ARITHMETIC 151 12.1 Tenths Decimal Numbers Read, Think and Learn In the given diagram, one part is shaded out of ten parts. It means 1 10 = 0.1, which is read as zero point one or one-tenth. In the given diagram, two parts are shaded out of ten parts. It means 2 10 = 0.2, which is read as zero point two or two-tenths. In the given diagram, three parts are shaded out of ten parts. It means 3 10 = 0.3, which is read as zero point three or three-tenths. In the given diagram, five parts are shaded out of ten parts. It means 5 10 = 0.5, which is read as zero point five or five-tenths. In the number line, the interval between two numbers may be divided into ten equal parts to represent tenths. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10
152 The Leading Mathematics - 4 1. Write the coloured parts in fraction and decimal. (a) (b) (c) EXERCISE 12.1 Your mastery depends on practice. Practice like you play. Whole parts shaded 3 parts shaded = 1 3 10 = 1.3 (One point three) Integral part Decimal part We may represent the whole and the fractional part and the corresponding decimal representation in a number line as in the following : 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 1 1 10 1 2 10 1 3 10 1 4 10 1 5 10 1 6 10 1 7 10 1 8 10 1 9 10 1 10 10 1 = 1 + 1 = 2 Similarly, 2 3 10 = 2.3, 3 7 10 = 3.7, 8 8 10 = 8.8, 12 3 10 = 12.3 and so on. 3 10 = 0.3
ARITHMETIC 153 (d) (e) (f) 2.0 2.1 2.2 2.9 3.0 2 1 10 2 2 10 2 10 10 2 (a) 5.0 5.7 6.0 5 3 10 5 7 10 5 10 10 5 (b) 15.0 15.4 16.0 15 4 10 15 (c) 2. Write the following decimal numbers in words : (a) 0.6 (b) 0.9 (c) 1.7 (d) 2.1 (e) 3.4 (f) 13.5 3. Write in decimal form: (a) 4 tenths (b) 7 tenths (c) 25 tenths (d) 64 tenths (e) 77 tenths (f) 96 tenths 4. Copy and complete the following number lines :
154 The Leading Mathematics - 4 1. Write the different coloured parts in fraction and decimal : One part is shaded in 100 equal parts. In fraction, 1 100. Using decimal, 1 100 = 0.01 0.01 is read as zero point zero one. Red = 9 100 = 0.09, which is read as zero point zero nine Green = 11 100 = 0.11, which is read as zero point one one Hundredths in Number Line One tenth in the number line may be divided into 10 equal parts so that the interval between two numbers is divided into hundred equal parts, called hundredths. (a) (b) (c) 12.2 Hundredths Decimal Numbers EXERCISE 12.2 Your mastery depends on practice. Practice like you play. Read, Think and Learn
ARITHMETIC 155 (d) (e) (f) 2. Copy and complete the given table : Fraction 7 100 9 100 22 100 37 100 53 100 69 100 87 100 99 100 Name Seven hundredth Decimal 0.07 Name Zero point zero seven 3. Write in decimal form: (a) 25 hundredths (b) 135 hundredths (c) 1285 hundredths 4. Write in words: (a) 0.12 (b) 0.35 (c) 1.25 (d) 4.05 (e) 14.75 5. Copy and complete the following number lines. (a) (b) (c) (d) 4.20 4.21 4.30 4 21 100 12.70 12.80 12 73 100 17.90 18.00 17 95 100 1.00 1.05 1.07 1.10 1 1 100 1 4 100 1 10 100
156 The Leading Mathematics - 4 12.3 Place Value of Decimal Number Read, Think and Learn Place value table is as follows : Integral part (whole no.) Decimal Decimal part Thousands Hundreds Tens Ones Point Tenths Hundredths Thousandths 1000 100 10 1 . 1 10 = 0.1 1 100 = 0.01 1 1000 = 0.001 Take a decimal number 2734.125, in which 2734.125 Decimal (Point) Thousandths Hundredths Tenths Thousands Hundreds Tens Ones Show the above decimal number in the place value table as follows: Integral part (whole no.) Decimal Decimal part Thousands Hundreds Tens Ones Point Tenths Hundredths Thousandths 2 7 3 4 . 1 2 5 Express 2734.125 as expanded form as given below : 2734.125 = 2 × 1000 + 7 × 100 + 3 × 10 + 4 × 1 + 1 × 1 10 + 2 × 1 100 + 5 × 1 1000 = 2000 + 700 + 30 + 4 + 0.1 + 0.02 + 0.005 = 2 thousands + 7 hundreds + 3 tens + 4 ones + 1 tenths + 2 hundredths + 5 thousandths.
ARITHMETIC 157 1. Show the following decimal numbers in the place value table : (a) 0.1 (b) 2.13 (c) 56.135 (d) 785.135 (e) 413.01 2. Write the decimal numbers from the following : (a) 3 tenths 5 hundredths (b) 3 hundreds 3 ones 5 hundredths (c) 2 + 1 10 + 2 200 (d) 2 × 100 + 1 × 10 + 3 × 1 10 + 4 × 1 100 3. Express the following decimal numbers in expanded form : (a) 0.20 (b) 4.12 (c) 32.35 (d) 251.265 (e) 5789.231 EXERCISE 12.3 Your mastery depends on practice. Practice like you play. 12.4 Changing Fraction into Decimal Read, Think and Learn Fraction Decimal Decimal Name 5 10 0.5 Five tenths 23 10 2.3 Two ones 3 tenths 5 100 0.05 Five hundredths 35 100 0.35 Three tenths five hundredths 12 47 100 12.47 One tens two ones four tenths seven hundredths 2 473 1000 2.473 Two ones 4 tenths seven hundredths 3 thousandths
158 The Leading Mathematics - 4 1. Change the following fractions into tenths : (a) 1 5 (b) 3 2 (c) 4 2 5 (d) 1 1 2 (e) 7 3 5 (f) 12 4 5 (g) 17 1 5 (h) 39 1 2 2. Express the following fractions into hundredths : (a) 1 20 (b) 6 25 (c) 24 50 (d) 3 25 (e) 24 25 (f) 47 50 (g) 25 4 (h) 60 25 (i) 63 5 (j) 4 5 (k) 3 2 (l) 41 50 EXERCISE 12.4 Your mastery depends on practice. Practice like you play. Change 1 2 into tenths. Here, 1 2 = 1 × 5 2 × 5 = 5 10 = 0.5 Convert 1 25 into hundredths. Here, 1 25 = 1 × 5 25 × 4 = 4 100 = 0.04 Express 11 4 into hundredths. Here, 11 4 = 11 × 25 4 × 25 = 275 100 = 2.75 Change 21 8 into thousands. Here, 2 1 8 = 21 × 125 8 × 125 = 2 125 1000 = 2.125 How to do denominator 10 ? 2 × 5 = 10 = = 0.5 = 1 25 4 100 = 0.04
ARITHMETIC 159 (m) 5 3 25 (n) 35 7 20 (o) 42 3 4 (p) 68 1 2 (q) 25413 5 (r) 452 4 25 (s) 589 3 20 (t) 479 1 4 3. Convert the following fractions into thousandths : (a) 1 2 (b) 3 4 (c) 5 8 (d) 4 25 (e) 17 50 (f) 201 250 (g) 7 5 (h) 31 25 (i) 13 8 (j) 207 125 (k) 257 500 (l) 37 50 (m) 2 1 4 (n) 15 1 25 (o) 103 57 125 (p) 4511 2 (q) 34214 25 (r) 6787 8 (s) 983347 500 (t) 991 99 125 12.5 Changing Decimal into Fraction Read, Think and Learn 3.7 = 37 10 3.7 = 3 + 0.7 = 3 + 7 10 = 3 7 10 0.27 = 027 100 = 27 100 2.128 = 2128 1000 = 2128 1000 = 2 128 1000 = 2 16 × 8 125 × 8 = 2 16 125 For identifying denominator of the required fraction, write 1 instead of decimal point and add zero because there is only one digit after decimal point. After decimal point, there are two digits, in the case of hundredths. 2128 2 –2000 128 1000 Oh! it is another method.
160 The Leading Mathematics - 4 Express the decimal numbers into fraction or mixed fraction in the simplest form. 1. (a) 0.3 (b) 0.2 (c) 0.6 (d) 0.8 (e) 0.9 (f) 1.7 (g) 12.6 (h) 26.4 (i) 36.9 (j) 54.8 (k) 63.7 (l) 45.6 2. (a) 0.23 (b) 0.48 (c) 0.56 (d) 0.78 (e) 0.98 (f) 1.24 (g) 8.46 (h) 10.26 (i) 34.68 (j) 50.75 (k) 52.17 (l) 56.16 3. (a) 0.237 (b) 0.125 (c) 0.144 (d) 0.455 (e) 0.555 (f) 1.248 (g) 8.294 (h) 26.268 (i) 128.378 (j) 329.998 (k) 512.715 (l) 516.616 EXERCISE 12.5 Your mastery depends on practice. Practice like you play. Change into fraction : (a) 0.8 = 08 10 = 4 × 2 5 × 2 = 4 5 (b) 0.25 = 025 100 = 1 × 5 × 5 4 × 5 × 5 = 1 4 (c) 0.27 = 027 100 = 27 100 (d) 3.478 = 3 478 1000 = 3 239 × 2 300 × 2 = 3239 500 If you ate some pieces of circular bread which are equally divided. Write the eaten breads in to fraction and convert into decimal also. Prepare a report and present it in your classroom. PROJECT WORK
ARITHMETIC 161 CHAPTER 13 Percentage How many shaded portions are there in the above triangle? Tell the fraction of the shaded portion of the triangle. How many parts of the stick are with red colour? How many parts of the stick points are with blue? Tell the fractions for the red and blue colours of the stick. How much percentage remains the battery in the first mobile? How much percentage reaches the battery in the second mobile? How much percentage gives the discount on the sales of the shop? How much percentage is paid for the goods of the shop? WARM-UP Lesson Topics Pages 13.1 Introduction to Percentage 162 13.2 Changing Fraction into Percent 163 13.3 Converting Percent into Fraction 165 13.4 Expressing Percent into Decimal and Decimal into Percent 166 13.5 Verbal Problems on Fraction, Decimal and Percentage 168 19% 70% UP TO 50% DISCOUNT SUPER SALE
162 The Leading Mathematics - 4 1. Write the following in the form of percent. (a) 80 percent (b) 28 percent (c) 78 percent (d) 99 percent In the figure, 23 out of 100 equal parts are shaded. The shaded parts indicate the fraction 23 100. Another way of expressing fraction with denominator 100 is by means of percentage having the meaning of out of hundred. We write 23% and read as “23 per cent. Equivalently, 0.23 = 23%. Percentage is a fraction with denominator 100 i.e. it means “Out of 100”. e.g. 27 100 = 27%, 50 100 = 50%, etc. The symbol % stands to mean percentage. Coloured Parts = 23% Blank Parts = 67% Total Parts = 100% 13.1 Introduction to Percentage EXERCISE 13.1 Your mastery depends on practice. Practice like you play. 23 100 + 67 100 = 23 + 67 100 + 100 100 =1 0.23 + 0.67 = 1.00 = 1 Read, Think and Learn
ARITHMETIC 163 2. Write the percentage of the coloured parts and the blank parts in each figure. (a) (b) (c) 3. Express the following fractions in percentage. (a) 15 100 (b) 27 100 (c) 47 100 (d) 105 100 (e) 120 100 (f) 999 100 Consider a fraction 3 5. What percent is 3 5 ? Now, 3 5 = 3 × 20 5 × 20 = 60 100 = 60 × 1 100 = 60% Similarly, 1 2 = 1 × 50 2 × 50 = 50 100 = 50 × 1 100 = 50% In other hand, 2 5 = 2 5 × 100% = 200 5 % = 40% 200 40 –20 0 –0 0 5 13.2 Changing Fraction into Percent Read, Think and Learn I know, the percent means out of 100. i.e. Fraction with denominator 100 5 × 20 = 100
164 The Leading Mathematics - 4 1. Express the following fractions into percentage: (a) 1 2 (b) 4 5 (c) 1 4 (d) 3 10 (e) 17 20 (f) 23 25 (g) 5 2 (h) 7 5 (i) 9 2 (j) 75 50 (k) 99 10 (l) 29 10 (m) 51 25 (n) 2 3 4 (o) 5 7 10 (p) 131 2 (q) 15 7 50 (r) 1317 25 EXERCISE 13.2 Your mastery depends on practice. Practice like you play. 100 20 –10 0 –0 0 5 Convert 23 5 into percentage. Here, 23 5 = 2 × 5 + 3 5 = 10 + 3 5 = 13 5 × 100% = 13 × 20% = 260% 1 4 = 1 4 × 100% = 25% 100 25 – 8 20 –20 0 4
ARITHMETIC 165 13.3 Converting Percent into Fraction Read, Think and Learn v Samir takes 50% profit by selling an article. How many parts does he gain? 50% means 50 parts is shaded out of 100 equal parts. 50% are exactly divided into two parts and one of them is coloured as shown in the figure \ 50% = 1 2 = 0.5 v 30% students are absent on the class 4. How many parts are absent of total students? Similarly, 30% = 3 10 = 0.3 v Express 40% into fraction. Here, 40% = 40 × 1 100 = 40 100 = 2 × 2 × 2 × 5 2 × 2 × 5 × 5 = 2 5 Again, 40% = 40 100 = 0.40 = 0.4 v Convert 225% into mixed fraction. Here, 225% = 225 × 1 100 = 225 100 = 3 × 3 × 5 × 5 2 × 2 × 5 × 5 = 3 × 3 2 × 2 = 9 4 = 2 1 4 Again 225% = 225 100 = 2.25 9 2 –8 1 4
166 The Leading Mathematics - 4 13.4 Expressing Percent into Decimal and Decimal into Percent Read, Think and Learn 1. Convert the following percentage into fraction. (a) 50% (b) 25% (c) 20% (d) 75% (e) 1% (f) 64% (g) 16% (h) 13% (i) 35% (j) 60% (k) 68% (l) 76% (m) 80% (n) 90% (o) 99% (p) 82% (q) 94% (r) 87% (s) 98% (t) 88% 2. Express the following percentage into mixed fraction. (a) 110% (b) 113% (c) 125% (d) 120% (e) 135% (f) 138% (g) 155% (h) 164% (i) 170% (j) 180% (k) 198% (l) 220% (m) 240% (n) 248% (o) 252% (p) 305% (q) 344% (r) 450% (s) 460% (t) 498% EXERCISE 13.3 Your mastery depends on practice. Practice like you play. Percent to Decimal 25% = 25 × 1 100 = 25 100 = 0.25 127% = 127 × 1 100 = 127 100 = 1.27 5.6% = 5.6 × 1 100 = 56 10 × 1 100 = 56 1000 = 0.056 Note : The decimal point is moved two places left in this case. Step-1: Replace % by 100 1 and obtain fraction. Step-2: Convert the decimal into decimal number
ARITHMETIC 167 1. Convert the following percentage into decimal numbers : (a) 2% (b) 5% (c) 7% (d) 12% (e) 18% (f) 20% (g) 35% (h) 40% (i) 56% (j) 70% (k) 78% (l) 90% (m) 99% (n) 110% (o) 130% (p) 144% (q) 220% (r) 350% (s) 480% (t) 525% 2. Express the following decimal numbers into percentage. (a) 0.03 (b) 0.09 (c) 0.1 (d) 0.25 (e) 0.27 (f) 0.3 (g) 0.43 (h) 0.48 (i) 0.87 (j) 0.98 (k) 1.28 (l) 3.20 (m) 8.3 (n) 4.25 (o) 7.39 (p) 2.5 (q) 10.2 (r) 12.23 (s) 14.15 (t) 19.99 EXERCISE 13.4 Your mastery depends on practice. Practice like you play. Decimal to Percent 0.4 = 4 10 × 10 10 = 40 100 = 40 × 1 100 = 40% 0.35 = 35 100 = 35 × 1 100 = 35% 0.327 = 327 1000 = 327 10 × 1 100 = 32.7% Note : In this case, the decimal point is shifted two places to the right. Step-1: Convert decimal number into fraction. Step-2: Make denominator 100 in the fraction. Step-3: Replace 1 100 by % Express your obtained marks of the full marks 40 in mathematics in fraction and decimal forms. What is the percent of marks obtained in mathematics? Find it. Prepare a report and present it in your classroom. PROJECT WORK
168 The Leading Mathematics - 4 13.5 Verbal Problems on Fraction, Decimal and Percentage v There are 55 boys in class 4 out of 100 students. Write the number of boys and girls in fraction, decimal and percentage. Given, Total number of students = 100 Number of boys = 55 Number of girls = 100 – 55 = 45 Now, Fraction of boys = 55 100 = 11 20 Fraction of girls = 45 100 = 9 20 Decimal of boys = 0.55 Decimal of girls = 0.45 Percentage of boys = 55% Percentage of girls = 45% EXERCISE 13.5 Your mastery depends on practice. Practice like you play. 1. Write the shaded portion in fraction decimal and percentage. (a) (b) Read, Think and Learn
ARITHMETIC 169 (c) (d) (e) (f) 2. (a) Jasmin secured 65 marks out of 100 in Maths. Write her marks in fraction, decimal and percentage. Marks in fraction = ............. Marks in decimal = ............. Marks in percentage = ............. (b) There are 37 boys in a class. Write it in fraction, decimal and percentage. Fraction of boys = ......... Decimal of boys = ........... Percentage of boys = .............
170 The Leading Mathematics - 4 (c) 7 students are absent in an examination. Write the number of absent students in fraction, decimal and percentage. Number of absent students in fraction = ............ Number of absent students in decimal = ............ Number of absent students in percentage = ............ 3. (a) There are 27 girls in a class out of 100. How many boys are there in the class? Also, express it in fraction, decimal and percentage. Given, total number of students in a class 100 Number of girls = 27 \ Number of boys = 100 – 27 = ...... Now, Fraction of boys = ............ Decimal of boys = ........... Percentage of boys = ............ (b) 35l of water is mixed in the drum of pure milk of 100l. Write the quantity of pure milk in fraction, decimal and percentage. Given, total quantity of mixture of milk = 100l Quantity of water in the mixture = ........... \ Quantity of pure milk in the mixture = .......... Now, Fraction of pure milk = ............ Decimal of pure milk = ............ Percentage of pure milk = .......... (c) 10 students are absent in a class of 100 students. Write the number of students also absent in the class in fraction, decimal and percentage. Given, total students in a class = ........... Number of absent students = ........... Number of present students = ...........
ARITHMETIC 171 Now, Fraction of present students = ............ Decimal of present students = ............ Percentage of present students = ............... 4. (a) Pramod sells a book of the cost Rs. 100 for Rs. 130. Write the selling price and profit in fraction, decimal and percentage. Given, cost price of a book = Rs. ............. Selling price of a book = Rs. .......... \ Profit amount = .......... Now, Profit in fraction = ............ Profit in decimal = ........... Profit in percentage = .......... (b) Binod buys a pen for Rs. 100 and sells a loss of Rs. 25. Write the loss amount and selling price in fraction, decimal and percentage. Given, cost price of a pen = ............. Loss amount = ...... \ Selling price of the pen = ........ Now, Loss amount in fraction = ........... Loss amount in decimal = ..........
172 The Leading Mathematics - 4 1. Four number are shown in the numbered cards as shown alongside. (a) Write the smallest number made by the above 4 digits and separate by commas. (b) Write the greatest number made by the above 4 digits and write it in national number system in word. (c) Round the greatest number nearest to hundreds. (d) Present the smallest number in place value chart. 2. The results of the 2078 Census has declared 5 districts with the highest population in Nepal as follows: (a) Write the population of Kathmandu in national number system by separating commas. (b) Write the population of Rupandehi in place value chart. 3. The results of the 2078 Census has declared 5 districts with the lowest population in Nepal as follows: (a) Write the population of Humla in place value chart. (b) Round the population of Manang nearest to hundreds. (c) Find the total population in Dolpa and Rasuwa Districts. (d) How many more people are in Humla than Manang? 4. The rates of 4 fruits per kilogram are as follows: Apple : Rs. 325 Orange : Rs. 165 Papaya : Rs 90 Grapes : Rs. 280 (a) What is the cost of 12 kg of apples? Multiply 325 × 12. (b) What is the cost of 10 kg of papayas? 5 7 8 9 District Population Kathmandu 20,41,587 Morang 11,48,156 Rupandehi 11,21,957 Jhapa 9,98,054 Sunsari 9,26,962 District Population Manang 5,658 Mustang 14,452 Dolpa 42,774 Rasuwa 46,689 Humla 55,394 MIXED PRACTICE–II Read, Understand, Think and Do
ARITHMETIC 173 (c) How many kg of papayas can be bought in Rs. 720? (d) Is Rs. 1000 sufficient for 4 kg oranges and 1 kg of apple? Calculate. 4. Ram had Rs. 40 in his pocket, he spent Rs. 10 and he distributed Rs. 10 for brother and Rs. 15 for sister but his mother gave him Rs. 15. (a) Write the above statement in mathematical form. (b) How much amount does Ram have? 5. Some fractions are shown in the figure. (a) Write the differences between proper and improper fraction. (b) Write proper fraction, improper fraction and mixed number from the above fractions. (c) In the given above 3 4 5 is a mixed number. Justify. 6. Here are given two like fractions in the figure. (a) Write the fraction of the shaded part to the unshaded part from the first figure. (b) Compare which of them has greater fraction shaded? (c) Can we add and subtract two given fractions? Write with reason. 7. In the given 100 square box, some are shaded and remaining are unshaded. (a) How many square boxes are shaded? (b) What percentage of the parts are shaded ? (c) How many additional square boxes should be shaded to get 50% shaded ? 3 5 3 5 3 3 5
174 The Leading Mathematics - 4 1. Four numbers are shown in the numbered card as shown below. 8 3 5 1 7 4 2 (a) Write the smallest number formed by the above digits by using commas in national system. [1] (b) Write the greatest number made by the above digits and write it in national number system in word. [1] (c) Round the smallest number nearest to hundreds. [1] (d) Present the greatest number in place value chart. [2] 2. Observe the cost of two models of mobiles sets HUAWEI and POCO aside. (a) A customer wants to buy both mobile sets. How much will s/he pay? [1] (b) Which mobile set is expensive and by how much? [1] (c) Another customer wants to buy 25 POCO mobile set. How much will s/he pay? [2] (d) How many times is the POCO expensive than HUAWEI ? Find it. [2] 3. Observe the shaded and unshaped parts in the given grid paper and answer the following questions. (a) Write the fraction of the shaded parts. [1] (b) Write the decimal of the unshaded parts. [1] (c) What percentages of the parts are shaded ? [1] (d) How many additional square boxes should be shaded to get 50% shaded? [2] 4. (a) Simplify: 535 + 565 × 14 – 391 ÷ 13 [2] (b) Simplify: 43 8 + 31 8 – 55 8 [2] Price: Rs.1265 Price: Rs.15180 HUAWEI Attempt all the questions. FM : 20 Time : 40 Min. CONFIDENCE LEVEL TEST II ARITHMETIC
ARITHMETIC 175 MEASUREMENT UNIT V Estimated Working Hours : 35 COMPETENCY Solution of behaviour problems of daily life related to measurement CHAPTERS 14 Time 15 Money 16 Distance 17 Capacity 18 Weight 19 Perimeter, Area and Volume LEARNING OUTCOMES After completion of this content area, the learner is expected to be able to: convert the units of time each other, add and subtract the following units of time; (year and month, week and day, day and hour, hour and minute), multiply and divide the rupees and paisa, convert the units of distance each other (centimeter and millimeter, meter and centimeter, kilometer and meter), add and subtract on centimeter and meter, meter and kilometer, convert litre and millilitre, add and subtract litre and millilitre, convert the units of weight each other (kilogram and gram, kilogram and quintal), add and subtract on gram, kilogram and quintal, find area and perimeter of rectangular and square surface by using square grids,
176 The Leading Mathematics - 4 CHAPTER 14 Time How many days are there in a year, a month and a week? How many hours are there in 1 day ? What are day and night ? Which types of hands are called hour hand, minute hand and second hand ? How many small line segments or scale are there in the clock? How many minutes are there in 1 hour ? What is the time in the adjoining clock ? Do you add and subtract any two numbers formed by two digits? WARM-UP Lesson Topics Pages 14.1 Review on Writing Time 177 14.2 Review on Telling Time 179 14.3 Relation between Day, Hour, Minute and Second 182 14.4 Relation between Year, Month, Week and Day 185 14.5 Adding Time 187 14.6 Subtracting Time 189 14.7 Verbal Problems of Time on Addition and Subtraction 191
ARITHMETIC 177 What is the time in watch and digital clock? Write. In watch; ........... and in digital clock; ............ Reading Hour and Minute Reading Hour, Minute and Second 12 3 9 10 1 7 4 11 2 8 5 6 The hour hand has slightly moved from 2 and the minute hand is at 4. The time is now 2:4 × 5 = 2:20 i.e. 2 hours 20 minutes, read as 20 minutes past 2. 12 3 9 10 1 7 4 11 2 8 5 6 The hour hand is far from 10 and nearer to 11, the minute hand is at 9 and the second hand is at 5. The time is now 10:9 : 5 × 5 10:45:25 i.e. 10 hours, 45 minutes and 25 seconds. By neglecting second, it is read up quarter to 11. i.e. 45 minutes past 10. A clock has three hands : Hour hand, minute hand and second hand. When they round one complete revolution, they move 60 units according as hands. Hour Hand : It indicates hour unit of time, which is the shortest and thick than other hands. Minute Hand : It indicates minute unit of time, which is longer than hour hand. Second Hand : It indicates second unit of time, which is longest and thinner than minute hand. There are 12 numbers from 1 to 12 in a clock. The units between each nearer pair is number is 5. In one revolution, each hand covers 60 units. 12 9 3 10 1 7 4 11 2 8 5 6 2:20 11:45 14.1 Review on Writing Time Read, Think and Learn
178 The Leading Mathematics - 4 1. Write the time shown in the following clocks : 12 3 9 10 1 7 4 11 2 8 5 6 12 3 9 10 1 7 4 11 2 8 5 6 12 3 9 10 1 7 4 11 2 8 5 6 12 3 9 10 1 7 4 11 2 8 5 6 12 3 9 10 1 7 4 11 2 8 5 6 12 3 9 10 1 7 4 11 2 8 5 6 12 3 9 10 1 7 4 11 2 8 5 6 12 3 9 10 1 7 4 11 2 8 5 6 2. Draw the hour hand and minute hand to show the given time. 12 3 9 10 1 7 4 11 2 8 5 6 2:15 12 3 9 10 1 7 4 11 2 8 5 6 3:50 12 3 9 10 1 7 4 11 2 8 5 6 5:48 12 3 9 10 1 7 4 11 2 8 5 6 10:12 12 3 9 10 1 7 4 11 2 8 5 6 5:15:20 12 3 9 10 1 7 4 11 2 8 5 6 6:25:50 12 3 9 10 1 7 4 11 2 8 5 6 10:15:30 12 3 9 10 1 7 4 11 2 8 5 6 12:38:25 EXERCISE 14.1 Your mastery depends on practice. Practice like you play.
ARITHMETIC 179 What time is in the watch ? Telling Time According to Minute Hand 12:05 – 5 minutes past 12 1:10 – 10 minutes past 1 2:14 – 14 minutes past 2 3:30 – 30 minutes past 3 or half past three 4:35 – 35 minutes past 4 or 25 minutes to 5 5:45 – 45 or 3 - quarter past 5 or quarter to 6 6:50 – 50 minutes past 6 or 10 minutes to 7 10 min. past 5 min. past 12 3 9 10 1 7 4 11 2 8 5 6 Quarter past 20 min. past 25 min. past 12 O'clock Half past 45 min. past 15 min to 50 min. past 10 min to 55 min. past 5 min to 40 min. past 20 min to 35 min. past 25 min to 14.2 Review on Telling Time Read, Think and Learn
180 The Leading Mathematics - 4 1. Write the time in words from the following clocks: 12 3 9 10 1 7 4 11 2 8 5 6 12 3 9 10 1 7 4 11 2 8 5 6 12 3 9 10 1 7 4 11 2 8 5 6 12 3 9 10 1 7 4 11 2 8 5 6 EXERCISE 14.2 Your mastery depends on practice. Practice like you play. Telling Time According to Hour Hand (AM and PM) AM (am) PM (pm) Day 12 3 9 10 1 7 4 11 2 8 5 6 12 3 9 10 1 7 4 11 2 8 5 6 Noon Mid Night 12 9 3 10 1 7 4 11 2 8 5 6 Measurement 117 Telling Time According to Minute Hand 12:05 – 5 minutes past 12 1:10 – 10 minutes past 1 2:14 – 14 minutes past 2 3:30 – 30 minutes past 3 or half past three 4:35 – 35 minutes past 4 or 25 minutes to 5 5:45 – 45 or 3 - quarter past 5 or quarter to 6 6:50 – 50 minutes past 6 or 10 minutes to 7 Telling Time According to Hour Hand (AM and PM) AM (am) PM (pm) Day 12 3 9 10 1 7 4 11 2 8 5 6 The AM (ante meridian) of the day initiates from 12 O'clock midnight to 12 O'clock noon. 12 3 9 10 1 7 4 11 2 8 5 6 The PM (post meridian) of the day initiates from 12 O'clock noon to 12 O'clock midnight. Noon Mid Night 12 9 3 10 1 7 4 11 2 8 5 6 Time from one mid-night to next mid-night is called a day. There are 24 hours in a day. The time taken in one full rotation of the earth in its axis is called one day. My school time is 9:45 am to 4:30 pm. It take breakfast at 6:30 am. I go to school at 9 am. I sleep from 9:30 pm to 5 am. I take tiffin at 1:30 pm. I ate dinner at 8 pm. Note : 12 O’clock does not attain am or pm or both. It is called noon. 10 min. past 5 min. past 12 3 9 10 1 7 4 11 2 8 5 6 Quarter past 20 min. past 25 min. past 12 O'clock Half past 45 min. past 15 min to 50 min. past 10 min to 55 min. past 5 min to 40 min. past 20 min to 35 min. past 25 min to 5.1 (B) Review on Telling Time Read, Think and Speak What time is in the watch ? The AM (ante meridian) of the day initiates from 12 o'clock midnight to 12 o'clock noon. The PM (post meridian) of the day initiates from 12 o'clock noon to 12 o'clock midnight. Time from one mid-night to next mid-night is called a day. There are 24 hours in a day. The time taken in one full rotation of the earth in its axis is called one day. My school time is 9:45 am to 4:30 pm. It take breakfast at 6:30 am. I go to school at 9 am. I sleep from 9:30 pm to 5 am. I take tiffin at 1:30 pm. I ate dinner at 8 pm. Note : 12 O’clock does not attain am or pm or both. It is called noon.
ARITHMETIC 181 12 3 9 10 1 7 4 11 2 8 5 6 12 3 9 10 1 7 4 11 2 8 5 6 12 3 9 10 1 7 4 11 2 8 5 6 12 3 9 10 1 7 4 11 2 8 5 6 2. Write the following time in words : (a) 2:30 (b) 3:15 (c) 1:45 (d) 5:05 (e) 7:48 (f) 10:20 (g) 9:25 (h) 6:37 (i) 7:44 (j) 8:14 (k) 4:31 (l) 3:55 (m) 4:38 (n) 10:16 (o) 11:59 3. Write the am or pm for the given activities. (a) He wakes up in the morning at half past seven. (b) Sita goes to school at quarter past nine. (c) John completes the homework at 12 minutes to 7 in the evening. (d) Yana drinks tea at 18 minutes past 6 in the morning. (e) Hari’s father goes to morning walk at 25 minutes to five. (f) Joseph takes the dinner at quater to eight.
182 The Leading Mathematics - 4 In one complete turning, the second hand covers 60 seconds (i.e. 12 × 5 = 60 secs.) and in this period, the minute hand moves one small unit, called one minute (1 min). Therefore, 60 seconds = 1 minute, i.e. 60 secs = 1 min. In one complete turning the minute hand, it covers 60 minutes and in this period, the hour hand moves one part out of 12, called one hour (1hr). Therefore, 60 minutes = 1 hour. i.e. 60 mins = 1 hr When the hour hand turns two complete revolutions, it makes one day. Therefore, 2 × 12 hours = 24 hours = 1 day. i.e. 24 hrs. = 1 day. Hence, among these units, day is larger unit of time and after that hour, minute and second respectively. To convert the larger unit to smaller, multiply the quantity of the relation between them. But to convert small unit to large unit, divide by the quantity of the relation between them. × 24 Day Hour 24 ÷ × 60 Minute 60 ÷ × 60 Second 60 ÷ Converting Chart 12 9 3 10 1 7 4 11 2 8 5 6 hour hand minute hand second hand 14.3 Relation between Day, Hour, Minute and Second Read, Think and Learn
ARITHMETIC 183 CLASSWORK EXAMPLES Example 1 Convert 1 hour 18 minutes into seconds. Solution : Here, 1 hour 18 minutes = 60 minutes + 18 minutes [ \ 1 hr = 60 mins] = 78 minutes = 78 × 1 minute [\ 1 min = 60 secs] = 78 × 60 seconds = 4680 seconds. Example 2 Convert 315 seconds into minutes and seconds. Solution : Here, 315 seconds = 315 ÷ 60 minutes = 5 mins. 15 secs. Example 3 Change 1650 minutes into days, hours and minutes. Solution : Here, 1650 minutes = 1650 ÷ 60 hours = 27 hrs. 30 mins. = 27 ÷ 24 days. 30 mins = 1 day 3 hrs. 30 mins. EXERCISE 14.3 Your mastery depends on practice. Practice like you play. 1. Convert into hours : (a) 3 days (b) 2 days 3 hrs (c) 6 days 9 hrs (d) 9 days 7 hrs 315 27 –300 150 60 mins secs 1650 27 –120 450 –420 30 60 hrs mins 27 1 –24 30 24 day hrs
184 The Leading Mathematics - 4 2. Express into minutes : (a) 5 hrs (b) 7 hrs. 25 mins (c) 12 hrs. 49 mins (d) 1 day (e) 2 days 4 hrs (f) 5 days 5 hrs and 15 mins 3. Change into seconds : (a) 5 mins (b) 24 mins 18 secs (c) 34 mins 24 secs (d) 1 hr (e) 3 hrs 7 mins (f) 5 hrs. 24 mins 35 secs 4. Convert the following times into minutes and seconds : (a) 26 secs (b) 750 secs (c) 1460 secs 5. Change the following times into hours, minutes and seconds : (a) 300 mins (b) 756 mins (c) 1355 mins (d) 3925 secs (e) 18728 secs (f) 29288 secs 6. Convert the following times into days, hours, minutes and seconds : (a) 48 hrs (b) 75 hrs (c) 235 hrs (d) 1476 mins (e) 86418 mins (f) 270925 secs (g) 259585 secs (h) 190818 secs (i) 487500 secs List your daily activities. Write the duration of these activities in minutes and second if possible. Convert these times in seconds and present it in the classroom. PROJECT WORK
ARITHMETIC 185 14.4 Relation between Year, Month, Week and Day Measurement 121 Sunday Monday Tu e sday Wedn se ad u Th y sr day Fr di ay Saturday Sun Moon Mars ucre M uJ yr i p ret Venus Saturn 1 W 1 Week = 7 days 1 Month = 30 days (31 days) (28 or 29 days in February) = 4 weeks 1 Year = 12 months = 52 weeks = 365 days (Leap year has 366 days) 52 ÷ 30 ÷ × 52 × 30 × 365 365 ÷ × 12 Year Month 12 ÷ × 4 Week 4 ÷ × 7 Day 7 ÷ 5.1 (D) Relation between Year, Month, Week and Day Read, Think and Speak Converting Chart 1 Week = 7 days 1 Month = 30 days (31 days) (28 or 29 days in February) = 4 weeks 1 Year = 12 months = 52 weeks = 365 days 52 ÷ 30 ÷ × 52 × 30 × 365 365 ÷ × 12 Year Month 12 ÷ × 4 Week 4 ÷ × 7 Day 7 ÷ Read, Think and Learn Leap year has 366 days.
186 The Leading Mathematics - 4 1. Convert the following times into days : (a) 7 weeks (b) 12 weeks 2 days (c) 14 weeks 5 days (d) 4 months (e) 5 months 14 days (f) 6 months 2 weeks 3 days (g) 2 years (h) 3 years 2 months (i) 5 years 3 weeks (j) 4 years 29 days (k) 3 years 3 months 4 days (l) 2 years 4 weeks and 6 days 2. Convert the following times into weeks and days : (a) 27 days (b) 65 days (c) 84 days (d) 99 days (e) 129 days (f) 175 days (g) 205 days (h) 300 days (i) 474 days 3. Express the following times into months and days: (a) 35 days (b) 50 days (c) 73 days (d) 98 days (e) 129 days (f) 165 days (g) 195 days (h) 217 days (i) 356 days 4. Change the following times into years, months, weeks and days. (a) 369 days (b) 455 days (c) 784 days (d) 125 days (e) 17 days (f) 79 days (g) 12 weeks (h) 29 weeks (i) 74 weeks (j) 105 weeks (k) 176 weeks (l) 365 weeks (m) 13 months (n) 29 months (o) 64 months (p) 135 months (q) 200 months (r) 374 months EXERCISE 14.4 Your mastery depends on practice. Practice like you play. Write the date of your birth in years, months and days. Convert this date into days only and present it in your classroom. PROJECT WORK
ARITHMETIC 187 Add the following times. (a) 14.5 Adding Time EXERCISE 14.5 Your mastery depends on practice. Practice like you play. Read, Think and Learn Add 12 mins 45 secs and 7 mins 37 secs. Find the sum of 7 years 11 months and 4 years 9 months. Mins Secs 4 2 4 5 + 7 3 7 1 9 8 2 + 1 –60 2 0 2 2 60 secs = 1 min and 82 > 60 So, subtract 60 from 82 and add 1 min in 19 mins. 12 months = 1 yrs. 20 > 12. So, subtract 12 months from 20 months and add 1 year in 11 years. \ The sum is 20 mins 22 secs. \ The required sum is 12 yrs 8 months. Yrs Months 7 11 + 4 9 11 2 0 + 1 –12 1 2 8 Mins Secs 4 1 4 + 3 3 Mins Secs 1 7 0 7 +12 4 4 Mins Secs 3 1 1 9 +17 3 5 Mins Secs 4 3 5 6 + 2 5 8
188 The Leading Mathematics - 4 Days Hours 1 2 1 0 + 3 8 Days Hours 7 1 9 + 6 1 5 Days Hours 1 2 1 5 + 8 1 8 Days Hours 2 3 2 3 + 2 1 8 Weeks Days 7 3 + 2 2 Weeks Days 3 5 + 1 6 Weeks Days 9 4 + 8 3 Weeks Days 1 2 2 + 8 6 Months Days 4 1 7 + 3 1 2 Months Days 9 2 5 + 3 2 6 Months Days 7 2 7 + 3 2 6 Months Days 6 1 4 + 2 1 6 Years Months 4 6 + 3 4 Years Months 3 1 0 + 2 8 Years Months 4 9 + 3 11 Years Months 8 8 + 2 7 (b) (c) (d) (e) (f) (g) Years Weeks 4 4 9 + 2 4 7 Years Weeks 9 1 9 + 5 4 2 Years Weeks 1 5 4 2 + 9 3 8 Years Weeks 2 5 4 7 +17 0 9 Years Days 7 165 + 6 107 Years Days 1 2 315 + 8 107 Years Days 1 4 245 + 7 357 Years Days 2 1 197 +12 279
ARITHMETIC 189 14.6 Subtracting Time EXERCISE 14.6 Your mastery depends on practice. Practice like you play. Read, Think and Learn Subtract 5 days 19 hours from 12 days 8 hours. Find the difference between 14 weeks 3 days and 9 weeks 5 days. 8 < 19, so borrow 1 from days to hours, 1 day + 8 hrs = 24 + 8 = 32 hrs 3 < 5, so borrow 1 from weeks to days. 1w + 3D = 7D + 3D = 10D \ The difference is 6 days 13 hours. \ The difference is 4 weeks 5 days. Day Hours 11 3 2 1 2 8 – 5 1 9 6 1 3 Weeks days 1 3 1 0 1 4 3 – 9 5 4 5 Subtract the following times Mins Secs 4 1 4 – 3 6 Mins Secs 1 7 3 7 –12 4 4 Mins Secs 3 1 4 9 –17 3 5 Mins Secs 4 3 5 6 – 2 5 8 (a) (b) Hours Mins 5 2 5 – 2 1 7 Hours Mins 1 7 3 5 – 5 2 5 Hours Mins 1 2 4 7 – 6 3 2 Hours Mins 1 5 5 8 – 8 3 4
190 The Leading Mathematics - 4 Days Hours 1 2 1 0 – 3 8 Days Hours 7 1 9 – 6 1 5 Days Hours 1 2 1 5 – 8 1 8 Days Hours 2 3 2 3 – 2 1 8 Weeks Days 7 3 – 2 2 Weeks Days 3 5 – 1 6 Weeks Days 9 4 – 8 3 Weeks Days 1 2 2 – 8 6 Months Days 4 1 7 – 3 1 2 Months Days 9 2 5 – 3 2 6 Months Days 7 2 7 – 3 2 6 Months Days 6 1 4 – 2 1 6 Years Months 4 6 – 3 4 Years Months 3 1 0 – 2 8 Years Months 4 9 – 3 11 Years Months 8 8 – 2 7 Years Weeks 4 4 9 – 2 4 7 Years Weeks 9 1 2 – 5 4 9 Years Weeks 1 5 4 2 – 9 3 8 Years Weeks 2 5 4 7 – 1 7 0 9 Years Days 7 165 – 6 107 Years Days 1 2 315 – 8 107 Years Days 1 4 245 – 7 357 Years Days 2 1 197 –12 279 (c) (d) (e) (f) (g) (h)
ARITHMETIC 191 14.7 Verbal Problems of Time on Addition and Subtraction Read, Think and Learn Puspakamal started digging the field at 9:40 am and worked for 2 hours 35 minutes. At what time did he finish digging the field ? Solution : Hrs Mins 9 4 0 + 2 3 5 11 7 5 + 1 –60 1 2 1 5 \ Puspakamal finished digging the field at12:15 pm. Baburam finished his speech at 2:13 pm. He had speech for 3 hours 37 minutes. When had he started speech ? Solution : Separate hrs and mins in 9:40 am and arrange hrs and mins. Hrs Mins 1 3 7 3 1 4 1 3 – 3 3 7 1 0 3 6 Since 13 < 37 so, borrow 1 hour and 13 min + 1hr = 13 + 60 = 73 mins. Again, 7 can't be subtracted from 3. So, again borrow 1 from 7, it becomes 13 and so on. \ Baburam had started his speech at 10:36 am.
192 The Leading Mathematics - 4 1. Samyak started the homework at 5:25 in the morning and worked until 2 hours 45 minutes. When did he stop his homework ? 2. An aeroplane flew from Pokhara to Jomsom at 11:55 am and took 35 minutes to complete the journey. At what time did it land at Jomsom ? 3. The teacher entered the class at 10:50 and taught continuously for 1 hour 45 minutes. At what time did he come out from the class ? 4. A porter carrying a load has finished his job at 4:30 pm. He had carried the load for 3 hours 50 minutes. At what time had he started to carry the load ? 5. A tourist takes 5 days 4 hours to reach Larke Pass from Dhading Besi. He walked 3 days 7 hours towards the Larke Pass. Now, how long should walk for him ? 6. It took 3 months 17 days to construct the first floor of a house, 2 months 12 days for the second floor and 2 months 24 days for the third floor. How long time did it take the to complete the house ? 7. A trekker reached at the high base camp of ‘Tilicho lake’ by trekking 4 days 9 hours from Besisahar and he arrived at the Tilicho lake by treking 5 days 3 hours from Besisahar. How long time was taken to reach the Tilicholake lake from the high base camp for him? 8. A movie ended at 12:25:30. It lasted for 2 hours 42 minutes and 45 seconds. At what time had the movie started ? EXERCISE 14.7 Your mastery depends on practice. Practice like you play.
ARITHMETIC 193 CHAPTER 15 Money Do you recognize the Nepali coins and paper notes? How much total money is there on the hand? How much amount is there in 55 at 4 times? Can you multiply 234 and 9 ? Can you divide 2115 by 9 ? WARM-UP Lesson Topics Pages 15.1 Review on Nepali Currency 194 15.2 Review on Addition and Subtraction of Money 196 15.3 Multiplication of Rupees and Paisa 199 15.4 Division of Rupees and Paisa 201 15.5 Word Problems on Multiplication and Division of Money 203
194 The Leading Mathematics - 4 128 Allied Mathematics-4 .... Paisa.... Paisa .....Paisa ..... Paisa ...... Paisa ..... Paisa Re. ..... Rs. ..... Rs. .... Rs. .... Rs. ..... Rs. .... Rs. ..... Rs. ....... Rs. ..... Nepali Coins Nepali Notes Re. .... Re. .... Re. ..... Rs. .... Rs. .... Rs. ..... Rs. .... Rs. .... Rs. ....... Rs. .... CHAPTER - 5.2 : MONEY 5.2 (A) Review on Nepali Currency Read, Think and Speak What are the amounts of the given Nepali coins and paper notes? 128 Allied Mathematics-4 .... Paisa.... Paisa .....Paisa ..... Paisa ...... Paisa ..... Paisa Re. ..... Rs. ..... Rs. .... Rs. .... Rs. ..... Rs. .... Rs. ..... Rs. ....... Rs. ..... Nepali Coins Nepali Notes Re. .... Re. .... Re. ..... Rs. .... Rs. .... Rs. ..... Rs. .... Rs. .... Rs. ....... Rs. .... CHAPTER - 5.2 : MONEY 5.2 (A) Review on Nepali Currency Read, Think and Speak What are the amounts of the given Nepali coins and paper notes? 128 Allied Mathematics-4 .... Paisa.... Paisa .....Paisa ..... Paisa ...... Paisa ..... Paisa Re. ..... Rs. ..... Rs. .... Rs. .... Rs. ..... Rs. .... Rs. ..... Rs. ....... Rs. ..... Nepali Coins Nepali Notes Re. .... Re. .... Re. ..... Rs. .... Rs. .... Rs. ..... Rs. .... Rs. .... Rs. ....... Rs. .... CHAPTER - 5.2 : MONEY 5.2 (A) Review on Nepali Currency Read, Think and Speak What are the amounts of the given Nepali coins and paper notes? Re. ......... Rs. ......... Rs. ......... Rs. ......... Rs. ......... Rs. ......... Rs. ......... Rs. ......... Rs. ......... Rs. ......... 15.1 Review on Nepali Currency Read, Think and Learn 128 Allied Mathematics-4 .... Paisa.... Paisa .....Paisa ..... Paisa ...... Paisa ..... Paisa Re. ..... Rs. ..... Rs. .... Rs. .... Rs. ..... Rs. .... Rs. ..... Rs. ....... Rs. ..... Nepali Coins Nepali Notes Re. .... Re. .... Re. ..... Rs. .... Rs. .... Rs. ..... Rs. .... Rs. .... Rs. ....... Rs. .... CHAPTER - 5.2 : MONEY 5.2 (A) Review on Nepali Currency Read, Think and Speak What are the amounts of the given Nepali coins and paper notes? Nepali coins ......... paisa ......... paisa ......... paisa ......... paisa ......... paisa ......... paisa Re. ......... Re. ......... Re. ......... Re. ......... Rs. ......... Rs. ......... Rs. ......... Rs. ......... Rs. ......... 128 Allied Mathematics-4 .... Paisa.... Paisa .....Paisa ..... Paisa ...... Paisa ..... Paisa Re. ..... Rs. ..... Rs. .... Rs. .... Rs. ..... Rs. .... Rs. ..... Rs. ....... Rs. ..... Nepali Coins Nepali Notes Re. .... Re. .... Re. ..... Rs. .... Rs. .... Rs. ..... Rs. .... Rs. .... Rs. ....... Rs. .... CHAPTER - 5.2 : MONEY 5.2 (A) Review on Nepali Currency Read, Think and Speak What are the amounts of the given Nepali coins and paper notes? Nepali notes
ARITHMETIC 195 Measurement 129 1. Write the amount by adding the given Nepalese currencies : (a) (b) (c) (d) 2. Convert the following money into paisa. (Re. 1 = 100P) (a) Rs. 2 (b) Rs. 12 (c) Rs. 30 P 10 (d) Rs. 45 P 65 (e) Rs. 55 P 30 (f) Rs. 65 P 34 (g) Rs. 72 P 55 (h) Rs. 90 P 60 (i) Rs. 100 P 10 (j) Rs. 111 P 15 (k) Rs. 212 P 75 (l) Rs. 250 P 85 3. Convert the following paisa into rupees and paisa. (1P 1 = Rs. 1 ÷ 100) (a) 150 paisa (b) 225 paisa (c) 335 paisa (d) 435 paisa (e) 545 paisa (f) 625 paisa (g) 774 paisa (h) 885 paisa (i) 925 paisa (j) 1112 paisa (k) 1227 paisa (l) 1385 paisa EXERCISE 5.2 (A) Your mastery depends on practice. Practice like you play. Converting Chart × 100 Paisa 100 ÷ Rupee Measurement 129 1. Write the amount by adding the given Nepalese currencies : (a) (b) (c) (d) 2. Convert the following money into paisa. (Re. 1 = 100P) (a) Rs. 2 (b) Rs. 12 (c) Rs. 30 P 10 (d) Rs. 45 P 65 (e) Rs. 55 P 30 (f) Rs. 65 P 34 (g) Rs. 72 P 55 (h) Rs. 90 P 60 (i) Rs. 100 P 10 (j) Rs. 111 P 15 (k) Rs. 212 P 75 (l) Rs. 250 P 85 3. Convert the following paisa into rupees and paisa. (1P 1 = Rs. 1 ÷ 100) (a) 150 paisa (b) 225 paisa (c) 335 paisa (d) 435 paisa (e) 545 paisa (f) 625 paisa (g) 774 paisa (h) 885 paisa (i) 925 paisa (j) 1112 paisa (k) 1227 paisa (l) 1385 paisa EXERCISE 5.2 (A) Your mastery depends on practice. Practice like you play. Converting Chart × 100 Paisa 100 ÷ Rupee Measurement 129 1. Write the amount by adding the given Nepalese currencies : (a) (b) (c) (d) 2. Convert the following money into paisa. (Re. 1 = 100P) (a) Rs. 2 (b) Rs. 12 (c) Rs. 30 P 10 (d) Rs. 45 P 65 (e) Rs. 55 P 30 (f) Rs. 65 P 34 (g) Rs. 72 P 55 (h) Rs. 90 P 60 (i) Rs. 100 P 10 (j) Rs. 111 P 15 (k) Rs. 212 P 75 (l) Rs. 250 P 85 3. Convert the following paisa into rupees and paisa. (1P 1 = Rs. 1 ÷ 100) (a) 150 paisa (b) 225 paisa (c) 335 paisa (d) 435 paisa (e) 545 paisa (f) 625 paisa (g) 774 paisa (h) 885 paisa (i) 925 paisa (j) 1112 paisa (k) 1227 paisa (l) 1385 paisa EXERCISE 5.2 (A) Your mastery depends on practice. Practice like you play. Converting Chart × 100 Paisa 100 ÷ Rupee Measurement 129 1. Write the amount by adding the given Nepalese currencies : (a) (b) (c) (d) 2. Convert the following money into paisa. (Re. 1 = 100P) (a) Rs. 2 (b) Rs. 12 (c) Rs. 30 P 10 (d) Rs. 45 P 65 (e) Rs. 55 P 30 (f) Rs. 65 P 34 (g) Rs. 72 P 55 (h) Rs. 90 P 60 (i) Rs. 100 P 10 (j) Rs. 111 P 15 (k) Rs. 212 P 75 (l) Rs. 250 P 85 3. Convert the following paisa into rupees and paisa. (1P 1 = Rs. 1 ÷ 100) (a) 150 paisa (b) 225 paisa (c) 335 paisa (d) 435 paisa (e) 545 paisa (f) 625 paisa (g) 774 paisa (h) 885 paisa (i) 925 paisa (j) 1112 paisa (k) 1227 paisa (l) 1385 paisa EXERCISE 5.2 (A) Your mastery depends on practice. Practice like you play. Converting Chart × 100 Paisa 100 ÷ Rupee × 100 Paisa 100 ÷ Rupee Converting Chart EXERCISE 15.1 Your mastery depends on practice. Practice like you play. 1. Write the amount by adding the given Nepalese currencies : (a) (b) (c) (d) 2. Convert the following money into paisa. (Re. 1 = 100P) (a) Rs. 2 (b) Rs. 12 (c) Rs. 30 P 10 (d) Rs. 45 P 65 (e) Rs. 55 P 30 (f) Rs. 65 P 34
196 The Leading Mathematics - 4 Sonam sold a pen for Rs. 65.50, a copy for Rs. 32.75 and a pencil for Rs. 5.45. Find the total selling amount. Solution : 111.10 Selling price of a pen = Rs. 65.50 Selling price of a copy = Rs. 32.75 Selling price of a pencil = + Rs. 5.45 Total selling price = Rs. 103.70 Malaika had Rs. 2475 and 75 paisa in her pocket. She bought a pants for Rs. 1597 and 50 paisa. How much money is left with her ? Solution : Rs. Paisa Amount with Malaika = 2 4 7 5 . 7 5 Cost price of a pants = –1597.50 Left amount with her = 8 7 8 . 2 5 15.2 Review on Addition and Subtraction of Money Read, Think and Learn (g) Rs. 72 P 55 (h) Rs. 90 P 60 (i) Rs. 100 P 10 (j) Rs. 111 P 15 (k) Rs. 212 P 75 (l) Rs. 250 P 85 3. Convert the following paisa into rupees and paisa. (1P = Rs. 1 ÷ 100) (a) 150 paisa (b) 225 paisa (c) 335 paisa (d) 435 paisa (e) 545 paisa (f) 625 paisa (g) 774 paisa (h) 885 paisa (i) 925 paisa (j) 1112 paisa (k) 1227 paisa (l) 1385 paisa
ARITHMETIC 197 1. The price of each item is given below. Write the answers of the following questions : Measurement 131 1. The price of each item is given in below. Write the answers of the following questions : Rs. 55.65 Rs. 5.65 Rs. 7.35 Rs. 395.85 Rs. 42.55 Rs. 375.25 Rs. 45.75 (a) Find the total cost of the copy and the pen. (b) How much amount is to be paid for the calculator and the pencil ? (c) How much more expensive is the ink-pot than the note copy ? (d) Find the difference between the price of the book and the eraser. (e) Find the total cost of the pen and the pencil and the change received from the Rs. 100 note. (f) Meera bought the book and the copy and gave Rs. 500 note. How much money is returned by the shopkeeper ? 2. Gopal bought a T-shirt for Rs. 475.75 and a pair of shoes for Rs. 897.97. How much money did he spend ? 3. Jack has 1875 rupees and 45 paisa. His father gave 2017 rupees and 85 paisa to him. How much money did he have now ? 4. Sita got Rs. 2595.50 from his father and bought a dress for Rs. 1978.75. How much money was left with her ? 5. Salman bought a football for Rs. 1575.85 and a globe for Rs. 989.35. He gave Rs. 3000 to the shopkeeper. How much money would the shopkeeper return ? 6. Yina had Rs. 1400.75. She lost Rs. 250.25 and spent Rs. 785.85 to buy an electric iron. How much money did she have now ? Project Work-5.5 Write the price of any five goods that are used in kitchen. Add these prices. How much cost for them? Prepare a report and present in your classroom. EXERCISE 5.2 (B) Your mastery depends on practice. Practice like you play. (a) Find the total cost of the copy and the pen. (b) How much amount is to be paid for the calculator and the pencil ? EXERCISE 15.2 Your mastery depends on practice. Practice like you play. Find the total cost of an apple, a mango and an orange whose rates are as alongside. If the customer gives Rs. 100 note to the shopkeeper, how much amount will return to the customer? Solution : Here, 21.10 Cost of an apple = Rs. 15.75 Cost of a mango = Rs. 18.90 Cost of an orange = + Rs. 9.27 Total selling price = Rs. 43.92 Again, Rs. 100.00 – Rs. 43.92 Rs. 56.08 130 \ Allied Rs. 56.08 will return to the customer. Mathematics-4 Sonam sold a pen for Rs. 65.50, a copy for Rs. 32.75 and a pencil for Rs. 5.45. Find the total selling amount. Solution : 111.10 Selling price of a pen = Rs. 65.50 Selling price of a copy = Rs. 32.75 Selling price of a pencil = + Rs. 5.45 Total selling price = Rs. 103.70 Malaika had Rs. 2475 and 75 paisa in her pocket. She bought a pant for Rs. 1597 and 50 paisa. How much money is left with her ? Solution : Rs. Paisa Amount with Malaika = 2475.75 Cost price of a pants = –1597.50 Left amount with her = 878.25 Find the total cost of an apple, a mango and an orange whose rates are alongside. If the customer gives Rs. 100 note to the shopkeeper, how much amount return to the customer? Solution : Here, 21.10 Cost of an apple = Rs. 15.75 Cost of a mango = Rs. 18.90 Cost of an orange = + Rs. 9.27 Total selling price = Rs. 43.92 Again, Rs. 100.00 – Rs. 43.92 Rs. 56.08 \ Rs. 56.08 return to the customer. Rs.15.75 Rs.18.90 Rs.9.27 5.2 (B) Review on Addition and Subtraction of Money Read, Think and Learn
198 The Leading Mathematics - 4 (c) How much more expensive is the ink-pot than the note copy ? (d) Find the difference between the price of the book and the eraser. (e) Find the total cost of the pen and the pencil and the change received from a 100 rupee note. (f) Meera bought the book and the copy and gave a 500 rupee note. How much money is returned by the shopkeeper ? 2. Garima bought a umbrella for Rs. 475.75 and a pair of shoes for Rs. 897.97. How much money did she spend ? 3. Jack had 1875 rupees and 45 paisa. His father gave 2017 rupees and 85 paisa to him. How much money does he have now ? 4. Sita got Rs. 2595.50 from his father and bought a dress for Rs. 1978.75. How much money is left with her ? 5. Salman bought a football for Rs. 1575.85 and a globe for Rs. 989.35. He gave Rs. 3000 to the shopkeeper. How much money would the shopkeeper return ? 6. Yina had Rs. 1400.75. She lost Rs. 250.25 and spent Rs. 785.85 to buy an electric iron. How much money does she have now ? Write the price of any five goods that are used in the kitchen. Add these prices. How much will cost for them? Prepare a report and present it in your classroom. PROJECT WORK
ARITHMETIC 199 15.3 Multiplication of Rupees and Paisa Read, Think and Learn There are 26 standard fountain pens of the cost Rs. 276.73 each, 7 ball pens of the cost Rs. 18.85 each and 4 pencils of the cost Rs. 7.25 each. Sunil wants to buy all the pencils. How much does he pay for it? How can we find it ? For this, we add the cost of each pencil 4 times. Solution : Here, the cost of 1 pencil = Rs. 7.25 \ The cost of 4 pencils = Rs. 7.25 + Rs. 7.25 + Rs. 7.25 + Rs. 7.25 = Rs. 7.25 × 4 = Rs. 29.00 Multiply : Rs. 18.85 × 7 Solution : 165 .3 0 Rs. 18.85 × 7 Rs. 131.95 \ The required product is Rs. 131.95. 111 0 1444 .1 0 Rs. 276.73 × 26 166038 +553460 Rs.7194.98 \ The required product is Rs. 7194.98. Multiply : Rs. 276.73 × 26 Solution : Similarly, how can we find the cost of 7 ball pens and the cost of 26 standard fountain pens ? Rs. P. 7.25 × 4 Rs. 29.00 But, how can we find the total cost of 5 ball pens, 3 pencils and 12 fountain pens? Discuss. Oh! this multiplication is same as the multiplication of ordinary numbers. Put the decimal point (.) before two digits from the right in the product.
200 The Leading Mathematics - 4 2. (a) (b) (c) (d) (e) (f) (g) (h) (i) Rs. 3 . 2 5 × 4 Rs. 16.00 × 8 Rs. 5 4 . 2 × 9 Rs.354.32 ×12 Rs.658.82 ×39 Rs.798.56 ×57 Rs.563.23 ×65 Rs.835.95 ×85 Rs.987.65 ×95 3. (a) Rs. 19.25 × 5 (b) Rs. 43.36 × 8 (c) Rs. 86.93 × 9 (d) Rs. 495.62 × 14 (e) Rs. 672.85 × 27 (f) Rs. 979.89 × 47 Rs. Paisa 3 5 8 5 ×37 Rs. Paisa 7 5 4 5 ×44 Rs. Paisa 8 5 3 9 ×55 Rs. Paisa 9 8 8 9 ×67 Rs. Paisa 325 7 5 ×27 Rs. Paisa 475 3 5 ×32 Rs. Paisa 875 3 7 ×46 Rs. Paisa 978 9 8 ×56 EXERCISE 15.3 Your mastery depends on practice. Practice like you play. 1. Multiply : (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) Rs. Paisa 2 4 2 7 × 2 Rs. Paisa 3 7 9 7 × 5 Rs. Paisa 5 7 2 7 × 8 Rs. Paisa 3 5 7 8 × 9