202110795-TRAVELLER_PREMIUM-STUDENT-TEXTBOOK-MATHEMATICS-G05-PART2

I Remember and Understand We use multiplication to find the value of many units of an item from the value of a single unit. We use division to find the value of a single unit of an item from the value of many units. We can also find the value of the different number of units by following these two steps. Step 1: Find the value of a single unit of an item from the value of the given units using division to obtain the same. Step 2: Using the value obtained in Step 1, find the value of many units using multiplication. Let us now see a few examples to understand the unitary method better. Example 1: The cost of 12 erasers is ` 36. What is the cost of 18 erasers? Solution: The cost of 12 erasers = ` 36 Step 1: The cost of 1 eraser = ` 36 ÷ 12 The method of finding = ` 3 the value of one unit and Step 2: The cost of 18 erasers = 18 × ` 3 then finding the value of = ` 54 many units is called the Unitary Method. Therefore, 18 erasers cost ` 54. Example 2: Three pens cost ` 39. How much does a dozen pens cost? Solution: The cost of 3 pens = ` 39 Step 1: The cost of 1 pen = ` 39 ÷ 3 = ` 13 Step 2: 1 dozen = 12 items The cost of a dozen pens = Cost of 12 pens = ` 13 × 12 =` 156 Therefore, a dozen pens costs ` 156. Example 3: The cost of 25 notebooks is ` 525. How many notebooks can be bought for ` 1575? Solution: The cost of 25 notebooks = ` 525 The cost of 1 notebook = ` 525 ÷ 25 = ` 21 Money 47

The amount with which notebooks are to be bought = ` 1575 The number of notebooks that can be bought = Total amount ÷ Cost of each notebook = ` 1575 ÷ ` 21 = 75 Therefore, 75 notebooks can be bought for ` 1575. ? Train My Brain Solve these: a) The cost of 12 mangoes is ` 360. Find the cost of 6 mangoes. b) The cost of 15 caps is ` 450. Find the cost of 3 caps. c) The cost of 20 chairs is ` 4000. Find the cost of 25 chairs. I Apply The unitary method can be used to compare two or more items. Consider these examples. Example 4: 4 people spend ` 640 to travel by bus to a hill station. If each ticket is the same price, how much would 8 people spend? Solution: Money spent by 4 people = ` 640 Money spent by 1 person = ` 640 ÷ 4 = ` 160 Number of people travelling now = 8 Money spent by 8 people on the same trip = ` 160 × 8 = ` 1280 Therefore, 8 people spend ` 1280 to take the same trip. Example 5: Roshan bought 15 kg of onions for ` 375. He has ` 800 with him. Can he buy 35 kg of onions? Solution: The cost of 15 kg of onions = ` 375 The cost of 1 kg of onions = ` 375 ÷ 15 = ` 25 The cost of 35 kg of onions = ` 25 × 35 = ` 875 Roshan has ` 800 with him. As the total cost of 35 kg of onions is ` 875, he does not have enough money to buy 35 kg of onions. 48

I Explore (H.O.T.S.) We can use the unitary method to find who has more or less amount or which item purchased is more or less expensive. Example 6: Mona observed that a pack of four soaps, each of 150 g, costs ` 60. Another pack of six soaps, each of 100 g costs ` 54. Which pack should Mona buy so that she spends a lesser amount? Solution: Weight of 4 soaps, each of 150 g = 150 g × 4 = 600 g The cost of 4 soaps = ` 60 The cost of 1 g of soap = ` 60 ÷ 600 = ` 1 = 1 × 100 paise = 10 paise 10 10 Weight of 6 soaps, each of 100 g = 100 g × 6 = 600 g The cost of 6 soaps = ` 54 The cost of 1 g soap = ` 54 ÷ 600 = ` 9 = 9 × 100 paise = 9 paise 100 100 Since 9 paise < 10 paise, Mona has to buy the pack of 6 soaps of 100 g each to spend a lesser amount. Example 7: A set of eight plastic sharpeners costs ` 48.80. A set of six steel sharpeners costs ` 48.60. Which set of sharpeners is expensive? Solution: The cost of 8 plastic sharpeners = ` 48.80 ` 6.10 ` 8.10 The cost of 1 plastic sharpener = ` 48.80 ÷ 8 The cost of 6 steel sharpeners = ` 48.60 ) )8 ` 48.80 6 ` 48.60 The cost of 1 steel sharpener = ` 48.60 ÷ 6 Since ` 8.10 > ` 6.10, the set of steel − 48 − 48 sharpeners is expensive. 8 6 −8 −6 0 0 −0 −0 00 Money 49

Example 8: The cost of 17 kg of guavas is ` 552.50. 32.50 Solution: What is the cost of 10 kg of guavas? The cost of 17 kg of guavas = ` 552.50 )17 552.50 − 51 The cost of 1 kg of guavas = ` 552.50 ÷ 17 42 = ` 32.50 − 34 The cost of 10 kg of guavas = ` 32.50 × 10 85 = ` 325 − 85 00 Therefore, 10 kg of guavas cost ` 325. − 00 00 Maths Munchies The currency note of ` 10000 is the highest denomination RBI has printed in its history. ` 1000 and ` 10000 notes were in circulation between 1938 and 1946 but were eventually demonetised. ` 1000, ` 5000 and ` 10000 notes were reintroduced in 1954 and demonetised in 1978. Recently, in 2016, the currency notes of ` 1000 and ` 500 have been demonetised in our country. ` 500 was reintroduced with new ` 2000 and ` 200 notes. Connect the Dots Social Studies Fun The pound is the currency used by Egypt, Falkland Islands, Gibraltar, Guernsey, Jersey, and the United Kingdom. It is called as Pound sterling. Centuries ago, it was known as Troy Pound. Science Fun In India, currency papers are made of cotton and cotton rag. The currency is not paper but a cloth that gives the look and feel of paper. 50

Drill Time 10.1 Unitary Method in Money Word problems 1) The cost of 15 apples is ` 84. What is the cost of 20 apples? 2) Eight pairs of slippers cost ` 328. How much does a dozen pair of slippers cost? 3) The cost of five textbooks is ` 525. How many textbooks can be bought for ` 945? 4) Salman observed that a pack of five face creams, each of 150 g, costs ` 500 and another pack of six face creams each of 100 g is ` 450. Which pack should Salman buy so that he spends a lesser amount? 5) The cost of 20 kg of potatoes is ` 310. What is the cost of 12 kg of potatoes? A Note to Parent The unitary method is an important skill used in day-to-day life. Help your child to practise the unitary method while buying monthly grocery. Money 51

11Chapter Decimals I Will Learn About • conversion of fractions to decimals and vice versa. • pictorial representation of decimals. • the place value chart and the expanded forms of decimals. • types of decimal fractions. • compare and order decimal numbers. 11.1 Introduction to Decimals I Think Pooja and her friends participated in the long jump event in their games period. Her sports teacher noted the distance they jumped, Pooja – 4.1 m on a piece of paper as shown here. Ravi – 2.85 m Rajiv – 3.05 m Pooja wondered why the numbers had a point between them as Amit – 2.50 m in the case of writing money. Do you know what the point means? I Recall We have already learnt about equivalent fraction in earlier chapters. Let us recall the concepts by solving following problems. a) Find the equivalent fraction of 3 with 24 as the numerator. 4 52

b) Find two equivalent fractions of 7 . 10 c) Find the equivalent fraction of 3 with 100 as the denominator. 10 d) Find the equivalent fraction of 4 with 80 as the numerator. 5 e) Find the equivalent fraction of 21 with 100 as the denominator. 25 I Remember and Understand We have already learnt about fractions. Decimals are fractions with denominators 10, 100, 1000... expressed without denominator. Let us learn more about decimals. Conversion of fractions to decimals Look at the given figure. We can write the coloured portion of the figure as 3 . As 10 this fraction has 10 as denominator, this number can be expressed as 0.3 in decimals. Similarly, the uncoloured part can be expressed in the form of a fraction as 7 and as 10 0.7 in decimal form. Numbers such as 0.3, 0.7, 3.0, 3.1, 4.7, 58.2 and so on are called decimal numbers or simply decimals. In case of improper fractions with 10, 100, 1000 and so on as denominators, we convert them to mixed fractions and then write the fraction part in mixed fraction as decimal after the point. The whole number is placed before the point. For example, 13 = 1 3 = 1.3 10 10 Consider the following example. Example 1: Convert the following proper fractions into their decimal forms. a) 4 b) 73 c) 9 d) 23 10 100 100 1000 Solution: To write the given fractions as decimals, follow these steps: Step 1: Write the numerator. Step 2: Count number of ‘0’s in the denominator. If the number of 0s are more than number of digits in the numerator, then put 0s to the left of the number to make the count of digits equal to the number of 0s. Place the decimal point to the left. Decimals 53

Step 3: Place a ‘0’ to the left of the decimal point. a) 0.4 b) 0.73 c) 0.09 d) 0.023 Example 2: Express these improper and mixed fractions as decimals. 43 a) 18 2 b) 10 c) 26 1 d) 4 9 10 10 10 Solution: To write the given fractions as decimals, follow these steps: Step 1: Convert improper fraction into mixed fractions. Step 2: Write the integral part as it is. Step 3: Place a point to its right. Step 4: Write the decimal form of the proper fraction part. a) 18 2 = 18.2 b) 43 = 4.3 10 10 c) 26 1 = 26.1 d) 49 = 4.9 10 10 Note:This method is used only when the denominators of the fractions are 10, 100, 1000 and so on. Shortcut method: To write fractions with denominators 10, 100 or 1000 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. For example, the decimal form of 232 = 2.32 100 Note: F or the decimal equivalent of a proper fraction, place a 0 as the integral part of the decimal number. Pictorial representation We can represent the decimals pictorially as follows. 2 tenth=s =2 0.2 10 5 tenth=s =5 0.5 10 54

8 tenth=s =8 0.8 10 10 tenth=s 1=0 1 10 The rectangle given is divided into ten parts of the same size. Then, each of the ten equal parts is 1 . It is read as one-tenth. The decimal form of each equal part is 0.1. 10 The numbers in the decimal part are read as separate digits. We read numbers such as 0.1, 0.2, 0.3,….as ‘zero point one’, ‘zero point two’, ‘zero point three’ and so on. Zero is written to indicate the place of the whole number. The fractional form of each equal 1 part is 10 . We get the first place after the decimal point by dividing the number by 10. It is called the tenths place (t). 1 hundredths = 1 9 hundredths = 9 33 hundredths = 33 100 100 100 = 0.01 = 0.09 = 0.33 57 hundredths 100 hundredths 57 = 0.57 100 = 1 100 100 We get the second place after the decimal point by dividing the number by 100. It is called the hundredths place (h). Similarly, we get the third place after the decimal point by dividing the number by 1000. It is called the thousandths place (th). Decimals 55

Equivalent decimals 4 tenths = 40 hundredths 0.4 0.40 The numbers after the decimal point have the same value. Hence, these decimals are called equivalent decimals. Thus, we can say that writing zeroes to the right of the final number after the decimal point does not change the value of the number. Example 3: Find two equivalent decimals of the following numbers. a) 0.7 b) 4.61 c) 20.41 d) 98.22 Solution: The two equivalent decimals of numbers are: a) 0.7 = 0.70, 0.700 b) 4.61 = 4.610, 4.6100 c) 20.41 = 20.410, 20.4100 d) 98.22 = 98.220, 98.2200 Place value chart for decimals Similar to the place value chart for numbers, we have a place value chart for decimals too. Let us recall the place value chart of numbers. 100 × 10 10 × 10 1 × 10 1 Thousands Hundreds Tens Ones 6 2 5 5 3 2 2 6 5 2 After the decimal point, 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 value 10 56

is 0.1 read as ‘zero point one’. Similarly, when we move one place to the right from one-tenth, we get one-hundredth ( 1 ), and then one-thousandth ( 1 ). 100 1000 We can extend the place value chart to the right as follows: Thousands Hundreds Tens Ones Decimal Tenths Hundredths Thousandths point 1000 100 10 1 (.) 1 1 13196 10 100 1000 1 4 26 . 0 3 8 The number 1426.038 is read as one thousand four hundred twenty-six point zero three eight. The point placed between the number is called the decimal point. The system of writing numbers using a decimal point is called the decimal system. Note: ‘Deci’ in Latin language means 10. Expansion of decimal numbers Using the place value chart, we can expand decimal numbers. Let us see a few examples. Example 4: Expand the following numbers. a) 13.457 b) 450.72 c) 2153.068 Solution: To expand the given decimal numbers, let us write them in the place value chart. Thousands Hundreds Tens Ones Decimal Tenths Hundredths Thousandths point 1 11 1000 100 10 1 ( . ) 10 100 1000 a) 13 . 4 5 7 b) 4 50 . 7 2 c) 2 1 53 . 0 6 8 Expansions: 11 1 a) 13.457 = 1 × 10 + 3 × 1 + 4 × 10 + 5 × 100 + 7 × 1000 Decimals 57

b) 450.72 = 4 × 100 + 5 × 10 + 7 × 1 + 2 × 1 10 100 11 c) 2153.068 = 2 × 1000 + 1 × 100 + 5 × 10 + 3 × 1 + 6 × 100 + 8 × 1000 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 number of digits after the decimal point. Example 5: Write these decimals as fractions. a) 2.3 b) 13.107 c) 105.43 d) 0.52 Solution: 23 13107 a) 2.3 = 10 b) 13.107 = 1000 10543 52 c) 105.43 = 100 d) 0.52 = 100 Alternate method: Decimals having an integral part can be written as mixed fractions. For example, 2.3 = 2 and 3 tenths = 23 ; 10 13.107 = 13 and 107 thousandths = 13 107 ; 1000 105.43 = 105 and 43 hundredths = 105 43 and so on. 100 ? Train My Brain Solve the following: a) Expand 35.098. b) Write 4.78 as a fraction. c) Express 37 as a decimal. 100 58

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 each of their amounts in words. Solution: To write the decimals in words, separate the integral and the decimal parts using ‘and’. Amount In words ` 432.50 Rupees four hundred thirty-two and fifty paise ` 233.20 Rupees two hundred thirty-three and twenty paise ` 515.60 Rupees five hundred fifteen and sixty paise ` 670.80 Rupees six hundred seventy and eighty paise Example 7: The weights (in grams) of some children are given in the table: Name Weight (in grams) Rahul 23456 Anil 34340 Anjali 28930 Soham 25670 Convert each of their 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. Decimals 59

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 Example 8: Express the fraction 1 as a decimal. 5 Solution: We can convert the fraction into an equivalent fraction having 10 as the denominator by multiplying the numerator and denominator by 2. Thus, 1× 2 = 2 5×2 10 Converting the equivalent fraction into a decimal we get, 2 = 0.2 10 I Explore (H.O.T.S.) Example 9: Write the decimals that represent the shaded part. a) b) c) 60

d) Solution: a) The fully shaded part represents a whole. So, the decimal that represents the given figure is 1.3. b) The required decimal is 0.6. c) 10 + 43 = 143 = 1114.04303 10 100 100 d) 100 + 100 + 29 = 2120212090902.29 100 100 100 Example 10: 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) 11.2 Compare and Order Decimals I Think Pooja went to purchase a bag to gift her mother on her birthday. She selected two bags with price tags showing ` 455.80 and ` 455.40. She couldn’t understand which of the two bags was more expensive. Can you guess the price of the expensive bag? Decimals 61

I Recall We have learnt to convert fractions to decimals. Let us quickly revise by converting the following fractions to decimals. a) 2 b) 71 c) 81 d) 321 e) 56 1000 100 100 1000 100 I Remember and Understand Let us learn about equivalent decimals, like decimals and unlike decimals. Decimal places: The digits in the decimal part are called decimal places. For example, 4109.34 has two decimal places; 1183.6 has only one decimal place. Equivalent decimals: The decimal numbers which have equal value are called equivalent decimals. For example, 0.3, 0.30, 0.300 are equivalent decimals. Like decimals: The decimal numbers that have the same number of decimal places are called like decimals. For example, a) 2.81, 35.94, 7.32, 145.67, 214.07 and b) 0.362, 51.093, 22.678, 8091.221, 1.003 are all like decimals. Unlike decimals: The decimal numbers that have different number of decimal places are called unlike decimals. For example, 1) Adding any number of a) 5.11, 89.018, 3.4, 671.92 0s to the right side of the b) 59.009, 231.8, 9.05, 12.25 are all unlike decimals. decimal point does not Example 11: Which is the greater of the given change its value. 2) Unlike decimals can be decimals? converted to like decimals a) 69.2 and 69.02 by adding zeros at the b) 77.10 and 77.012 right end. c) 3.5631 and 3.61 Solution: a) 69.2 and 69.02 To compare two decimals, follow these steps: 62

Step 1: Convert the given decimal numbers into like decimals. Step 2: 69.20, 69.02 Step 3: Compare their integral parts. The decimal with the greater integral part is greater. Here, 69 = 69 If the integral parts are the same, then we have to compare the tenths digits. The decimal with the greater digit in the tenths place is greater. If the tenths digits are also the same, compare the hundredths digits and so on. 69.20 69.02 6=6 9=9 2>0 Therefore, 69.20 > 69.02. Note: Always start comparing from the largest place value in the integral part. b) 77.10 and 77.012 Step 1: Convert the unlike decimals into like decimals: 77.10 = 77.100 Step 2: Compare the integral parts: 77 = 77 Step 3: Compare the tenths digits: 1 > 0 Therefore, 77.10 > 77.012. c) 3.5631 and 3.61 Step 1: Convert the unlike decimals into like decimals: 3.61 = 3.6100 Step 2: Compare their integral parts: 3 = 3 Step 3: Compare the tenths digits: 5 < 6 Therefore, 3.5631 < 3.6100. Example 12: Which is the smaller of each of the given pairs of decimal numbers? a) 367.80 and 362.801 b) 21.673 and 21.673 c) 11.729 and 11.726 Decimals 63

Solution: a) 367.80 and 362.801 Converting the unlike decimals into like decimals: 367.80 = 367.800 Comparing their integral parts, 367 > 362 Therefore, 362.801 is smaller. b) 21.673 and 21.673 The given decimals are like decimals. Compare their integral parts: 21 = 21 Compare: Tenths digits: 6 = 6, Hundredths digits: 7 = 7 Thousandths digits: 3 = 3 Therefore, 21.673 = 21.673. c) 11.729 and 11.726 Given decimals are like decimals. Comparing their integral parts: 11 = 11 Compare: Tenths digits: 7 = 7 Hundredths digits: 2 = 2 Thousandths digits: 9 > 6 Therefore, 11.726 is smaller. Comparing decimal numbers helps us in arranging them in ascending and descending orders. Let us see a few examples. Example 13: Arrange the following decimal numbers in the ascending order. a) 2.1, 2.01, 3.06, 0.831 b) 15.12, 19.18, 26.7, 1.007 c) 37.502, 36.512, 67.3, 22 Solution: a) 2.1, 2.01, 3.06, 0.831 Express the unlike decimals as like decimals. 2.100, 2.010, 3.060, and 0.831 0.831 < 2.010 < 2.100 < 3.060 Therefore, the ascending order is 0.831, 2.01, 2.1, 3.06. b) 15.12, 19.18, 26.7, 1.007 64

Express the unlike decimals as like decimals. 15.120,19.180, 26.700 and 1.007 1.007 < 15.120 < 19.180 < 26.700 Therefore, the ascending order is 1.007, 15.12, 19.18, 26.7. c) 37.502, 36.512, 67.3, 22 Express the unlike decimals as like decimals. 37.502, 36.512, 67.300 and 22.000 22.000 < 36.512 < 37.502 < 67.300 Therefore, the ascending order is 22, 36.512, 37.502, 67.3. Example 14: Arrange these decimal numbers in the descending order. a) 43.25, 43.2, 43.21, 43.127 b) 63.901, 63.09, 63.009, 6.39 c) 11.2, 11.028, 1.127, 13.02 Solution: a) 43.25, 43.2, 43.21, 43.127 Express the unlike decimals as like decimals 43.250, 43.200, 43.210, 43.127 43.250 > 43.210 > 43.200 > 43.127 Therefore, the descending order is 43.25, 43.21, 43.2, 43.127. b) 63.901, 63.09, 63.009, 6.39 Express the unlike decimals as like decimals 63.901, 63.090, 63.009, 6.390 63.901 > 63.090 > 63.009 > 6.390 Therefore, the descending order is 63.901, 63.09, 63.009, and 6.39. c) 11.2, 11.028, 1.127, 13.02 Express the unlike decimals as like decimals 11.200, 11.028,1.127, 13.020 13.020 > 11.200 > 11.028 > 1.127 Therefore, the descending order is 13.02, 11.2, 11.028, 1.127. Decimals 65

? Train My Brain Compare these decimals: a) 9.75 and 9.45 b) 69.3 and 69.30 c) 56.070 and 56.007 I Apply Let us now see a few real-life examples involving comparison of decimals. Example 15: Ramu saves ` 361.80 while Raghu saves ` 351.90. Who saves more money? Solution: To know who saves more money, we have to find which decimal is greater of ` 361.80 and ` 351.90. 361.80 351.90 3=3 6>5 361.80 > 351.90 Therefore, Ramu saves more money. Example 16: Leela scored 32.5 marks in English, 48.5 in Mathematics and 32.75 in Science. Arrange her marks in descending order and find the subject in which she scored the maximum marks. Solution: English Mathematics Science 32.5 48.5 32.75 Express the unlike decimals as like decimals 32.5 = 32.50 and 48.5 = 48.50 Descending order: 48.50, 32.75, 32.50 48.5 is the greatest number. Therefore, Leela scored the maximum marks in Mathematics. 66

Example 17: Ravi bought two watermelons. One of them weighs 12.352 kg and the other weighs 12.365 kg. Which watermelon is heavier? Solution: Weight of one watermelon = 12.352 kg Weight of the second watermelon = 12.365 kg 12.352 12.365 1=1 2=2 3=3 5<6 So, 12.352 < 12.365 or in other words, 12.365 > 12.352. Therefore, the second watermelon is heavier than the first. I Explore (H.O.T.S.) Let us see other real-life examples of comparing and ordering decimals. Example 18: In a swimming competition, there are five competitors. Four of the swimmers have had their turns. The time they took are 9.8 s, 9.75 s, 9.79 s and 9.81 s. In how much time must the last swimmer complete the distance to win the competition? Solution: Arrange the given times in ascending order: 9.75 < 9.79 < 9.80 < 9.81 The lowest decimal is 9.75. Therefore, the time taken by the last swimmer must be less than 9.75 s in order to win the competition. Example 19: Six students have participated in a running race. Their timings to finish the race are 1.53 min, 3.41 min, 4.24 min, 2.12 min, 8.25 min and 8.54 min. Who won the race? Solution: Arrange the given scores in ascending order: 1.53 < 2.12 < 3.41 < 4.24 < 8.25 < 8.54 The student who covers the distance in the least time is the winner. Therefore, the student who completed the race in 1.53 min is the winner. Decimals 67

Maths Munchies Faster method to convert a fraction to decimal 1 Consider this example: Convert 5 into its decimal form. Step 1: Multiply the numerator and the denominator of the fraction with a number to get 10 as the denominator. Multiply the numerator and the denominator by 2 so that 5 × 2 = 10. Step 2: Write in the fraction form as per step 1. So, this will give us 1 × 2 = 2 . 5 2 10 Step 3: Write in the decimal form. So, 0.2 is the decimal form of 1 . 5 Connect the Dots Social Studies Fun The Earth takes 23 hours, 56 minutes and 4.09 seconds to complete a rotation. But, to make it easy to calculate time, we take this as 24 hours. English Fun A word contains ten letters, out of which three are vowels. Write the fraction of the number of consonants. Express the fraction thus obtained, in the decimal form. 68

Drill Time 11.1 Introduction to Decimals 1) Write the following numbers in the decimal place value chart. a) 42.874 b) 315.097 c) 2795.741 d) 127.243 2) Write the expanded forms of the given decimals and then write them in words. a) 3578.048 b) 450.981 c) 32.62 d) 432.789 3) Convert the given unlike decimals into like decimals. a) 52.7, 25.28, 321.265, 101.51 b) 42.52, 4.7, 32.472, 48.8 c) 1.7, 32.4, 328.732, 1.82 d) 7.42, 1.821, 7.01, 432.2 4) Convert the following decimals into fractions: a) 2.56 b) 14.02 c) 105.89 d) 52.60 e) 8.01 5) Convert the following fractions into decimals: a) 2 b) 23 c) 45 d) 73 e) 834 10 100 1000 10 100 6) Write the following decimals in words: a) 73.5 b) 413.45 c) 0.73 d) 13.45 e) 1.87 7) Word problems a) The measures of some objects are given in the table. Height of a flagpole 9.50 m Length of a dining table 1.20 m Distance between two cities 325.75 km 127.80 cm Height of a plant Write these measures in words. b) 475 out of 1000 parents who attended a parent-teacher meet were women. Write the decimal equivalent of the fraction of men who attended the meet. Decimals 69

11.2 Compare and Order Decimals 8) Compare the decimals a) 32.401 and 14.602 b) 82.190 and 33.333 c) 68.103 and 11.34 d) 6.666 and 6.66 e) 12.412 and 82.410 9) Arrange the decimals in ascending and descending orders. a) 20.496, 20.216, 20.187 20.079 b) 56.41, 56.34, 56.298, 56.170 c) 32.278, 30.198, 20.373, 31.476 d) 44.444, 44.441, 44.440, 44.442, 44.445 e) 95.956, 95.957, 95.955, 95, 950 A Note to Parent Give your child a shopping bill and make them write the decimal numbers in it. Then ask them to write the decimal numbers as fractions and in words. Such an exercise will give him or her a good practice of decimals. 70

12Chapter ODpeecrimatailons I Will Learn About • addition and subtraction decimal fractions. • multiplication of decimal fractions with 10, 100 and 1000. • multiplication of decimal numbers by whole and decimal numbers. 12.1 Add and Subtract Decimals I Think Pooja went to an ice cream parlour to purchase some ice creams. She bought strawberry for ` 25.50, vanilla for ` 15.30 and chocolate for ` 32.20. She gave ` 100 to the shopkeeper. She wanted to calculate the total price before the shopkeeper gave the bill. Since the prices were in decimals, she was unable to calculate. Do you know how to find the total cost of the ice creams that Pooja bought? How much change would she get in return? I Recall Addition and subtraction of decimal numbers are similar to that of usual numbers. Let us recall the conversion of unlike decimals to like decimals. 71

Convert the given unlike decimals into like decimals. a) 4.32, 4.031, 4.1, 7.823 b) 0.7, 0.82, 4.513, 0.72 c) 1.82, 7.01, 5.321, 0.8 d) 7.32, 7.310, 7.8, 5.2 I Remember and Understand Addition and subtraction of decimal numbers with the thousandths place is similar to that of decimals with the hundredths place. Write the given decimal numbers such that the digits in their same places are exactly one below the other. Note: T he decimal points of the numbers must be exactly one Before adding below the other. or subtracting decimals, convert Let us see a few examples. the unlike decimals to like Example 1: a) Find the sum of 173.80 and 23.61. decimals. b) Subtract 216.73 from 563.72. Solution: a) b) 12 16 1 5 2/ 6/ 12 1 7 3 .8 0 5 6/ 3/ . 7/ 2/ + 2 3 .6 1 –21 6 . 7 3 1 9 7 .4 1 34 6 . 9 9 Example 2: Solve: a) 294.631 + 306.524 b) 11.904 – 6.207 Solution: a) 1 1 1 b) 11 8 9 14 1/ 1/ . 9/ 0/ 4/ 29 4 . 631 +30 6 . 524 – 6 . 20 7 60 1 . 155 5 . 69 7 ? Train My Brain Solve: a) 347.87 + 67.43 b) 16.53 – 10.73 c) 22.63 – 18.32 72

I Apply Let us see a few real-life examples involving addition and subtraction of decimals. Example 3: Dolly bought 0.450 kg of tomatoes. She used 0.150 kg of it to make tomato pickle. What is the weight (in kg) of the tomatoes left with Dolly? Solution: Quantity of tomatoes bought = 0.450 kg Quantity of tomatoes used for tomato pickle = 0.150 kg Quantity of tomatoes left with Dolly = 0.450 kg – 0.150 kg = 0.300 kg Therefore, 0.300 kg of tomatoes are left with Dolly. Example 4: Vinod purchased a shirt for ` 275.40, a pair of trousers for ` 1462.30 and a pair of shoes for ` 524.95. Find the total money spent by Vinod. Solution: The amount spent by Vinod on a shirt = ` 275.40 The amount spent on a pair of trousers = ` 1462.30 The amount spent on a pair of shoes = ` 524.95 The total amount spent by Vinod = ` 275.40 + ` 1462.30 + ` 524.95 = ` 2262.65 Therefore, Vinod spent a total of ` 2262.65. Example 5: By how much should 67.23 be decreased to get 28.59? Solution: The required number is the difference of 16 11 67.23 and 28.59 = 67.23 – 28.59 5 6/ 1/ 13 Therefore, 67.23 is to be decreased by 38.64 6/ 7/ . 2/ 3/ −2 8 . 5 9 to get 28.59. n 38.6 4 Example 6: Mrs. Roopa bought 13.75 litres of milk. She used 9.2 litres of milk for making paneer. Find the quantity of the milk remaining. Solution: The quantity of milk bought by Mrs. Roopa = 13.75 litres The quantity of milk used to make paneer = 9.2 litres The quantity of milk remaining = (13.75 – 9.2) litres = 4.55 litres Therefore, 4.55 litres of milk is remaining. Decimal Operations 73

Example 7: Pawan needs 1.40 m of cloth for a shirt and 2.45 m of cloth for a pair of trousers. His father gave a piece of cloth which is 0.65 m less than that needed. What was the length of the cloth given by Pawan’s father? Solution: The length of the cloth needed for a shirt = 1.40 m The length of the cloth needed for a pair of trousers = 2.45 m Total length of the cloth needed = 1.40 m + 2.45 m = 3.85 m The length by which the cloth was short = 0.65 m T herefore, the length of the cloth given by Pawan’s father is 3.85 m – 0.65 m = 3.20 m. I Explore (H.O.T.S.) Let us see a few more examples involving addition and subtraction of decimals. Example 8: Subtract the sum of 6.223 and 37.512 from the sum of 42.106 and 5.07. Solution: We should find (42.106 + 5.07) – (6.223 + 37.512) Step 1: Add 42.106 and 5.07. 4 2.1 0 6 + 5.0 7 0 4 7.1 7 6 Step 2: Add 6.223 and 37.512. 1 0 6 . 2 23 + 3 7 . 5 12 4 3 . 7 35 Step 3: Subtract the sum in step 2 from the sum in step 1. 6 11 4 7/ . 1/ 7 6 − 4 3 . 7 35 0 3 . 4 41 Example 9: Pooja saw a doll in a toy shop. The cost of the doll was ` 85.65. She wanted to buy it, but she fell short of ` 5.75. How much money did Pooja have? 74

Solution: The cost of the doll = ` 85.65 7 14 16 Amount she fell short of = ` 5.75 8/ 5/ . 6/ 5 Money that Pooja had = ` 85.65 – ` 5.75 = ` 79.90 − 5.75 Therefore, Pooja had ` 79.90. 7 9.90 12.2 Multiply Decimals I Think Pooja bought six different types of toys for ` 236.95 each. She calculated the total cost and paid the amount to the shopkeeper. Do you know how to find the total cost of the toys? I Recall We have already learnt multiplication of numbers. Let us recall the same by answering the following. H TO Th H T O H TO 267 3218 576 ×14 ×34 ×12 I Remember and Understand Multiplication of decimals is similar to multiplication of numbers. Multiply decimals by 1-digit and 2-digit numbers Let us understand multiplication of decimals through a few examples. Decimal Operations 75

Example 10: Solve: a) 276.32 × 6 b) 25.146 × 23 Solution: a) 276.32 × 6 To multiply the given numbers, follow these steps: Step 1: Multiply the numbers as usual without considering the decimal point. T Th Th H T O Step 2: 4 3 11 2 7 6 32 ×6 1 6 5 7 92 Count the number of decimal places in the given number. The number of decimal places in 276.32 is two. Step 3: Count from the right, the number of digits in the product as the number of decimal places in the given number. Then place the decimal point. Therefore, 276.32 × 6 is 1657.92. b) 25.146 × 23 T Th Th H T O 11 1 11 2 5146 ×23 1 + 7 5438 5 0 2920 5 7 8. 3 5 8 Therefore, 25.146 × 23 is 578.358. Multiply decimals by 10,100 and 1000 Example 11: Solve: b) 3.4567 × 100 c) 3.4567 × 1000 a) 3.4567 × 10 Solution: To multiply a decimal number by 10, 100 and 1000, follow these steps: Step 1: Write the decimal number as it is. Step 2: Shift the decimal point to the right by as many digits as the number of zeros in the multiplier. 76

Therefore, a) 3.4567 × 10 = 34.567 (The decimal point is shifted to the right by one digit as the multiplier is 10 which has one zero.) b) 3.4567 × 100 = 345.67 (The decimal point is shifted to the right by two digits as the multiplier is 100 which has two zeros.) c) 3.4567 × 1000 = 3456.7 (The decimal point is shifted to the right by three digits as the multiplier is 1000 which has three zeros.) Multiply a decimal number by another decimal number Multiplication of a decimal number by another decimal number is similar to the multiplication of a decimal number by a number. Let us understand this through an example. Example 12: Solve: 7.12 × 3.7 Solution: Multiply the given numbers as When two decimal numbers are Step1: usual without considering the multiplied, decimal point. a) count the total number of digits 1 after decimal point in both the 7 12 numbers. Say it is ‘n’. × 37 11 b) multiply the two decimal 4 9 84 numbers as usual and place the +2 1 3 6 0 decimal point in the product after 26 3 44 ‘n’ digits from the right. Step 2: Count the number of decimal places in both the multiplicand and the multiplier and add them. The number of decimal places in 7.12 is two. The number of decimal places in 3.7 is one. Total number of decimal places = 2 + 1 = 3 Step 3: Count as many digits in the product from the right as the total number of decimal places. Then place the decimal point. Therefore, 7.12 × 3.7 is 26.344. Sometimes, the number of digits in the product is less than the sum of the number of decimal places in the multiplicand and the multiplier. In such cases, place zeros to the immediate right of the decimal point in the product such that the number of decimal places is equal to the sum of the decimal places in the multiplicand and the multiplier. Decimal Operations 77

? Train My Brain Solve: a) 56.7 × 10 b) 3.08 × 100 c) 8.50 × 1000 I Apply Let us see a few real-life examples where we use multiplication of decimal numbers. Example 13: Sania bought 10 dozen bananas, each dozen costing ` 120.50. What amount does Sania have to pay altogether? Solution: The cost of 1 dozen bananas = ` 120.50 The cost of 10 dozen bananas = ` 120.50 × 10 =` 1205.00 Therefore, Sania has to pay a total of ` 1205.00. Example 14: The weight of a bag of wheat is 19.85 kg. Find the weight of 14 such bags. Solution: The weight of one wheat bag = 19.85 kg The weight of 14 such bags = 19.85 kg × 14 = 277.9 kg Therefore, 14 bags weigh 277.9 kg. I Explore (H.O.T.S.) Let us solve a few more examples of multiplication of decimal numbers. Example 15: Find the missing numbers. a) ____ × 100 = 467.2 b) 53.052 × ____ = 530.52 c) ____ × 10 = 3764 d) 901.5 × ____ = 90150 Solution: a) 4.672 78

b) 10 c) 376.4 d) 100 Example 16: Roopa bought 8 bags for ` 246.12 each and Pooja bought 6 bags for ` 348.16 each. Who paid less for the bags and by how much? Solution: The cost of the bag that Roopa bought = ` 246.12 The cost of 8 bags = ` 246.12 × 8 =` 1968.96 The cost of the bag that Pooja bought = ` 348.16 The cost of 6 bags = ` 348.16 × 6 =` 2088.96 As ` 1968.96 < ` 2088.96, Roopa paid less for the bags. The amount that Roopa paid less = ` 2088.96 – ` 1968.96 = ` 120 Therefore, Roopa paid ` 120 less than Pooja for the bags. Maths Munchies Estimation is a very useful method to get the product of two Rounding decimal numbers. For example, to find 2.8 × 68, round off 68 to off 70 and 2.8 to 3. So, 3 × 70 = 210. Connect the Dots Social Studies Fun Usually many measurements such as the height of mountains, the depth of the sea and so on are given to us in approximate values. Their exact values are generally in decimals. For example, the height of Mount Everest is 8.848 kilometres. Decimal Operations 79

Science Fun The longest bone in the human body is the thigh bone. Its length is about 19.9 inches or 50.546 cm. Drill Time 12.1 Add and Subtract Decimals 1) Add: a) 528.364 and 974.623 b) 523.97 and 49.25 c) 23.547 and 14.974 d) 242.57 and 132.60 2) Subtract: a) 954.367 – 412.650 b) 234.45 – 142.52 c) 74.812 – 35.634 d) 732.532 – 522.147 3) Word problems a) By how much should 41.65 be increased to get 98.53? b) Saritha bought 56.6 litres of water. She used 9.2 litres of water for washing her uniform. Find the quantity of water left. 12.2 Multiply Decimals 4) Multiply the following: a) 2.498 × 10 b) 32.64 × 53 80

c) 5.645 × 1000 d) 682.93 × 2.8 e)1.742 × 3.81 5) Word problems a) The daily wages of a labourer is ` 120.85. Find the daily wages of 26 labourers. b) The daily consumption of petrol by a truck is 101.25 litres. How many litres of petrol does it consume in a fortnight? (1 fortnight = 15 days) A Note to Parent Ask your child to note the weights (correct to two decimal places) of all the members of your family on a digital scale. He or she can compare these weights and arrange them in the ascending order. Decimal Operations 81

13Chapter Percentages 25% 20% I Will Learn About Off Off .50 400.50 2250.50 • the relationship between percentages, decimals and fractions. • pictorial representation of percentage. 13.1 Introduction to Percentage I Think Pooja and her mother went to a shopping mall. There she saw a banner as shown here and asked her mother about the sign written beside 50. Do you know what sign it is? I Recall We have already learnt how to convert a decimal into a fraction. Let us recall the concept by writing the following decimals as fractions: a) 0.76 b) 0.34 c) 0.57 d) 0.45 e) 0.92 82

I Remember and Understand Observe the following fractions: • To convert any fraction into a percentage, multiply the a) 4 b) 72 c) 82 d) 14 fraction by 100%. 100 100 100 100 • To convert a percentage into a All these fractions have 100 as their fraction, divide the percentage denominator. Such fractions can be expressed by 100 and write the number as percentage. without the % symbol. Convert fraction into percentage Let us consider an example. Example 1: Convert the following fractions into percentages: a) 76 b) 34 c) 43 d) 5 e) 3 100 100 50 10 5 Solution: S.No. Fraction Conversion Percent Read as a) 76 × 100 % = 76 % 76 % Seventy-six percent 76 100 100 b) 34 34 × 100 %= 34 % 34 % Thirty-four percent 100 100 c) 43 43 × 100 % 86 % Eighty-six percent 50 50 = 43 × 2 %= 86 % d) 5 5 ×100 % 50 % Fifty percent 10 10 = 5 × 10 %= 50 % e) 3 3 × 100 % 60 % Sixty percent 5 5 = 3 × 20 %= 60 % Convert percentage into fraction Let us consider an example. Example 2: Convert the following percentages into fractions: a) 73 % b) 1 % c) 6.5 % d) 10 % e) 18.6 % Percentages 83

Solution: S.No. Percent Fraction a) 73 % 73 b) 1 % 100 1 c) 6.5 % 100 6.5 = 65 100 1000 d) 10 % 10 100 e) 18.6% 18.6 = 186 100 1000 Pictorial representation Look at the following circles. Each of the circles is divided into parts coloured differently. These parts can be written in percentages. Let us understand the pictorial representation of fractions with the help of this example. Circle Fraction Percentage a) Of the 4 equal parts into Percentage of orange parts b) which the circle is divided, 1 = 1 × 100 % = 25 % part is coloured orange and 4 3 parts are coloured green. Percentage of green parts = Therefore, the fractions 3 × 100 % = 75 % representing them are 1 4 and 3 respectively. 4 4 Of the 5 equal parts into Percentage of pink parts = which the circle is divided, 2 × 100 % = 40 % 2 parts are coloured pink 5 and 3 parts are coloured orange. Therefore, the Percentage of orange parts fractions representing them = 3 × 100 % = 60 % are 2 and 3 respectively. 5 55 84

Circle Fraction Percentage Of the 10 equal parts into Percentage of red parts = 2 × 100 % = 20 % which the circle is divided, 2 parts are coloured red 10 c) and 8 parts are coloured Percentage of orange parts = 8 × 100 % = 80 % orange. Therefore, the fractions representing them 10 are 2 and 8 respectively. 10 10 Convert percentage into decimal To convert a percentage into a decimal, write the number without the percent symbol and place a decimal point after two digits from its right. Let us consider an example. Example 3: Convert into decimals: a) 200% b) 13% c) 150% d) 25% e) 300% Solution: S.No. Percent Decimal a) 200 % 2.0 b) 13 % 0.13 c) 150 % 1.5 d) 25 % 0.25 e) 300 % 3.0 ? Train My Brain Answer the following: a) Convert 81 into percentage. 100 b) Convert 23% into fraction. c) Convert 122% into decimal. Percentages 85

I Apply Let us now see some real-life examples in which conversion of decimals and percentages are used. Example 4: There are 40 mangoes and 60 apples in a basket. What percent of the fruits in the basket are mangoes and apples? Solution: Total number of fruits = 40 + 60 =100 Fraction of mangoes = 40 100 Percentage of mangoes = 40 × 100 % = 40% 100 Fraction of apples = 60 100 Percentage of apples = 60 × 100 % = 60 % 100 Example 5: Madhu secured 9 in Mathematics and 46 in Science. 10 50 In which subject did Madhu perform better? Solution: Mathematics score is out of 10 marks and Science score is out of 50 marks. So, we cannot compare both directly. We have to find the percentage of his scores in the two subjects to compare them. 9 as a percentage = 9 × 100 % = 90% 10 10 46 as a percentage = 46 × 100% = 92% 50 50 92% > 90% Therefore, Madhu performed better in Science. I Explore (H.O.T.S.) Let us solve a few more examples of percentages. Example 6: Out of a class of 35 students, 28 students know swimming. What percent of students do not know swimming? Solution: Total number of students = 35 86

Number of students who know swimming = 28 Number of students who do not know swimming = 35 – 28 = 7 Fraction of students who do not know swimming =7 35 Percent of students who do not know swimming =7 × 100 % = 1 × 100 % 35 5 =20% Example 7: Sanjay has ` 800. He spent 20% on petrol and ` 240 on food. How much percent of the total amount is left? Solution: Sanjay’s income = ` 800 Percent of income spent on petrol = 20% Amount spent on petrol = 20 × 800 = ` 160 100 Amount spent on food = ` 240 Total amount spent = ` 160 + ` 240 = ` 400 Amount left with Sanjay = ` 800 – ` 400 = ` 400 Percent of amount left with Sanjay =` 400 × 100% = 50% 800 Therefore, 50% of the total amount is left. Maths Munchies How to find the percentage of a fraction quickly. a) When the denominator is 50, we multiply both the numerator and denominator by 2. b) When the denominator is 25, we multiply both the numerator and denominator by 4. c) When the denominator is 20, we multiply both the numerator and denominator by 5. Percentages 87

Connect the Dots English Fun The word percentage comes from the Latin ‘per-centum’ which means for every 100. Science Fun Did you know that: a) 40% of the Giant Panda’s hair is black. b) 95% of the jellyfish is water. c) 70% of the body of an adult is made up of water. Drill Time 13.1 Introduction to Percentage 1) Convert these fractions into percentages: a) 21 b) 67 c) 20 d) 83 e) 32 50 100 50 150 100 2) Convert these percentages into fractions: a) 0.45% b) 7.6% c) 43% d) 53% e) 24% 3) Identify the percentages of the green coloured parts in the following circles. a) b) c) 88

4) Complete the table. Percent S.No Decimal Fraction a) 1.5 b) 8 10 c) 26% d) 18 e) 0.65 100 5) Word problems a) There are 30 blue ribbons and 50 red ribbons in a box. What percent of ribbons in the box are blue and red? b) Of a group of 25 children in a locality,18 know singing. What percent of children do not know singing? A Note to Parent Ask your child to observe the percentage of ingredients on the labels of two different packaged foods. Encourage the child to pay attention to the label of ingredients and the expiry date. Percentages 89

14Chapter Measurement I Will Learn About • the relation between different units of length, weight and capacity. • converting larger units to smaller units and vice versa. • applying the four operations in solving problems involving length, weight and capacity. • computing the area and perimeter of simple geometrical shapes. 14.1 Conversion of Units of Measurement I Think Pooja uses 17.5 cm of wool to make a friendship bracelet. How can Pooja find out how much wool she will need to make 3 such friendship bracelets? I Recall We know the standard units of length are cm, m and km. The standard units of weight are mg, g and kg. Similarly, the standard units of capacity are mℓ, ℓ and kℓ. We can convert one unit of measurement into another using the relation between them, i.e., 1 m = 100 cm 1 cm = 10 mm 1 g = 1000 mg 1 ℓ = 1000 mℓ 1 km = 1000 m 1 m = 1000 mm 1 kg = 1000 g 1 kℓ = 1000 ℓ To convert measures from a larger unit to a smaller unit, we multiply. To convert measures from a smaller unit to a larger unit, we divide. 90

Let us solve the following to recall the concept. a) Convert 4 kg 200 g into g. b) Convert 3 ℓ 194 mℓ into mℓ. c) Convert 4716 g into kg and g. d) Convert 6295 m into km and m. I Remember and Understand Let us understand the conversions of units through a few examples. Example 1: Convert the following: a) 1800 mg into g b) 4 km 460 m into km c) 5 ℓ 70 mℓ into ℓ d) 82.3 m into mm e) 24.339 kg into kg and g Solution: Solved Solve these a) 1800 mg into g 3640 g into kg 1 g = 1000 mg Therefore, 1800 mg = 1800 g = 1.800 g. 1000 b) 4 km 460 m into km 11 kℓ 420 ℓ into kℓ 1 km = 1000 m Therefore, 460 m = 460 km = 0.46 km. 1000 4 km 460 m = 4 km + 0.46 km = 4.46 km c) 5 ℓ 70 mℓ into ℓ 8 kg 19 g into kg 1 ℓ = 1000 mℓ Therefore, 70 mℓ = 70 ℓ = 0.07 ℓ. 1000 5 ℓ 70 mℓ = 5 ℓ + 0.07 ℓ = 5.07 ℓ d) 82.3 m into mm 7.35 kℓ into ℓ 1 m = 1000 mm Therefore, 82.3 m = 82.3 × 1000 mm = 82300 mm e) 24.339 kg into kg and g 6.029 km into km and m 1 kg = 1000 g Therefore, 24.339 kg = 24 kg + 0.339 kg = 24 kg + 0.339 × 1000 g = 24 kg 339g Measurement 91

Example 2: Compare the given measures using <, > or =. One has been done for you. a) 65 ℓ > 64490 mℓ b) 1500 g ______ 1 kg For comparing c) 3.22 m ______ 322 cm d) 2202 m ______ 2.2 km two different units of measurement, e) 7190 mg ______ 7.09 g f) 8.45 kℓ ______ 8450 ℓ first convert them into the same ? Train My Brain unit. Answer the following: a) Convert 3.289 kg into kg and g. b) Convert 2983 mℓ into ℓ. c) Convert 7 m 9 cm into m. I Apply We can apply different operations on length, weight or volume just as we do with numbers. Example 3: Solve the following: a) Add 42.628 g and 67.453 g. b) Subtract 62.142 mℓ from 85.033 mℓ. c) Multiply 254 m by 14 and covert into km. d) Divide 6129 cm by 3 and convert into mm. Solution: Solved Solve these a) Add 42.628 g + 67.453 g Add 59.302 ℓ and 32.158 ℓ. 11 1 4 2.628 + 6 7.453 1 1 0.081 Therefore, 42.628 g + 67.453 g = 110.081 g. 92

Solved Solve these Subtract 9.318 km from 35.294 km. b) 85.033 mℓ – 62.142 mℓ 9 3 2 Multiply 41.8 kg by 26. 4 1/0 13 /0 3/ 1 8 5/ . 14 –62 . 89 22 . Therefore, 85.033 mℓ – 62.142 mℓ = 22.891 mℓ. c) 254 m × 14 21 2 54 × 14 1 0 16 +2 5 40 3 5 56 Therefore, 254 m × 14 = 3556 m 1 km = 1000 m Therefore, 3556 m = 3556 km = 3.556 km 1000 d) 6129 cm ÷ 3 Divide 208 cm by 4. 2043 )3 6129 − 6↓ 01 − 00 012 − 12 09 − 09 00 Therefore, 6129 cm ÷ 3 = 2043 cm 1 cm = 10 mm Therefore, 2043 × 10 = 20430 mm Measurement 93

I Explore (H.O.T.S.) Let us see a few real-life examples of operations on the units of measurement. Example 4: Sakshi buys 72.39 kg flour every month for her bakery. How much flour does she buy in a year? Solution: Quantity of flour bought by Sakshi every month = 72.39 kg Number of months in a year = 12 Quantity of flour bought by Sakshi in a year = 72.39 kg × 12 = 868.68 kg Therefore, Sakshi buys 868.68 kg flour in a year. Example 5: Lohit has a piece of wood of length 117 m. He wants to cut it into 3 pieces of the same length. How long would each piece be in centimetres? Solution: Length of the piece of wood that Lohit has = 117 m Number of equal pieces Lohit wants to cut the wood into = 3 Length of each piece of wood = 117 m ÷ 3 = 39 m = 3900 cm Therefore, each piece of wood would be 3900 cm long. 14.2 Area and Perimeter I Think Pooja wanted to cut some handkerchiefs of different shapes from a piece of cloth. She also wanted to attach lace to their edges on all sides. But she did not know how much cloth she needed. She also wanted to know what length of lace is required. How do you think she can find the length of the cloth and the length of the lace needed for the same? I Recall Recall that perimeter is the length of the outline of a shape. To find the perimeter of a rectangle or square, we add the lengths of all its four sides. The units of perimeter of a shape is the same as the units of the lengths of its sides. 94

Area of a shape is the amount of surface or region covered by it. The area of a shape is expressed in square units (the unit of length of the side of the shape). Area of a rectangle = length × breadth = ℓ × b sq. units Area of a square = side × side = s × s sq. units Let us solve the following to recall the concept. Find the perimeter and area of each of the given shapes. a) 5 cm b) 8 cm 4 cm c) 5 cm 5 cm 7 cm I Remember and Understand We know that the perimeter is the length of the outline of a shape. We can also calculate it for shapes other than a square and a rectangle. Let us see a few examples. Example 6: Find the perimeter of each of the given shapes. 5 cm 6 cm a) 4.5 cm b) 3 cm 3 cm 2 cm 5.5 cm 3 cm 3 cm 3 cm 6 cm Solution: a) Perimeter = Sum of all the sides = (5 + 5.5 + 3 + 2 + 4.5) cm = 20 cm b) Perimeter = Sum of all the sides = (6 + 3 + 3 + 6 + 3 + 3) cm = 24 cm Example 7: Find the perimeter and area of each of the given figures if the side of each square is 1 cm. Measurement 95

a) b) c) Solution: a) Perimeter of the given figure = (2 + 2 + 2 + 3 + 2 + 4 + 6 + 3) cm = 24 cm Side of each square = 1 cm So, its area = 1 × 1 sq. cm = 1 sq. cm. The number of squares coloured = 16 Therefore, the area of the given figure is 16 sq. cm. b) Perimeter of the given figure = (4 + 1 + 2 + 4 + 4 + 1 + 2 + 4) cm = 22 cm The number of squares coloured = 26 The area of each square of side 1 cm = 1 sq. cm. Therefore, the area of the given figure is 26 sq. cm. c) Perimeter of the given figure = (6 + 5 + 6 + 1 + 3 + 1 + 2 + 1 + 3 + 1 + 4 + 1) cm = 34 cm The number of squares coloured = 22 The area of each square of side 1 cm = 1 sq. cm. Therefore, the area of the given figure is 22 sq. cm. Area of a triangle Observe the triangles formed in these figures. The diagonal of a rectangle or a square divides it into two equal triangles. Thus, the surface or region covered by the triangle formed 1 cm = 1 of the total region covered by the rectangle or square. 1 cm 2 Therefore, the area of a triangle formed from a rectangle 1 = 2 × the area of the rectangle 96