132 × 100 p + 28 p column method. The rupees = 13200 p + 28 p and paise should be written = 13228 p with the dot (.) exactly one below the other. Money 129

Note: An easy method to convert rupees into paise is to remove the rupee symbol of rupees and the dot (.) and write the rupees and paise together. So, ` 132.28 = 13228 p. An amount of more than 100 paise, can be expressed in rupee and paise. The last two digits in the number is paise and the rest of the digits represent rupees. Example 2: Convert 24365 paise into rupees and paise. TTh Th H T O Solution: 24365 p = 24365 ÷ 100 = ` 243 + 65 p = ` 243.65 2 4 365 Note: An easy method 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 `. So, 24365 p = ` 243.65. We add or subtract money just as we add or subtract numbers. Let us see a few examples where we add or subtract money with conversion. Example 3: Add 54738 paise and ` 130.83. ` p 1 Solution: To add 54738 paise and ` 130.83, we convert 1 38 83 paise into rupees. 5 4 7. 21 54738 paise = ` 547.38 + 1 3 0. ` 6 7 8. By adding using the column method, we get ` 678.21 as the sum. Example 4: Subtract ` 247.65 from 53354 paise. `p Solution: To subtract ` 247.65 from 53354 paise, 12 12 14 we convert paise into rupees. 422 4 14 53354 paise = ` 533.54 5 3 3.5 4 By subtracting using the column method, − 2 4 7.6 5 we get ` 285.89 as the difference. ` 2 8 5.8 9 ? Train My Brain Solve the following: a) Convert 67923 paise into rupees. b) Convert ` 890.03 into paise. c) Add 22341 paise and ` 367.91 130

I Apply Now let us solve some real-life examples involving money. Example 5: Sheeba spent ` 50 to buy 5 bars of chocolate. What is the cost of each bar of chocolate? Solution: Amount Sheeba spent on buying chocolates = ` 50 Number of chocolate bars Sheeba bought = 5 To find the cost of one chocolate bar, we divide ` 50 by 5. We know that the quotient when 50 is divided by 5 is 10. Therefore, each chocolate bar costs ` 10. Example 6: Ramu wants to buy 7 kg of apples costing ` 99.50 per kg. If he has ` 650, does he have enough amount? ` p Cost of 1 kg apples = ` 99.50 63 Solution: Quantity of apples Ramu wanted to buy = 7 kg 9 9 . 5 0 Total cost needed to buy 7 kg of apples = × 7 ` 99.50 × 7 kg ` 696.50 The total cost of 7 kg of apples is ` 696.50. But, Ramu has only ` 650 with him. As, ` 696.50 > ` 650, Ramu does not have enough money with him to buy 7 kg of apples. I Explore (H.O.T.S.) Let us see some more real-life examples involving addition and subtraction of money. Example 7: Tanya had ` 525 and her sister Tanvi had ` 330. They bought a gift costing ` 495.75 for their brother on his birthday. How much amount is left with them? Solution: Amount Tanya had = ` 525 Amount Tanvi had = ` 330 Total amount they had = ` 525 + ` 330 = ` 855 Total amount = `p The amount spent for gift = Amount left with them = 855 . 00 – 495 . 75 359 . 25 Therefore, Tanya and Tanvi have ` 359.25 left with them. Money 131

Example 8: The costs 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? Does he get any change back? If yes, how much change does he get? Solution: 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. As, ` 450 < ` 500, Suresh gets change from the shopkeeper. The change he gets = ` 500 − ` 450 = ` 50 Maths Munchies To convert rupees to paise, add two zeros at the end of the number and remove the decimal point. 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. Social Studies Fun The earliest metal coins were used in China. Try to find out different coins with their values and their shapes. 132

Drill Time 10.1 Conversion between Rupees and Paise 1) Convert the following to paise. a) ` 632.18 b) ` 952.74 c) ` 231.48 d) ` 537.58 e) ` 724.80 2) Convert paise to rupees. a) 52865 b) 64287 c) 13495 d) 34567 e) 78654 3) Add: b) ` 3467.45 + ` 2356.50 a) ` 875.62 + 96498 p d) ` 456.23 + 27950 p c) 25382 p + ` 652.37 e) ` 123.75 + 642.90 p 4) Subtract: b) 85732 p – ` 237.84 a) ` 132.75 – 11290 p d) ` 456.72 – 23434 p c) ` 578.14 – ` 345.89 e) ` 784.50 – ` 234.25 5) Word problems a) 5 packets of chips cost ` 20. How much will one such packet cost? b) A football costs ` 159.99. What is the cost of 26 such footballs? A Note to Parent Show your child currency notes of different denominations such as ` 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 133

CHAPTER Measurement11 60 Chapter 5575 5011 Measurement70 65Cm 45 40 35 30 25 20 15 10 I Will Learn About 5 0 20 • conversion of units of length, weight and volume. • estimation and verification of length, weight and volume. • area and perimeter of simple shapes. 11.1 Conversion of Units of Length I Think Surbhi went with her mother to a shop to buy cloth for her frock. Her mother asked the shopkeeper to give two metres of the cloth. How do you think the shopkeeper should measure two metres of the cloth? I Recall We know that people sometimes measure lengths of objects using their hands or feet. But the size of the body parts differ from one person to another. So, the length of the same object also differs when measured by different people. Suppose a boy and a man measure the same object. We see that the measures of the object are different. So, measures such as hand span, cubit, leg span and so on are called non-standard units. 134

To express measurements correctly, standard units were developed. The measurement of objects remains the same anywhere in the world, when these standard units are used. Measures of Length: Centimetre: It is a unit of length used to measure the lengths of a pencil, the sides of a book and so on. We write centimetres in short as cm. Metre: It is the standard unit of length. It is used to measure the lengths of a piece of cloth, a wall and so on. We write metres in short as m. Kilometre: It is a unit of length larger than a metre. It is used to measure the distance between two places, length of a river and so on. We write it as km. 5 cm 3m 2 km I Remember and Understand We can convert one unit of measurement into another using the relation between them, i.e., 1 m = 100 cm To convert measures from a larger unit to a smaller unit, we 1 km = 1000 m multiply. Let us understand the conversion through a few To convert measures from a examples. smaller unit to a larger unit, we divide. Example 1: Convert: a) 5 m 7 cm into cm b) 6 km 4 m into m c) 815 cm into m and cm d) 4805 m into km and m Measurement 135

Solution: Solve these Solved 2 m 9 cm = _______________ cm a) To convert metres into centimetres, multiply by 100. 3 km 4 m = 5 m 7 cm = ____________ cm _______________ m 1 m = 100 cm 270 cm = ________ m ________ cm So, 5 m = 5 × 100 cm 6045 m = = 500 cm ________ km________ m 5 m 7 cm = (500 + 7) cm = 507 cm Therefore, 5 m 7 cm is 507 cm. b) To convert kilometres into metres, multiply by 1000. 6 km 4 m = ___________ m 1 km = 1000 m So, 6 km = 6 × 1000 m = 6000 m 6 km 4 m = (6000 + 4) m = 6004 m Therefore, 6 km 4 m = 6004 m. c) To convert centimetres into metres, divide by 100. 815 cm = _________ m ________ cm 815 cm = (800 + 15) cm 100 cm = 1 m So, 800 cm = 800 ÷ 100 m =8m Therefore, 815 cm = 8 m 15 cm. d) To convert metres into kilometres, divide by 1000. 4805 m = _________ km ________ m 4805 cm = (4000 + 805) km, 1000 m = 1 km So, 4000 m = 4000 ÷ 1000 km = 4 km Therefore, 4805 cm = 4 km 805 m We can add or subtract lengths just as we add or subtract numbers. Remember to write the units after the sum or difference. Note: Suppose the length of an object is expressed in km and m and there are only 2 digits in the metre. Place a 0 at the hundreds place and make it a 3-digit number. We do this because 1000 m = 1 km. 136

Addition of lengths Example 2: Add: a) 25 m 16 cm and 32 m 30 cm b) 34 km 450 m and 125 km 235 m Solution: Follow these steps to add the given lengths: Steps Solved Solved Solve these Step 1: Write the m cm km m m cm numbers in columns 25 16 34 450 19 27 as shown. + 32 30 + 125 235 + 40 20 Step 2: Add the m cm km m km m 34 450 12 150 numbers under the 25 16 + 125 235 + 14 340 685 smaller unit and write + 32 30 the sum. 46 Step 3: Add the m cm km m km m numbers under the 25 16 34 450 10 100 larger unit and write + 32 30 + 125 235 + 100 100 the sum. 57 46 159 685 Subtraction of lengths Example 3: Subtract: a) 125 m 20 cm from 232 m 30 cm b) 234 km 15 m from 425 km 355 m Solution: Follow these steps to subtract the given lengths: Steps Solved Solved Solve these Step 1: Write the m cm km m km m numbers in columns 232 30 425 355 14 350 as shown. − 125 20 − 234 015 − 12 150 Step 2: Subtract the m cm km m m cm numbers under the 232 30 425 355 26 42 smaller unit and write − 125 20 − 234 015 − 13 21 the difference. 10 340 Measurement 137

Steps Solved Solved Solve these Step 3: Subtract the m cm km m m cm numbers under the 2 12 3 12 larger unit and write 23 2 30 425 355 59 26 the difference. − 12 5 20 − 234 015 − 39 14 10 7 10 191 340 \\ \\ \\ \\ ? Train My Brain b) Convert 8 km into m. d) 42 m 30 cm – 30 m 20 cm Solve the following: a) Convert 5 m 7 cm into cm. c) 10 km 20 m + 20 km 10 m I Apply Let us solve some real-life examples where we use the addition and subtraction of lengths. Example 4: Reema rode her bicycle for 9 km 6 m. Prajakta rode her bicycle for 8 km 24 m. Calculate the distance travelled by them in metres. Solution: The distance travelled by Reema on her bicycle = 9 km 6 m The distance travelled by Prajakta on her bicycle = 8 km 24 m Distance travelled altogether = 9 km 6 m + 8 km 24 m km m 9 006 = 17 km 30 m + 8 024 17 030 We know that 1 km = 1000 m So, 17 km = 17 × 1000 m = 17000 m 17 km 30 m = (17000 + 30) m = 17030 m Therefore, Reema and Prajakta rode a distance of 17030 metres altogether. Example 5: Sunny bought a rope of length 20 m 12 cm. Bunny bought another rope of length 12 m 20 cm. What is the total length of the rope that they bought? 138

Solution: The length of the rope bought by Sunny = 20 m 12 cm m cm 20 12 The length of the rope bought by Bunny = 12 m 20 cm 12 20 The total length of the ropes = 20 m 12 cm + 12 m 20 cm + 32 32 Therefore, the total length of the rope bought by both of them is 32 m 32 cm. Example 6: Raj’s house was at a distance of 36 km 119 m from his uncle’s house. He travelled by car for 14 km 116 m from his uncle’s house. How much more distance should Raj cover to reach his home? Solution: Distance between Raj’s house and his uncle’s house = 36 km 119 m Distance travelled by Raj from his uncle’s house = 14 km 116 m Distance left to be covered by Raj to reach his house km m = 36 km 119 m – 14 km 116 m 36 119 Therefore, the distance yet to be covered by Raj to − 1 4 1 1 6 22 003 reach his home is 22 km 3 m. I Explore (H.O.T.S.) Let us now see some more examples where we use the concept of standard units of lengths. Example 7: Isha’s mother told her that she will get one chocolate for every 100 metres she runs. She ran 400 m on the first day. At the end of the second day, her mother gave her 16 chocolates. Calculate the total distance covered by Isha on the second day. Express your answer in km and m. Solution: Number of chocolates that Isha gets for every 100m she runs = 1 The number of chocolates Isha got from her mother = 16 The total distance ran by Isha on the two days = 16 × 100 m = 1600 m Distance Isha ran on the first day = 400 m Distance Isha ran on the second day = 1600 m – 400 m = 1200 m = 1000 m + 200 m = 1 km 200 m Therefore, Isha ran 1 km 200 m on the second day. Example 8: The figure given below is a map. It shows the different ways to reach the places shown. Measurement 139

Swati’s house 3 km 7 km 500 m Market 4 km 350 m 3 km 250 m 3 km 800 m Playground 2 km 250m School 6 km 700 m Rahul’s house Look at the map and answer these questions. a) Whose house is closer to the playground and by what distance? b) Which is the shortest route to playground from Rahul’s house? c) What is the shortest distance from Swati’s house to Rahul’s house? d) What is closer to Rahul’s house: School or market? Solution: From the map, we see that a) S wati’s house is closer to the playground than Rahul’s house. The difference between the distances = 6 km 700 m – 4 km 350 m = 2 km 350 m T herefore, Swati’s house is closer to the playground than Rahul’s house by 2 km 350 m. b) The distance between Rahul’s house and the playground by the direct road = 6 km 700 m. T he distance between Rahul’s house and the playground through the school = 3 km 250 m + 2 km 250 m = 5 km 500 m T herefore, the shortest route to the playground from Rahul’s house is through the school. c) H ere, we consider any three possibilities. T he distance from Swati’s house to Rahul’s house through the market = 7 km 500 m + 3 km 800 m = 11 km 300 m T he distance from Swati’s house to Rahul’s house through the school 140

= 3 km + 3 km 250 m = 6 km 250 m T he distance from Swati’s house to Rahul’s house through the playground = 4 km 350 m + 6 km 700 m = 11 km 50 m Therefore, the shortest distance from Swati’s house to Rahul’s house is 6 km 250 m. d) The distance between Rahul’s house and school = 3 km 250 m The distance between Rahul’s house and market = 3 km 800 m Therefore, school is closer to Rahul’s house. 11.2 Standard Units of Mass and Volume I Think Surbhi went to the market to buy 1 litre of oil. The shopkeeper gave her two bottles of 500 millilitres each. Did Surbhi get the correct quantity of oil? I Recall The weight of an object is the measure of its heaviness. Different objects have different weights. We use standard units to measure the weights of objects around us. The standard unit of weight is kilogram. We write kilogram in short as ‘kg’. Another unit of weight is gram. We write gram in short as ‘g’. The smallest unit of weight is milligram. We write milligram in short as ‘mg’. Milligram (mg) is the unit used for weighing medicines, tablets and so on. Gram (g) is used for weighing objects such as pens, books, spices and so on. Measurement 141

Kilogram (kg) is used for weighing heavier objects such as rice, wheat, flour and so on. The quantity of liquid (water, oil, milk and so on) that a container can hold is called its capacity or volume. Similar to weight, the standard units of capacity are millilitres, litres and kilolitres. The standard unit of capacity or volume is litre, denoted by ‘ℓ’. The unit smaller than a litre that is used for measuring capacity is called millilitre. We write it in short as ‘mℓ’. We use kilolitres to measure liquids of quantity greater than litres. It is written as ‘kℓ’. I Remember and Understand Sometimes, to measure the weight of an object, we need Relation between the smaller unit instead of the larger unit. For this, we need to units of weight and convert the units for appropriate measurement. Let us see how volume we can convert the units of mass. 1 g = 1000 mg Conversion of weights 1 kg = 1000 g We can convert one unit of measurement into another using the relation between them. 1 ℓ = 1000 mℓ 1 kℓ = 1000 ℓ Let us understand the conversion through a few examples. Example 9: Convert the following: a) 4 kg to g b) 3 kg 150 g to g Solution: Solved Solve these a) T o convert kilograms to grams,multiply by 1000. 6 kg to grams 4 kg to grams 1 kg = 1000 g So, 4 kg = 4 × 1000 g = 4000 g. 142

Solved Solve these b) To convert kilograms and grams to grams, convert 4 kg 20 g to grams kilograms to grams and add it to the grams. 3 kg 150 g to grams 1 kg = 1000 g So, 3 kg = 3 × 1000 g = 3000 g. 3 kg 150 g = 3000 g + 150 g = 3150 g Conversion of volume We can also convert one unit of measurement into another using the relation between them. Let us understand the conversion through a few examples. Conversion of larger units to smaller units To convert litres into millilitres, multiply by 1000. Example 10: Convert the following: a) 3 ℓ to mℓ b) 2ℓ 269 mℓ to mℓ Solution: Solved Solve these a) To convert litres into millilitres, multiply by 1000. 7 ℓ to millilitres 3 ℓ to millilitres Train My Brain 1 ℓ = 1000 mℓ 3 ℓ = 3 × 1000 mℓ = 3000 mℓ b) T o convert litres and millilitres into millilitres, convert 3 ℓ 750 mℓ to millilitres litres to millilitres and add it to the millilitres. 2ℓ 269 mℓ to millilitres 1 ℓ = 1000 mℓ So, 2 ℓ = 2 × 1000 mℓ = 2000 mℓ. 2 ℓ 269 mℓ = 2000 mℓ + 269 mℓ = 2269 mℓ Measurement 143

? Train My Brain Solve the following: a) Convert 5 kg into g. b) Convert 10 kg 250 g into g. c) Convert 8 ℓ into mℓ. d) Convert 34 ℓ 420 mℓ into mℓ. I Apply We add or subtract weights or volume just as we add or subtract numbers. Remember to write the unit after the sum or difference. Note: Suppose the weight of an object is expressed in g and mg and there are only 2 digits in the milligram. Place a 0 in the hundreds place and make it a 3-digit number. We do this because 1000 mg = 1 g. Addition of weights Example 11: Add: a) 15 g 150 mg and 23 g 285 mg b) 17 kg 706 g and 108 kg 189 g Solution: Follow these steps to add the given weights: Steps Solved Solved Solve these Step 1: Write the g mg kg g kg g numbers in the 15 150 17 706 11 230 columns as shown. + 23 285 + 108 189 + 8 760 Step 2: Add the g mg kg g g mg numbers under the 1 1 smaller unit and 26 190 write the sum. 15 150 17 706 + 23 260 + 23 285 + 108 189 Step 3: Add the g mg numbers under 435 895 the larger unit and 33 333 write the sum. g mg kg g + 22 333 1 11 17 706 15 150 + 108 189 + 23 285 125 895 38 435 144

Subtraction of weights Example 12: Subtract: a) 153 g 100 mg from 262 g 300 mg b) 234 kg 150 g from 355 kg 305 g Solution: Follow these steps to subtract the given weights: Steps Solved Solved Solve these Step 1: Write the g mg kg g kg g numbers in columns 262 300 355 305 505 600 as shown. − 153 100 − 234 150 − 200 400 Step 2: Subtract the g mg kg g g mg numbers under the 2 10 smaller unit and 262 300 15 260 write the difference. − 153 100 3 5 5 \\3 \\0 5 − 15 260 − 234 150 200 155 Step 3: Subtract the g mg kg g g mg numbers under the 5 12 2 10 larger unit and write 2 \\6 \\2 3 0 0 23 555 the difference. − 153 100 3 5 5 \\3 \\0 5 − 16 454 109 200 − 234 150 121 155 Addition of volumes Example 13: Add: 13 ℓ 450 mℓ and 32 ℓ 300 mℓ Solution: Follow these steps to add the given volumes: Steps Solved Solve these ℓ mℓ Step 1: Write the ℓ mℓ 21 200 numbers in columns as 13 450 shown. + 32 300 + 11 303 Step 2: Add the ℓ mℓ ℓ mℓ numbers under the 13 450 24 129 smaller unit and write + 32 300 + 31 110 the sum. 750 Measurement 145

Steps Solved Solve these Step 3: Add the ℓ mℓ ℓ mℓ numbers under the 13 450 52 000 larger unit and write + 32 300 + 41 000 the sum. 45 750 Subtraction of volumes Example 14: Subtract: 351 ℓ 200 mℓ from 864 ℓ 350 mℓ Solution: Follow these steps to subtract the given volumes: Steps Solved Solve these Step 1: Write the numbers ℓ mℓ ℓ mℓ in columns as shown. 864 350 316 186 − 351 200 − 116 205 Step 2: Subtract the ℓ mℓ ℓ mℓ numbers under the 864 350 119 209 smaller unit and write the − 351 200 − 11 101 difference. 150 Step 3: Subtract the ℓ mℓ ℓ mℓ numbers under the 864 350 291 112 larger unit and write the − 351 200 − 180 100 difference. 513 150 I Explore (H.O.T.S.) Let us now see the use of the standard units of weight and volume in real-life situations. Example 15: K iran bought 13 kg flour in the first month and 10 kg 240 g in the second month. Venu bought 11 kg 750 g in the first month and 12 kg 400 g in the second month. Who bought more quantity of flour in two months and by how much? Solution: Quantity of flour bought by Kiran = 13 kg + 10 kg 240 g = 23 kg 240 g 146