ARITHMETIC 51 6. Write the following in Devanagari system by using comma (,): (a) rf}/f;L (b) b'O{ ;o k}FtfnL; (c) b'O{ xhf/ PSsfO; (d) Psf;L xhf/ kfFr ;o c7f;L (e) 5 nfv b'O{ ;o Ps (f) gf} nfv gf} xhf/ gf} 7. Write the numerals from the given place value table and abacus. (a) (b) (c) (d) (e) (f) 8. Write the following numerals in the place value table and abacus. (a) 20157 (b) 85642 (c) 78543 (d) 99589 T-Th Th H T O 4 5 9 8 1 T-Th Th H T O 9 8 9 4 5 T-Th Th H T O 8 9 4 0 5 T-Th Th H T O 7 9 0 0 8 T-Th HTh T O T-Th HTh T O Find the population of your local level (ward number) by requesting your parents. Write it in Hindu-Arabic, Devanagari and Roman numeral systems and present it in place value table and abacus. PROJECT WORK
52 The Leading Mathematics - 4 Ten times Ten Thousand = How much ? Ten times Ten Thousand = 10 × 10000 = 100000 = One Lakh Similarly, Ten times One lakh = How much ? 4.2 Counting Ten Lakhs Read, Think and Learn Observe the least numbers and numerals as below; Number of Digits Numbers Number Name Least number of 1 digit 1 One (O) Least number of 2 digits 10 Ten (T) Least number of 3digits 100 Hundred (H) Least number of 4 digits 1000 Thousand (TH) Least number of 5 digits 10000 Ten Thousands (T-Th) Least number of 6 digits 100000 One Lakh (L) Least number of 7 digits 1000000 Ten Lakhs (TL) = = 10 × 1,00,000 Ten one lakh Ten lakh
ARITHMETIC 53 Rs. 5000000 Rs. 2700000 What is the cost of the plot of land ? What is the cost of the printing machine ? In number system, comma (,) is used for separating the number family such as unit family, thousand family, lakh family, etc. By using comma (,), 50,00,000 and 27,00,000. Read the multiples of ten lakhs. 10 × 1,00,000 Ten one lakh Ten lakh = = = = 2 × 10,00,000 Two ten lakh 20,00,000 Twenty lakh = = 3 × 10,00,000 Three ten lakh 30,00,000 Thirty lakh Lakh Family Thousand Family Unit Family TL L T-Th Th H T O 1 0 0 0 0 0 0 TL L T-Th Th H T O 1000000 (Ten Lakh) in Place value Table and abacus,
54 The Leading Mathematics - 4 = = 4 × 10,00,000 Four ten lakh 40,00,000 Forty lakh = = 5 × 10,00,000 Five ten lakh 50,00,000 Fifty lakh = = 6 × 10,00,000 Six ten lakh 60,00,000 Sixty lakh = = 7 × 10,00,000 Seven ten lakh 60,00,000 Seventy lakh = = 8 × 10,00,000 Eight ten lakh 80,00,000 Eighty lakh = = 9 × 10,00,000 Nine ten lakh 90,00,000 Ninety lakh = = 10 × 10,00,000 Ten ten lakh 1,00,00,000 Hundred lakh= One crore
ARITHMETIC 55 EXERCISE 4.2 Your mastery depends on practice. Practice like you play. 1. Write the numbers of the multiples of 10 lakh in digits and words. 2. (a) There are ......... hundred in one lakh. (b) There are ......... thousand in twenty lakh. (c) There are ......... hundred in ten lakh. (d) There are ......... thousand in fifty lakh. (e) There are ......... thousand in one crore. 3. (a) How many thousands are there in one lakh ? (b) How many hundreds are there in ten lakh ? (c) How many hundreds are there in sixty lakh ? (d) How many ten thousands are there in one crore ? (e) How many lakhs are there in one crore ? 4. Observe the bundles of thousands alongside. If one bundle represents ten lakh, answer the following questions. (a) How many thousands are there in one bundle? (b) How many ten lakhs are there? (c) How many lakhs are there? (d) How many thousands are there?
56 The Leading Mathematics - 4 Hindu-Arabic Number System uses the place value system in the group of tens as shown in the table below : Number of Digits Group of Tens Number of Figures Number Name 1 100 1 One 2 101 10 Ten (Ten of one) 3 102 100 Hundred (Tens of ten) 4 103 1,000 Thousand (Tens of hundred) 5 104 10,000 Tens thousand (Tens of thousand) 6 105 1,00,000 Lakh (Tens of ten thousand) 7 106 10,00,000 Ten lakh (Tens of lakh) 8 107 1,00,00,000 Crore (Tens of ten lakh) The periods of Hindu-Arabic Number System has units, thousands, lakhs and crores, etc. in National numeration system. Thousands Ones = Thousands (Th) Thousand Family Tens = Ten thousands (T-Th) Units Ones (O) Tens (T) Unit Family Hundreds (H) Lakhs Ones = Lakhs (L) Lakh Family Tens = Ten lakh (T-L) Crores Ones = Crores (C) Crore Family Tens = Ten crores (T-C) Every periods are separated by comma (,) in the numbers. 1, 2, 3, 4, 5, 6, 7, 8, 9 4.3 Place Value (National System) Read, Think and Learn
ARITHMETIC 57 The Population of Kathmandu district is 1744240 in the census - 2011. 44 thousands 4 is in ones place. The place value of 4 is 4 × 1000 = 4000. 4 is in tens place. The place value of 4 is 4 × 10000 = 40000. 17 lakhs 7 is in ones place. The place value of 7 is 7 × 100000 = 700000. 1 is in tens place. The place value of 1 is 1 × 1000000 = 1000000 17,44,240 240 units 0 is in ones place. The place value of 0 is × 1 = 0. 4 is in tens place. The place value of 10 is 4 × 10 = 40. 2 is in hundreds place. The place value of 2 is 2 × 100 = 200. From the above discussion, Family Place Digits Place value Lakhs (17) Tens = Ten Lakhs (TL) 1 10,00,000 Ones = Lakhs (L) 7 7,00,000 Thousands (44) Tens = Ten Thousands (T–Th) 4 40,000 Ones = Thousands (Th) 4 4,000 Units (240) Hundreds (H) 2 200 Tens (T) 4 40 Ones (O) 0 0 Total 17,44,240 The place value table for 17,44,240 Lakhs Thousands Units Or Lakhs Thousands Ones Tens Ones Tens Ones Hundreds Tens Ones TL L T–Th Th H T O 1 7 4 4 2 4 0 1 7 4 4 2 4 0 We read the number as, seventeen lakhs forty four thousand two hundred and forty. Place Value in 7- Digit Numbers
58 The Leading Mathematics - 4 EXERCISE 4.3 Your mastery depends on practice. Practice like you play. 1. Show the following numbers in place value table and write in words : (a) 12,47,349 (b) 24,76,503 (c) 65,27,319 (d) 99,99,999 (e) 13,68,749 (f) 48,27,893 2. Write the number and number name from the given place value table. (a) Lakhs Thousands Ones TL L T-TH TH H T O 4 7 3 2 1 5 6 (b) Lakhs Thousands Ones TL L T-TH TH H T O 5 7 0 2 1 0 4 (c) Lakhs Thousands Ones TL L T-TH TH H T O 6 2 4 3 1 5 6 (d) Lakhs Thousands Ones TL L T-TH TH H T O 7 8 2 3 9 4 5 3. Write the numbers of the following number names and show them in the place value table : (a) Ten lakh twenty five thousand four hundred and sixty seven (b) Thirty five lakh sixty nine thousand and hundred and eleven (c) Fifty two lakh one thousand and twenty six (d) Sixty three lakh five hundred and eight
ARITHMETIC 59 (e) Seventy lakh three thousand and four (f) Eighty lakh ten thousand and three hundred 4. Write down the place and place value of the coloured digits in the following numbers : (a) 1924893 (b) 2437840 (c) 4921347 (d) 5217849 (e) 6347892 (f) 7820471 (g) 8027843 (h) 9789929 5. Write the answers of the following questions : (a) In the number 2782520, what does 7 stand for ? (b) In the number 8926762, what does 8 stand for ? (c) How many lakhs are there in 2700382 ? (d) How many thousands are there in 8937184 ? 6. The population of a town is 8347256. Answer the following questions. (a) Write the numeral in words after using comma (,). (b) Show the numeral in place value table. (c) What is the place value of 3 in the numeral? (d) How many people will be added to the population to make it 8348000? Find the price of your house or land by requesting your parents and present it in place value table and abacus. PROJECT WORK
60 The Leading Mathematics - 4 Lakhs Thousands Units TL L T-Th Th H T O 8 4 5 6 2 1 9 Here, 8 is in ten lakhs place and its value is 8 × 10,00,000 = 80,00,000. 4 is in lakhs place and its value is 4 × 1,00,000 = 4,00,000. 5 is in ten thousands place and its value is 5 × 10,000 = 50,000. 6 is in thousands place and its value is 6 × 1000 = 6,000. 2 is in hundreds place and its value is 2 × 100 = 200. 1 is in tens place and its value is 1 × 10 = 10. 9 is in ones place and its value is 9 × 1 = 9. Then, Expanded form 80,00,000 + 4,00,000 + 50,000 + 6,000 + 200 + 10 + 9 = 8 × 10,00,000 + 4 × 1,00,000 + 5 × 10,000 + 6 × 1,000 + 2 × 100 + 1 × 10 + 9 × 1 = 8 × 106 + 4 × 105 + 5 × 104 + 6 × 103 + 1 × 101 + 9 × 102 = Power of 10 form Number Name Eighty four lakh fifty six thousand two hundred and nineteen, in which 8 ten lakhs, 84 lakhs, 845 ten thousands, 8456 thousands TL L T-Th Th H T O 4.4 Expanded Form of Numbers Read, Think and Learn
ARITHMETIC 61 1. Write the numbers obtained by the following place value table in expanded form, power of 10 form and in words : (a) Lakhs Thousands Ones TL L T-TH TH H T O 7 8 9 2 5 4 1 (b) Lakhs Thousands Ones TL L T-TH TH H T O 4 5 0 7 8 1 9 2. Write the numbers obtained by the following abacus in expanded form, power of 10 form and in words: (a) (b) (c) (d) 3. Observe the following numerals and answer the following questions. (a) 48,57,321 (b) 27,80,591 (c) 28,34,047 (d) 10,27,984 (i) Write the given numerals in expanded form. (ii) Write the given numerals in words. (iii) Show the given numerals in place value table and abacus. TL L T-Th Th H T O TL L T-Th Th H T O TL L T-Th Th H T O TL L T-Th Th H T O EXERCISE 4.4 Your mastery depends on practice. Practice like you play.
62 The Leading Mathematics - 4 4.5 Numbers from 1,00,000 to 9,99,999 Read, Think and Learn Do you know, what is the population of Lalitpur district in the census 2078 BS? Total Population = 5,51,667 Male = 2,77,131 Female = 2,74,536 1,00,000 + 1 One lakh + one 1,00,001 One lakh and one 1,00,000 1 2,00,000 3,00,000 2 1 20 100 50 2,00,000 + 20 + 2 = 2,00,022 Two lakh + Twenty + Two = Two lakh and twenty two. 3,00,000 + 100 + 50 + 1 = 3,00,151 Three lakh + One hundred + Fifty + One = Three lakh one hundred fifty one
ARITHMETIC 63 EXERCISE 4.5 Your mastery depends on practice. Practice like you play. 1. Write the next seven numbers each starting from the given number : (a) 2,34,017 (b) 4,54,358 (c) 5,02,027 (d) 7,04,007 (e) 8,45,784 (f) 9,98,249 (g) 2,34,018 (h) 4,46,358 (i) 7,04,507 (j) 8,45,984 (k) 6,52,780 (l) 7,60,214 2. Write the number name of the following numbers after using comma (,): (a) 354708 (b) 527879 (c) 700205 (d) 827002 (e) 954024 (f) 989207 (g) 527879 (h) 708200 (i) 972532 (j) 545342 (k) 781240 (l) 651247 3. (a) How many lakhs are there in 734532 ? (b) How many lakhs are there in 920501 ? (c) How many thousands are there in 825008 ? 4. Observe the price of the given bike and answer the following questions. Rs. 375500 (a) Write the price by using comma (,). (b) Write the price of the bike in words. (c) How many thousands are there in its price?
64 The Leading Mathematics - 4 4.6 Numbers from 10,00,000 to 19,99,999 Read, Think and Learn Do you know, what is the population of Morang district in the census 2078 BS? Total Population = 11,48,156 Male = 5,57,512 Female = 5,90,644 10,00,000 + 2 Ten lakh + two 10,00,002 Ten lakh and one 10,00,000 2 10,00,000 10,00,000 5 10 100 2,00,000 2,000 500 10,00,000 + 100 + 5 = 10,00,105 Ten lakh + One hundred + Five = Ten lakh one hundred five 10,00,000 + 2,00,000 + 2,000 + 500 + 10 = 12,02,510 Twelve lakh two thousand five hunded ten
ARITHMETIC 65 1. Write seven numbers each starting from the given number : (a) 10,20,275 (b) 12,24,098 (c) 13,24,997 (d) 14,34,859 (e) 15,85,925 (f) 16,95,821 (g) 17,59,281 (h) 18,85,928 (i) 18,96,589 (j) 19,99,995 (k) 15,47,834 (l) 16,84,577 2. Write the number name of the following numbers : (a) 11,07,805 (b) 13,02,007 (c) 15,27,292 (d) 17,98,270 (e) 18,85,784 (f) 11,99,9859 (g) 17,87,051 (h) 10,02,927 (i) 19,90,001 (j) 19,82,007 (k) 12,36,587 (l) 15,49,822 3. Fill in the blanks: (a) There are .............. lakhs in 1258061. (b) There are .............. lakhs in 1569827. (c) There are .............. thousands in 1902548. 4. Study the price of the plot of the land and answer the following questions. (a) Write the price of the land by using comma (,). (b) Write its price in words in the national system. (c) Show its price in abacus. (d) How many thousands are there in its price. EXERCISE 4.6 Your mastery depends on practice. Practice like you play. Rs. 1850000/- Land for Sale
66 The Leading Mathematics - 4 4.7 Numbers from 20,00,000 to 39,99,999 20,00,000 20,00,000 30,00,000 1,00,000 100 50 2 2,00,000 2,000 5 1 20,00,000 + 1 Twenty Lakh + one 20,00,001 Twenty lakh and one = 30,00,000 + 1,00,000 + 100 + 50 + 2 = 31,00,152 Thirty lakh + one lakh + one hundred + fifty + two = Thirty one lakh one hundred and fifty two 20,00,000 + 2,00,000 + 2000 + 5 = 22,02,005 Twenty lakh + two lakh + two thousand + five = Twenty two lakh two thousand and five. Read, Think and Learn
ARITHMETIC 67 1. Write seven numbers each starting from the given number : (a) 20,78,725 (b) 23,83,462 (c) 25,78,20 (d) 29,87,284 (e) 30,27,897 (e) 27,23,451 2. Write the number name of the following numbers : (a) 21,47,832 (b) 22,87,584 (c) 24,97,820 (d) 26,89,227 (e) 29,87,829 (f) 31,49,217 (g) 33,97,824 (h) 36,29,874 (i) 38,83,149 (j) 39,89,781 (k) 31,54,785 (l) 26,45,891 3. Observe the given car and answer the following questions. (a) Use the comma (,) in the given price of the car. (b) Write the price in words in the national system. (c) Show the price of the car in place value chart. (d) How many ten thousands are there in its price. 4. Study the price of the given printing machine and write the answers of the following questions. (a) Write the price of the machine in words. (b) Show its price in the place value table. (c) What is the place value of 9 in its price. (d) How many hundreds are there in its price. Rs. 3578000/- Rs. 3955800/- EXERCISE 4.7 Your mastery depends on practice. Practice like you play.
68 The Leading Mathematics - 4 4.8 Numbers from 40,00,000 to 59,99,999 Read, Think and Learn 40,00,000 50,00,000 3,00,000 1000 500 1 2,00,000 200 2 1. Write seven numbers each starting from the given number : (a) 41,00,245 (b) 43,45,623 (c) 46,47,987 (d) 49,27,825 (e) 51,37,278 2. Write the number name of the following numbers : (a) 42,20,524 (b) 44,78,205 (c) 45,78,346 (d) 47,28,029 (e) 48,02,759 EXERCISE 4.8 Your mastery depends on practice. Practice like you play. 40,00,000 + 2,00,000 + 200 + 2 = 42,00,202 = 50,00,000 + 3,00,000 + 1000 + 500 + 1 = 53,01,501 Forty lakh + two lakh + two hundred + two = Forty two lakh two hundred and two. Fifty lakh + three lakh + one thousand + five hundred + one = Fifty three lakh one thousand five hundred and one
ARITHMETIC 69 4.9 Numbers from 60,00,000 to 79,99,999 46 Allied Mathematicss-4 1. Write seven numbers each starting from the given number : (a) 60,20,075 (b) 62,27,706 (c) 65,78,579 (d) 68,12,486 (e) 71,27,020 (f) 74,38,997 (g) 78,59,998 (h) 79,99,994 (i) 72,30,025 (j) 75,00,120 2. Write the number name of the following numbers : (a) 61,34,078 (b) 63,54,782 (c) 64,78,899 (d) 67,28,972 (e) 69,99,998 (f) 70,24,307 (g) 73,79,284 (h) 75,19,283 (i) 77,34,610 (j) 78,27,634 60,00,000 100 50 2 6,00,000 + 100 + 50 + 2 Sixty lakh + one hundred + fifty + two = 60,00,152 = Sixty lakh one hundred and fifty two = 70,00,000 + 2,00,000 + 3000 + 500 + 40 + 1 = Seven lakh + two lakh + three thousand + five hundred + forty + one = 72,03,541 = Seventy two lakh three thousand five hundred and forty one 70,00,000 2,00,000 3,000 500 40 1 2.1 (H) Numbers from 60,00,000 to 79,99,999 Read, Think and Speak EXERCISE 2.1 (H) Your mastery depends on practice. Practice like you play. Read, Think and Learn = 70,00,000 + 2,00,000 + 3000 + 500 + 40 + 1 = 72,03,541 Seventy lakh + two lakh + three thousand + five hundred + forty + one = Seventy two lakh three thousand five hundred and forty one 1. Write seven numbers each starting from the given number : (a) 60,20,075 (b) 62,27,706 (c) 65,78,579 (d) 68,12,486 (e) 71,27,020 (f) 74,38,997 (g) 78,59,998 (h) 79,99,994 (i) 72,30,025 (j) 75,00,120 (k) 24,58,713 (l) 15,87,450 2. Write the number name of the following numbers : (a) 61,34,078 (b) 63,54,782 (c) 64,78,899 (d) 67,28,972 (e) 69,99,998 (f) 70,24,307 (g) 73,79,284 (h) 75,19,283 (i) 77,34,610 (j) 78,27,634 (k) 36,54,287 (l) 58,74,901 EXERCISE 4.9 Your mastery depends on practice. Practice like you play. 70,00,000 2,00,000 3,000 500 40 1
70 The Leading Mathematics - 4 = 90,00,000 + 2,00,000 + 100 + 10 + 2 = 92,00,112 = Ninety lakh + two lakh + one hundred + ten + two = Ninety two lakh one hundred and twelve 1. Write the numbers starting from the given numbers : 81,10,700 84,37,859 86,45,713 88,99,287 90,20,287 93,87,896 97,84,978 99,99,994 2. Write the number name of the following numbers : (a) 83,24,073 (b) 85,47,829 (c) 87,87,345 (d) 88,78,420 (e) 89,99,999 (f) 90,47,821 (g) 92,43,734 (h) 94,21,498 (i) 96,82,573 (g) 98,99,273 (k) 98,54,124 (l) 85,41,201 4.10 Numbers from 80,00,000 to 99,99,999 EXERCISE 4.10 Your mastery depends on practice. Practice like you play. Concept of Numbers 47 1. Write the numbers starting from the given numbers : 81,10,700 84,37,859 86,45,713 88,99,287 90,20,287 93,87,896 97,84,978 99,99,994 2. Write the number name of the following numbers : (a) 83,24,073 (b) 85,47,829 (c) 87,87,345 (d) 88,78,420 (e) 89,99,999 (f) 90,47,821 (g) 92,43,734 (h) 94,21,498 (i) 96,82,573 (g) 98,99,273 80,00,000 2,000 1 8,00,000 + 2,000 + 1 Eight lakh + two thousand + one 80,02,001 Eight lakh, two thousand and one = 90,00,000 2,00,000 100 10 = 90,00,000 + 2,00,000 + 100 + 10 + 2 = Ninety lakh + two lakh + one hundred + ten + two = 92,00,112 = Ninety two lakh one hundred and twelve 2 2.1 (I) Numbers from 80,00,000 to 99,99,999 Read, Think and Speak EXERCISE 2.1 (I) Your mastery depends on practice. Practice like you play. Read, Think and Learn 90,00,000 2,00,000 100 10 2
ARITHMETIC 71 E There are one-digit Hindu-Arabic numbers of 1, 2, 3, 4, 5, 6, 7, 8, 9. Which is the smallest one ? Which is the greatest one ? E When 1 is added to 9, what do you get ? E 10 is the smallest number of two digits. Which is the greatest two-digit number ? From the above discussion, we obtain the following information : No. of Digits Greatest Number Add 1 Smallest Number of digits 1 9 +1 10 2 99 +1 100 3 999 +1 1,000 4 9999 +1 10,000 5 99999 +1 1,00,000 6 999999 +1 10,00,000 7 9999999 +1 1,00,00,000 10000000 is the smallest number of 8 digits. It is read as “One crore”. The population of Nepal is 2,91,64,578 in the census 2078 BS. It is read as two crore ninety one lakh sixty four thousand five hundred and seventy eight. 2 3 ? ? ? ? ? 4.11 Numbers up to One Crore Read, Think and Learn 1,00,00,000
72 The Leading Mathematics - 4 EXERCISE 4.11 Your mastery depends on practice. Practice like you play. 1. The given table shows the approximate population of SAARC countries in 2015. Write them in words. Countries Population Nepal 26620000 India 1210193422 Pakistan 170600000 Bhutan 708427 Shri Lanka 20238000 Bangladesh 142319000 Maldives 394999 Afghanistan 29835392 2. Write the greatest and the smallest number of 8 digits by using the following digits : (a) 2, 3, 4, 5, 6, 7, 8, 9 (b) 1, 2, 3, 4, 5, 6, 7, 8 (c) 0, 1, 2, 3, 4, 5, 6, 7 (d) 0, 1, 3, 4, 5, 5, 6, 9 (e) 1, 5, 7, 8, 4, 0, 1, 3 (f) 2, 0, 8, 0, 9, 7, 5, 1 (g) 3, 2, 7, 0, 0, 9, 4, 1 (h) 0, 2, 8, 6, 7, 7, 1, 1 Find the price of your house or land by requesting your parents. Write it in Hindu-Arabic and Devanagari numeral systems and present it in place value table and abacus. PROJECT WORK
ARITHMETIC 73 CHAPTER 5 ROUNDING OFF NUMBER Count the scales of the ruler in cm. How much money is there on the hand ? What is the length of the note book ? How many pages are there in your Maths book? How many students are there in your school? What is your weight? What are the lengths of Mahendra highways in Nepal? WARM-UP Lesson Topics Pages 5.1 Rounding Off the Nearest to Tens 74 5.2 Rounding Off the Nearest to 100 76
74 The Leading Mathematics - 4 5.1 Rounding Off the Nearest to Tens Read, Think and Learn 0 1 2 3 Near Far 4 5 6 7 8 9 10 3 is nearer to 0 and far from 10. So, the rounding off 3 to the nearest to 10 is 0. 20 21 22 23 Near Far 24 25 26 27 28 29 30 27 is near to 30 than that of 20. So, the rounding off 27 to the near to 10 is 30. Here, 255 is in the same distance from 250 and 260. In this case, we round off the greater tens. So, the rounding off 255 to the nearer 10 is 260. 250 251 Same 252 253 254 255 256 257 258 259 260 Same
ARITHMETIC 75 1. Round off the following height of students in the class 4 to the nearest 10 : Name Rama Sita John Jasna Joseph Ramesh Kanchha Height (inch) 38 42 35 37 39 34 41 Round off 2. Round off the following length of highways of Nepal to the nearest to tens. Highway Siddhartha Tribhuvan Prithvi Kodari Mechi Karnali Mahendra Length (km) 182 158 174 113 224 232 1028 Round off 3. Round off the following height of mountains of the world to the nearest 10. Mountain Mt. Everest Mt. K2 Kanchanjunga Lhotse Makalu Cho Oyu Height (m) 8848 8611 8586 8516 8485 8188 Round off Mountain Dhaulagiri Manaslu Nanga Parbat Annapurna Height (m) 8167 8163 8126 8091 Round off EXERCISE 5.1 Your mastery depends on practice. Practice like you play. If the last digit of the number is 1, 2, 3 or 4, round off to lower tens. If the last digit of the number is 5, 6, 7, 8 or 9, round off to upper tens.
76 The Leading Mathematics - 4 Oh! to round off the nearest 100, we observe the second last digit of the number. If the second last digit is equal or greater than 5, the rounding off the given number is upper hundreds, other than it is lower hundreds. 5.2 Rounding Off the Nearest to 100 Read, Think and Learn Where does Hari go to take Rs. 500 note toward 100 or 200 ? Hari is the nearest to Rs. 500 note toward 200. So, he goes towards 200. 178 is rounded off 200 under the nearest hundred. 100 110 Near 120 130 140 150 160 170 180 190 200 Far 178 The tiger is nearer to the goat than that of the deer. So, the tiger goes to goat. The rounding off 135 to the nearest hundred is 100. 100 110 Near 120 130 140 150 160 170 180 190 200 Far 135
ARITHMETIC 77 1. Round off the given numbers to the nearest 100 by using arrow head. 552 500 600 748 700 800 1850 1800 1900 1232 1200 1300 8570 8500 8600 9849 9800 9900 2. Round off the following length of rivers in Nepal to the nearest 100. River Karnali Gandaki Koshi Mahakali Mechi Bagmati Length (km) 507 680 729 350 360 196 Rounding off 3. Round off the following length of rivers in the World to the nearest 100. River Amazon Nile Yangtze Mississippi Yenisei Haanytle Ob-Irtysh Length (km) 6992 852 6300 6275 5539 5464 5410 Rounding off 4. Round off the following hight of pass (bhanjyang) to the nearest hundreds: Pass Lhola Nangpa Tesi lapcha Lipulekh Ganja Larke Thorang Frenchla Kagmara Height(m) 5420 5741 5755 5334 5406 5106 5416 5360 5115 Rounding off EXERCISE 5.2 Your mastery depends on practice. Practice like you play.
78 The Leading Mathematics - 4 5. Round off the following numbers as stated within brackets. (a) 219 (to the nearest 10) (b) 345 (to the nearest 10) (c) 429 (to the nearest 100) (d) 156 (to the nearest 100) (e) 596 (to the nearest 10) (f) 272 (to the nearest 10) 6. Round off the following numbers for the circled digit. (a) 4 9 (b) 6 8 (c) 27 3 (d) 2 8 1 (e) 4 8 9 (f) 4 5 0 (g) 235 7 (h) 94 9 9 (i) 34 7 8 (j) 48 4 9 (k) 95 2 7 (l) 478 2 Circled last digit means rounding off the nearest 10 and circled second last digit means rounding off nearest 100. 7. Rewrite the following sentences by using rounding off to the nearest 10 and 100. Example : The length of stick is 136 cm. Rounding off to the nearest 10: The length of stick is 140 cm. Rounding off to the nearest 100: The length of stick is 100 cm. (a) The height of a boy is 56 inch. (b) The length of a book is 24 cm. (c) The weight of your bag is 475 gm. (d) The area of your book is 165cm2 . (e) The volume of a room is 1080 cu.ft. (f) The distance between Kathmandu and Pokhara is 108 km. Find the total cost of your stationery goods (books, copies, box, pencils, etc.) by requesting your guardian. Round off this price into tens and hundreds. PROJECT WORK
ARITHMETIC 79 BASIC OPERATIONS UNIT III Estimated Teaching Periods : 21 COMPETENCY solution of mathematical problems of daily life including addition, subtraction, multiplication and division CHAPTERS 6 Addition 7 Subtraction 8 Multiplication 9 Division 10 Simplification LEARNING OUTCOMES After completion of this content area, the learner is expected to be able to: add the numbers up to 5 digits. subtract the numbers up to 5 digits. multiply 3-digit numbers by the number up to 3 digits. divide 3-digit numbers by the number up to 2 digits. solve the problems including addition and subtraction.
80 The Leading Mathematics - 4 CHAPTER 6 Addition How many fruits are there in the basket and outside the basket ? How many total fruits are there all together? How many girls and boys are there in your class? What is the total number of students in your class? What are the costs of the T-shirts? What is the total cost of both T-shirts? How much money do you get from your parents/guardians in a week for tiffin? How many total pages are there in Maths, Nepali and English books? WARM-UP Lesson Topics Pages 6.1 Review on Addition 81 6.2 Addition of Numbers up to 5 digits 83 Rs. 1250/- Rs. 1585/-
ARITHMETIC 81 Add the digits in related columns of places by taking carry over. Example 1 1543 plants are planted on an open ground and 2342 plants are planted on another open hill. How many total plants are planted ? How can we find the total planted plants? For this, we add both numbers 1543 and 2342. Solution : 1543 + 2342 = ? Oh! 3885 plants are planted in total on both open places. Example 2 There are 6358 fishes in one pond and 2684 fishes in another. How many total fishes are there on both ponds? How can we find the total fishes? For this, we add both numbers 6358 and 2684. Solution : 6358 + 2684 = ? There are 9042 fish on both pond. At first, add the digits in ones place, and then tens place, hundreds place and, at last, thousands place. Th H T O 1 5 4 3 + 2 3 4 2 3 8 8 5 Th H T O 1 1 1 6 3 5 8 + 2 6 8 4 9 0 4 2 6.1 Review on Addition Read, Think and Learn
82 The Leading Mathematics - 4 EXERCISE 6.1 Your mastery depends on practice. Practice like you play. 1. Add the following. (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) 2. Complete the table. + 990 991 992 993 994 995 996 997 998 999 0 111 222 333 1327 444 555 666 777 888 1884 999 7245 + 2632 3457 + 2432 4564 + 3125 5234 +1897 2872 +7124 5086 +4312 2482 +5014 5226 +3753 3029 495 + 7745 2686 860 + 75 2976 +5824 3736 +4328 Find the cost of your shirt, paints and shoes by requesting your guardian. Add up all of the expenses. Prepare a report and present it in your classroom. PROJECT WORK
ARITHMETIC 83 Example 1 My father bought a book rack for Rs. 21453 and a sofa for Rs. 52345. How much amount did he expend ? How can we find the expenditure amount ? For this, we add both amounts. How do we find the sum of the numbers 21453 and 52345? Solution : 6.2 Addition of Numbers up to 5 digits Read, Think and Learn 3 + 5 = 8 Adding column 1 4 + 3 = 7 Adding column 3 5 + 4 = 9 Adding column 2 1 + 2 = 3 Adding column 4 2 + 5 = 7 Adding column 5 T-Th Th H T O 2 1 4 5 3 + 5 2 3 4 5 7 3 7 9 8 Add the numbers in respective columns.
84 The Leading Mathematics - 4 Example 2 My sister bought a second hand scooter for Rs. 42875 and a bike for Rs. 29426. How much amount did she expend ? How can we find the expenditure amount ? For this, we add both amounts. How do we find the sum of the numbers 42875 and 89426? Solution : 42875 + 29426 = ? 5 + 6 = 11, 1 down, carryover 1 Carryover 7 + 2 + 1 = 10, 0 down, carryover 1 8 + 4 + 1 = 13, 3 down, carryover 1 9 + 2 + 1 = 12, 2 down, carryover 1 4 + 2 + 1 = 7, 7 down T-Th Th H T O 1 1 1 1 4 2 8 7 5 + 2 9 4 2 6 7 2 3 0 1 Add column wise and take carryovers to the next column.
ARITHMETIC 85 37245 +42632 (a) 13457 +63492 (b) 37256 +42312 (c) 59423 +26589 (d) 34287 +25892 (e) 50378 +49732 (f) 207486 +597014 (g) 500476 +99765 (h) 65325 +28767 (i) 23572 45289 +36260 (j) 38002 49976 + 7695 (k) 29527 92820 + 8675 (l) 32126 73429 2891 + 526 (m) 30527 285993 57639 + 287 (n) 15576 17628 1453 + 291 (o) 27687 82731 7639 + 287 (p) 30415 58325 3723 + 423 (q) 86628 295594 77824 + 498 (r) 14698 09840 9228 + 498 (s) 48648 82430 3677 + 5687 (t) EXERCISE 6.2 Your mastery depends on practice. Practice like you play. 1. Add the following :
86 The Leading Mathematics - 4 CHAPTER 7 Subtraction In which basket has more apples? How many more boys or girls are there in your class? Which one (t-shirt or shirt) is expensive and by how much? If you have Rs. 1000 and you buy a book for Rs. 455, how much money do you have left? WARM-UP Lesson Topics Pages 7.1 Subtraction of Numbers up to 5 digits 87 7.2 Problems on Addition and Subtraction 91 7.3 Problems on Addition and Subtraction 94 Rs. 1250/- Rs. 1585/-
ARITHMETIC 87 Oh ! 7 + 9 = 16 and 16 – 9 = 7 both are true. 722 + 79 = 801 and 801 – 79 = 722, are also true. Example 1 There were 63258 plants in a nursery. A ranger bought 32132 plants from the nursery. How many plants are there left in the nursery now ? How can we find the remaining plants ? For this, we subtract bought plants from total plants. How do we subtract 32132 from 63258? Solution : 63258 – 32132 = ? Oh! There are 31126 plants left in the nursery now. As in addition, subtract the numbers in the respective columns. 8 – 2 = 6 (Subtract in the 1st column) Subtranend Minued 2 – 1 = 1 (Subtract in the 3rd column) 5 – 3 = 2 (Subtract in the 2nd column) 3 – 2 = 1 (Subtract in the 4th column) 6 – 3 = 3 (Subtract in the 5th column) T-Th Th H T O 6 3 2 5 8 – 3 2 1 3 2 3 1 1 2 6 Can you do ? – 7 9 + – = = 722 79 + = = ? 7.1 Subtraction of Numbers up to 5 digits Read, Think and Learn
88 The Leading Mathematics - 4 Example 2 Subtract 497968 from 685762. Solution : 685762 – 497968 = ? EXERCISE 7.1 Your mastery depends on practice. Practice like you play. 1. Subtract and verify your answer by addition. (a) 28 – 13 (b) 522 – 484 (c) 376 – 128 (d) 746 – 537 (e) (f) (g) (h) (i) (j) (k) (l) Subtract 9 from 17 You cannot subtract 7 from 4, rename it 14. You cannot subtract 9 from 6, rename it 16. You cannot subtract 6 from 5, rename it 15. You cannot subtract 8 from 2, rename it 12. Burrowing 10 from 60. L T-Th Th H T O 5 17 14 16 15 12 6 8 5 7 6 2 – 4 9 7 9 6 8 1 8 7 7 9 4 If you cannot subtract, rename the number by regrouping. 489 – 278 5684 – 3991 7246 – 4387 27454 – 16967 587020 – 289313 782672 – 289313 778420 – 492483 899282 – 799479
ARITHMETIC 89 2. Subtract. (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) (m) (n) (o) (p) (q) (r) (s) (t) 75286 – 23143 59763 – 46421 75291 – 26342 32056 – 14067 52800 – 28437 95427 – 24568 20000 – 15928 350000 – 274287 95000 – 28437 52486 – 86879 55555 – 9999 30000 – 52 30205 – 15208 80900 – 12057 76950 – 49878 70853 – 45 45367 – 65848 98957 – 56871 78963 – 56876 89655 –89251
90 The Leading Mathematics - 4 3. Find the difference of : (a) greatest number of 4 digits and the least number of 4 digits. (b) greatest number of 5 digits and the least number of 5 digits. (c) greatest number of 6 digits and the greatest number of 5 digits. (d) greatest number of 5 digits and the greatest number of 4 digits. (e) smallest number of 6 digits and the greatest number of 5 digits. (f) smallest number of 5 digits and the greatest number of 4 digits. 4. Subtract : (a) 1259 from 10000 (b) 99999 from 100000 (c) 10009 from 100000 5. 5 2 8 7 9 4 Find the difference between the largest and the smallest number formed by six digits mentioned above. Find the cost of two different mobiles. Which mobile is expensive or the cheapest by how much ? Prepare a report and present it in your classroom. PROJECT WORK
ARITHMETIC 91 Can you do ? 9 8 + = = + 27 9 – = – ? In addition, a + b = b + a In subtraction, a – b = b – a But, a – b = a + (–b). Subtracting means adding negative number to a given number. 7.2 Problems on Addition and Subtraction Read, Think and Learn I have some cash. If you give me Rs. 15, I will have Rs. 27. How much money did I have at first? How can we find the previous amount ? For this, suppose the beginning amount is Rs. a. Then, write the mathematical sentence as, a + 15 = 27 Now, we find the value of a. a + 15 = 27 (The question reads what added to 15 gives 27.) or, a + 15 – 15 = 27 – 15 (Subtracting equal amount 15 from both sides.) or, a = 27 – 15 (a is the difference of 27 and 15.) \ a = 12 (Find answer.)
92 The Leading Mathematics - 4 Addition and subtraction are inverse operations to each other. CLASSWORK EXAMPLES Example 1 What must be added to 35 to make it 60 ? Solution : Here, Let the number to be added be a. Then a + 35 = 60 or, a = 60 – 35 (Why ?) \ a = 25. Example 2 What must be subtracted from 72 to make it 45 ? Solution : Here, Let the number to be subtracted be a. Then 72 – a = 45. or, 72 = a + 45 (Why ?) or, 72 – 45 = a (Why ?) \ a = 27. EXERCISE 7.2 Your mastery depends on practice. Practice like you play. 1. Find the value of the variables (use inverse operation). (a) 12 + a = 15 (b) 13 + b = 27 (c) c + 19 = 32 (d) d + 21 = 33 (e) 15 + e = 29 (f) f + 7 = 18 Did you notice here, you were to find the number to be added to 15, you have worked out the answer by subtracting 15. You have used the inverse operation.
ARITHMETIC 93 5 14 15 14 7 6 6 5 6 4 – 6 2 5 9 8 5 1 4 0 5 7 9 (g) 35 + m = 42 (h) n + 33 = 40 (i) q + 30 = 45 (j) x + 16 = 55 (k) 15 + w = 45 (l) g + 45 = 60 2. Find the value of the variables (use inverse operation). (a) a – 12 = 18 (b) b – 17 = 29 (c) c – 18 = 30 (d) d – 22 = 6 (e) 25 – a = 15 (f) 35 – b = 30 (g) 19 – s = 10 (h) n – 25 = 30 (i) x – 20 = 15 (j) q – 22 = 15 (k) 30 – m = 10 (l) 55 – x = 40 3. (a) What must be added to 19 to make it 27 ? (b) What must be added to 38 to make it 60 ? (c) What must be added to 52 to make it 90 ? (d) What must be added to 72 to make it 99 ? 4. (a) What must be subtracted from 28 to make it 16 ? (b) What must be subtracted from 52 to make it 36 ? (c) What must be subtracted from 60 to make it 48 ? (d) What must be subtracted from 78 to make it 35 ?
94 The Leading Mathematics - 4 Example 1 For the establishment of a small scale business of pig farming, Babin borrowed Rs. 950000 from Sunita. He pays back the amount of Rs. 589850 to her after one year. How much is left to pay ? Solution : Amount borrowed by Babin = Rs. 950000 Amount paid to Sunita = Rs. 589850 \ Amount left to pay Sunita = Rs. 950000 – Rs. 589850 = Rs. 360150 Thus, Rs. 360150 left to pay. Example 2 Krishna and Jesus earn Rs. 457905 and Rs. 308659 per year. Their total expenditure is Rs. 625985 in the year. What is their saving amount ? Solution : Income of Krishna = Rs. 457905 Income of Jesus = Rs. 308659 Since both amounts are income so, add them. Their income is Rs. 766564 Again, Their expenditure = Rs. 625985 Now, the expenditure is subtracted from the income alongside. Thus, their saving amount is Rs. 140579. 8 14 9 9 10 9 5 0 0 0 0 – 5 8 9 8 5 0 3 6 0 1 5 0 1 1 0 1 4 5 7 9 0 5 + 3 0 8 6 5 9 7 6 6 5 6 4 5 14 15 14 7 6 6 5 6 4 – 6 2 5 9 8 5 1 4 0 5 7 9 7.3 Problems on Addition and Subtraction Read, Think and Learn
ARITHMETIC 95 EXERCISE 7.3 Your mastery depends on practice. Practice like you play. 1. In a school, out of 25785 students 19987 are the girls. Find the number of boys. 2. There are 432132 people in Nepal’s smallest district Bhaktapur. In the census of 2021 in which 218418 were male. What was the female population ? 3. The height of the highest peak of the world 'Sagarmatha’ is 29029 feet. The height of the second highest peak ‘Mt. K2’ is 28251 feet. What is more height of the ‘Sagarmatha’ than the ‘Mt. K2’ ? 4. A businessman bought a laptop for Rs. 120525. If he sold it for Rs. 85790, how much money would he loss ? 5. In a village, the budget allocated for a year is Rs. 950000. Only Rs. 785825 is spent. How much is left to spend ? 6. A company produced 259857 packets of biscuits in one day. It supplied 198969 packets of biscuits to various dealers. How many packets of biscuits were left in the company ? 7. A broker bought a piece of land for Rs. 855750 and he sold it for Rs. 980765. Find his profit amount. 8. The total number of houses in Kathmandu district is 436344 in 2011 AD and that of Kaski district is 125673. How many more house are in Kathmandu district ? 9. The sum of two numbers is 347829 and one of them is 89575. Find the next number. 10. A man spent Rs. 37850 out Rs. 572325. What is his saving amount? 11. The yearly income of a husband and his wife are Rs. 435955 and Rs. 38525 respectively. If they spent Rs. 398500, find their saving amount. 12. The population of Manang, Mustang and Myagdi districts are 5658, 14452 and 107033 in the census 2021. How many more population is in Myagdi than the sum of population of Manang and Mustang ?
96 The Leading Mathematics - 4 CHAPTER 8 Multiplication How many apples are there in each box? What is the sum of apples altogether ? Can you express the sum of apples in multiplication form? How many pencils are there in each collection? What is the sum of pencils altogether ? Can you express the sum of pencils in multiplication form? WARM-UP Lesson Topics Pages 8.1 Review om Multiplying by 1-digit Numbers 97 8.2 Review on Multiplying by 2-digit Numbers 99 8.3 Multiplying by 10, 100 and 1000 101 8.4 Multiplying by 3-digit Numbers 102 8.5 Verbal Problems on Multiplication 105
ARITHMETIC 97 8.3 Review om Multiplying by 1-digit Numbers Read, Think and Learn 10 + 10 + 10 = 30 There are 3 groups of 10 \ 3 × 10 = 30 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 30 There are 10 groups of 3. \ 10 × 3 = 30 Oh! I remembered, multiplication is short form of repeated addition. And it is Hence, we have 3 × 10 = 10 × 3 = 30 commutative. Also, we know, a × 0 = 0 × a = 0, for any number a. a × 1 = 1 × a = a, for any number a. a × b = b × a = ab, for any numbers a and b. 3 tens and 2 ones 3 hundred and 1 ten 1 thousand and 9 hundred Multiply : 133 478 × 4 1 9 1 2 8 × 4 3 2 70 × 4 280 + 30 310 400 × 4 1600 +300 1900 Multiply 8 ones by 4 Multiply 7 tens by 4 and add 3 tens Multiply 4 hundreds by 4 and add 3 hundred
98 The Leading Mathematics - 4 23 × 3 42 × 4 57 × 8 79 × 5 98 × 5 123 × 2 345 × 6 578 × 7 789 × 4 978 × 5 256 × 5 378 × 4 894 × 6 987 × 7 859 × 8 6421 × 2 3467 × 3 2567 × 5 5789 × 6 8989 × 8 7894 × 4 8477 × 5 5867 × 7 8792 × 8 9999 × 9 25 × 6 27 × 5 77 × 4 99 × 7 68 × 8 1. Multiply the following : 2. Multiply the following : 3. Multiply the following : (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (f) (g) (h) (i) (j) (f) (g) (h) (i) (j) (a) (b) (c) (d) (e) (a) (b) (c) (d) (e) EXERCISE 8.1 Your mastery depends on practice. Practice like you play.
ARITHMETIC 99 Multiply the following. 1. (a) 47 × 21 (b) 89 × 32 (c) 78 × 45 (d) 69 × 57 (e) 39 × 49 (f) 82 × 47 (g) 75 × 35 (h) 92 × 88 (i) 97 × 79 (j) 88 × 99 (k) 85 × 55 (l) 80 × 65 (m) 95 × 78 (n) 78 × 97 (o) 99 × 99 6739 ×64 26956 +404340 431296 2213 6739 × 4 26956 Multiply 6739 by 4. 4425 6739 ×60 404340 Multiply 8739 by 60. Carryovers 4425 2213 6739 ×64 26956 +404340 431296 Carryovers when multiply by tens Multiply by ones 6739 × 4 Multiply by tens 6739 × 60 Carryovers when multiply by ones Carryovers Add For this, multiply : v We are a group of 64 people. Each of us plants 6739 plants on the open space within a month. How many plants do we plant on it ? 8.2 Review on Multiplying by 2-digit Numbers EXERCISE 8.2 Your mastery depends on practice. Practice like you play. 376 9 Lattice (Napier's Bones) Multiplication Method 1 1 2 3 6 2 3 4 4 1 2 9 6 6 4 2 3 4 6 8 8 5 2 1 2 4 1 Read, Think and Learn
100 The Leading Mathematics - 4 (k) 358 × 29 (l) 782 × 48 (m) 437 × 58 (n) 989 × 72 (o) 999 × 99 (f) 265 × 25 (g) 598 × 38 (h) 785 × 44 (i) 562 × 48 (j) 879 × 87 3. (a) 1324 × 12 (b) 2103 × 21 (c) 1230 × 32 (d) 3452 × 43 (e) 4728 × 35 (k) 4938 × 47 (l) 5987 × 56 (m) 6280 × 65 (n) 7384 × 35 (o) 6394 × 47 (f) 3589 × 37 (g) 4879 × 46 (h) 7890 × 53 (i) 8952 × 49 (j) 8972 × 58 4. (a) 7235 × 37 (b) 8789 × 48 (c) 7348 × 59 (d) 8978 × 87 (e) 9999 × 99 (k) 8720 × 89 (l) 9278 × 94 (m) 9479 × 95 (n) 9879 × 98 (o) 8278 × 94 (f) 5890 × 78 (g) 7809 × 87 (h) 9800 × 66 (i) 8970 × 88 (j) 7801 × 96 2. (a) 243 × 21 (b) 345 × 23 (c) 431 × 42 (d) 782 × 51 (e) 928 × 27