Oasis School Mathematics Book-5 51 Find the greatest and the smallest numbers formed from digits 2, 5, 0, 7, 8. Solution: Given digits: 2, 5, 0, 7, 8 Greatest number formed from the given digits = 87520 Again, smallest number formed from the given digits = 20578 example 1 1. complete the given table: Greatest number of 1-digit 9 Smallest number of 1-digit 1 Greatest number of 2-digits Smallest number of 2-digits Greatest number of 5 -digits Smallest number of 5-digits I have to arrange the digits in descending order to form the greatest number. 0 should not be kept at first. class Assignment Remember ! • To form the smallest number, arrange the given digits in ascending order. • To form the greatest number, arrange the given digits in descending order. • ‘0’ should not be placed first. Again, select the digits 2, 6, 4. The possible 3 digit numbers are 264, 246, 462, 426, 624, 642. Among these numbers, Greatest number = 642 → Digits are in descending order. Smallest number = 246 → Digits are in ascending order.
Oasis School Mathematics Book-5 52 Notation of number in Hindu Arabic and Devanagari is different but the system of counting is same in both cases. Our script to write a number is the Devanagari script. Hindu Arabic numbers: 0 1 2 3 4 5 6 7 8 9 Devanagari numbers : ) ! @ # $ % ^ & * ( Number name in Nepali: z"Go Ps b'O{ tLg rf/ kfFr 5 ;ft cf7 gf} Write the given number in Devanagari with its number name in Nepali. a. 56742 b. 763452 Solution: a. 56742 Given number: 56742 Number in Devanagari : %^&$@ Number name in Nepali : 5kGg xhf/ ;ft ;o aofnL; b. 763452 Given number: 763452 Number in Devanagari : &^#$%@ Number name in Nepali : ;ft nfv lq;¶L xhf/ rf; ;o afpGg example 1 2. Write the greatest and the smallest number formed by the given digits. Digits Smallest number Greatest number 4, 0, 1, 3, 8 10348 84310 2, 5, 7, 0 3 2, 5, 7, 0,1 7, 2, 3, 4, 5, 1 3, 0, 1, 6, 4, 2 Devanagari Number
Oasis School Mathematics Book-5 53 1. Show the following numbers in place value chart and write them in expanded form: a. 2684301 b. 321569325 c. 6318946230 d. 53064193272 e. 60507123701 2. Write the following in the standard form: a. 400 + 30 + 5 b. 3 × 1000 + 5 × 100 + 6 × 10 + 7 × 1 Exercise 3.2 c. 9 × 1000000 + 6 × 100000 + 5 × 10000 + 4 × 1000 + 3 × 100 + 2 × 10 + 7 × 1 d. 7 × 10000000 + 5× 1000000 + 2 × 100000 + 4 × 10000 + 3 × 1000 + 2 × 100 + 1 × 10 + 5 × 1 e. 6 × 1000000000 + 4 × 100000000 + 3× 10000000 + 2 × 1000000 + 1 × 100000 + 7 × 10000 + 4 × 1000 + 7 × 100 + 8 × 10 + 9 × 1 f. 5 × 1000000000 + 6 × 10000000 + 5× 100000 + 4 × 10000 + 3× 1000 + 2 × 100 + 5 × 10 + 8 × 1 3. a. Write the greatest and the smallest number of 5 digits. b. Write the greatest and the smallest number of 8 digits. c. Write the greatest and the smallest number of 7 digits. d. Write the smallest number of 6 digits and the greatest number of 5 digits. Also find their difference. e. What is the difference between the smallest number of 10 digits and the greatest number of 9 digits? 4. Write the greatest and the smallest number formed by the following digits: a. 4, 0, 7, 2, 8 b. 1, 7, 9, 6, 4, 2 c. 8, 1, 4, 6, 3, 2 d. 2, 1, 4, 6, 3, 7 e. 9, 3, 6, 4, 0 f. 7, 0, 8, 6, 5, 4, 9 Answers Consult your teacher.
Oasis School Mathematics Book-5 54 ;ª\Vofsf] gfd s;/L n]Vg] < sdf -,_ n] ;ª\Vofsf] lkl/o8 5'6\ofpF5, To;}n] :yfgLo k4lt cg';f/ sdf k|of] u ubf{ k5fl8af6 tLgcf]6f cª\s 5f]8]/ sdf k|of]u ug]{ To;kl5 b'O{ b'O{cf]6f cª\s 5f]8]/ k|of]u ug'{k5{ . #$&)$%$#( #$,&),$%,$#( o; ;ª\Vofsf] gfd n]Vbf, rfF}lt; s/f]8 ;Q/L nfv kF}tfln; xhf/ rf/ ;o pgfGrfln; . Exercise 3.3 1. lbOPsf ;ª\VofnfO{ :yfgLo k4ltcg';f/ :yfgdfg tflnsfdf k|:t't ug'{xf];\ . a. $@%&#)*@ b. $!)@$%^*@! c. (*&^%$#@! 2. :yfgLo k4ltcg';f/ sdf -,_ k|of]u u/L lbOPsf ;ª\Vofx?sf] gfd n]Vg'xf];\ . a. %!)*&#^$! b. *$%&#)!%@ c. &#*)!*@(# d. @)#)!@)^# e. %&#*^%(*& f. #*#^$@!)$ b]jgfu/L ;ª\Vofsf] :yfgdfg tflnsf :yfgLo k4lt (Local system of numeration) cg';f/ lkl/o8x? Ps, xhf/, nfv, s/f]8 cflb x'g\ . o;sf km/s km/s :yfg? Ps, bz, ;o, xhf/, bzxhf/, nfv, bz nfv, s/f]8 cflb x'g\ . ( cª\sn] ag]sf] s'g} Pp6f ;ª\Vof #$&)$%$#( lncf}+ . s/f]8 nfv xhf/ Ps bz s/f]8 s/f]8 bz nfv nfv bz xhf/ xhf/ ;o bz Ps # $ & ) $ % $ # ( rf}lt; s/f]8 ;Q/L nfv k}Ftfln; xhf/ rf/ ;o pgfGrfln;
Oasis School Mathematics Book-5 55 99 765421 9 9 9 9 9 1 0 0 10235 1000 30000 100000 read the following instruction and colour the answers with the given colour code. • Place value of 3 in the number 24631278 (Red) • Number of thousands in one million (Blue) • Greatest number of 5 digits (Sky blue) • Smallest number of 3 digits (Dark green) • Smallest number formed by the digits. 2, 3, 5, 1, 0 (Light green) • 1 more than the greatest number of 5 digits (Purple) • 1 less than smallest number of 3 digits (Pink) • Greatest number formed by the digits 2, 5, 7, 6, 4, 1 (Brown) Activity 3. lbOPsf ;ª\Vofsf] gfdaf6 ;ª\Vof n]Vg'xf];\ . a. afx| s/f]8 t]lTt; nfv a};6\7L xhf/ tLg ;o ;tf;L b. afpGg s/f]8 5 nfv rf}/f;L xhf/ PsfpGg c. Psrfln; s/f]8 5lAa; nfv t]lTt; xhf/ gf} ;o rf}/f;L Project Work On the chart paper, draw place value chart to show a number of 9-digits in both local numeration system and International numeration system.
Oasis School Mathematics Book-5 56 natural numbers The numbers 1, 2, 3, 4, 5, ...... which are used for counting are the natural numbers or counting numbers. 1, 2, 3, 4, ..... are the natural numbers. Whole numbers The set of natural numbers including zero are the whole numbers: 0, 1, 2, 3, 4....... are the whole numbers. even and odd numbers Numbers which are exactly divisible by 2 are called even numbers. Even numbers are the multiple of 2. 2, 4, 6, 8, 10 ..... etc. are the even numbers The greatest natural number and whole number is not defined. If the digit in the ones place is odd then the number is odd. If the digit in the ones place is even or zero, then the number is even. Even numbers are the paired numbers. Odd numbers are the unpaired numbers. The smallest natural number is 1 and the smallest whole number is 0. How to determine whether the given number is odd or even if the number is very large? Numbers which are not exactly divisible by 2 are the odd numbers. Odd numbers are not the multiple of 2. 1, 3, 5, 7, 9 ....... are the odd numbers. Note: • The sum and difference of two even numbers is even. • The sum of two odd numbers is even. • The sum and difference of an even and odd number is odd. 427590 is an even number. 237835 is an odd number. 126524 is an even number.
Oasis School Mathematics Book-5 57 2. identify whether the given numbers are odd or even: a. 2460 b. 82693 c. 45857 d. 94282 e. 56740 f. 79934 g. 81647 h. 25810 i. 56219 j. 259600 3. identify whether the given numbers are odd or even: a. Sum of two even numbers b. Sum of two odd numbers c. Sum of an even and an odd numbers d. Difference of two even numbers e. Difference of two odd numbers f. Difference of an odd and an even number 4. Identify whether the given numbers are odd or even (identify without addition or subtraction): a. 15 + 7 b. 12 - 6 c. 18 + 8 d. 234 + 825 e. 23 - 17 f. 265 - 134 1. Answer the following questions: a. Which are the smallest and the greatest natural numbers? b. Which are the smallest and the greatest whole numbers? c. Are all natural numbers whole numbers? d. Name the only one whole number which is not a natural number. e. What is the number called which is divisible by 2? f. A number is not a multiple of 2. What is the number called? Exercise 3.4 Answers Consult your teacher.
Oasis School Mathematics Book-5 58 Factors: look and learn: 12 = 12 × 1, 12 = 6 × 2, 12 = 4 × 3 12 is divisible by 1, 2, 3, 4, 6, and 12. Here, 1, 2, 3, 4, 6 and 12 are the factors of 12. Again, 20 = 20 × 1 → 20 and 1are the factors of 20. 20 = 10 × 2 → 20 and 2 are the factors of 20. 20 = 5 × 4 → 5 and 4are the factors of 20. Here, 1, 2, 4, 5, 10 and 20 are the factors of 20. Hence, a number is said to be a factor of another if it divides that number exactly. From the above example, discuss on the following points. • Is 1 a factor of every number? • Is a number is factor of itself? • Is the factor of a number is greater than the given number? Remember ! • 1 is a factor of every number. • Every natural number is a factor of itself. • A factor of a number is either less than or equal to the number. multiples: Look and learn: 5 × 1 = 5 5 × 2 = 10 5 × 3 = 15 5 × 4 = 20 5, 10, 15, 20 ... etc. are the multiples of 5. Again, 6 × 1 = 6 6 × 2 = 12 6 × 3 = 18 6 × 4 = 24 6 × 5 = 30 6, 12, 18, 24, 30 ... etc. are the multiples of 6. Hence, the multiples of a number are the product of the number by any number. Factors and Multiples
Oasis School Mathematics Book-5 59 2. Answer the following questions: a. What are the two factors of a prime number? b. Which number is the factor of each number? c. Which number is the multiple of each number? 1. Observe the given multiplication fact and identify whether the given statements are true or false. Fact : 3 × 7 = 21. a. 3 is a factor of 7. b. 7 is a factor of 21. c. 21 is a factor of 3. d. 21 is a multiple of 3 and 7 both. Observe the given multiplication fact and develop 3 different statements related to factor and multiple. • 7 × 11 = 77 • 5 × 9 = 45 From the above example, discuss the following points. • Is every number a multiple of 1? • Is every number a multiple of itself? • Is 0, a multiple of every number? Exercise 3.5 3 × 5 = 15 3 and 5 are any two factors of 15. 15 is a multiple of 3 and 5. Remember ! • Every number is a multiple of 1. • Every number is a multiple of itself. • 0 is a multiple of any number.
Oasis School Mathematics Book-5 60 3. Find the possible factors of: a. 12 b. 10 c. 18 d. 30 e. 45 f. 50 g. 96 h. 144 i. 150 j. 180 k. 256 4. Write down the first five multiples of: a. 5 b. 9 c. 12 d. 18 e. 25 f. 28 g. 32 h. 52 i. 56 j. 76 k. 96 l. 108 5. circle the multiples of given numbers: 5 10 14 20 25 28 32 35 7 7 11 21 23 28 40 79 11 11 20 22 30 44 45 55 6. Write all the prime numbers from: a. 10 to 20 b. 20 to 30 c. 30 to 40 d. 40 to 50 e. 50 to 70 f. 80 to 100 Answers Consult your teacher. Prime factors Let's find the factors of composite numbers: 24 = 24 × 1 24 = 12 × 2 24 = 8 × 3 24 = 6 × 4 \ The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24. Among these, 2 and 3 are prime numbers. So 2 and 3 are called prime factor of 24. Hence, the smallest possible factors of any number which are the prime numbers are called the prime factors of the number. example 1 Write all possible factors of 40 and make the list of prime factors. Solution: Here, 40 = 40 × 1 40 = 20 × 2 40 = 10 × 1 40 = 8 × 5
Oasis School Mathematics Book-5 61 Prime factorisation There are two methods of finding prime factors. They are, a. by making factor tree b. by successive division method Factorisation by successive division method: Let's take a composite number and factorise it by successive division method. Factorise: 144 example 2 Apply test of divisibility rule to factorise a number. The successive division is carried out by dividing the given number with respective prime number until the last dividend is prime. 144 ÷ 2 = 72 72 ÷ 2 = 36 36 ÷ 2 = 18 18 ÷ 2 = 9 9 ÷ 3 = 3 Factorisation by making factor tree: Let's take a number 56. Observe the given factorisation properly and get the idea of prime factorisation, using factor tree. Hence, 1, 2, 4, 5, 8, 10, 20 and 40 are factors of 40. Among them 2 and 5 are prime numbers. So, 2 and 5 are prime factors of 40 2 144 2 72 2 36 2 18 3 9 3 \ 144 = 2 × 2 × 2 × 2 × 3 × 3
Oasis School Mathematics Book-5 62 Factorise 150 by using a. factor tree method b. Successive division method Solution: Solution: example 3 \ 150 = 2 × 3 × 5 × 5 \ 150 = 2 × 3 × 5 × 5 150 ÷ = 75 75 ÷ 3 = 25 2 150 3 75 5 25 5 1. Write all the possible factors of the given numbers and make the list of prime factors: a. 24 b. 36 c. 48 d. 56 e. 80 f. 84 g. 96 h. 112 i. 128 j. 148 k. 150 l. 156 2. complete the given factor tree and write the given number as the product of prime factors: Exercise 3.6
Oasis School Mathematics Book-5 63 4. Find the prime factors of the following numbers by successive division method: a. 24 b. 32 c. 40 d. 64 e. 72 f. 84 g. 98 h. 110 i. 256 j. 196 k. 175 l. 216 m. 243 n. 343 o. 625 Answers Consult your teacher. • 3 is divisible by 1 and 3 itself So, 3 is also a prime number Similarly, 5, 7, 11, 13, etc. are prime numbers. Prime number • 2 is divisible by 1 and 2 itself. So, 2 is a prime number. A number which is divisible by 1 and by itself but not divisible by other number is called a prime number. 3. Find the prime factors of the following numbers by factor tree method and express the given number as the product of prime factors: a. 28 b. 44 c. 36 d. 60 e. 100 f. 150 g. 180 h. 128 i. 220 Prime and Composite Number
Oasis School Mathematics Book-5 64 composite number Let's take a number 4. It is divisible by 1 and 4 itself. Again, it is divisible by 2 also. Therefore, 4 is not a prime number. It is a composite number. Hence, a number which is exactly divisible by other numbers also except by 1 or by itself is called a composite number. 6, 8, 9, 10, 12, etc. are composite numbers. Prime and composite numbers from 1 to 50 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 Steps: • Circle 1 which is neither prime nor composite. • Circle all the even numbers except 2. • Circle the numbers divisible by 3, except 3. • Circle all the numbers which are divisible by 5, except 5. • Circle all the numbers which are divisible by 7, except 7. All the circled numbers are composite numbers except 1. All the remaining numbers are prime numbers. \ Prime numbers from 1 to 50 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47.
Oasis School Mathematics Book-5 65 Do you know! Two prime numbers which are close to each other with a gap of only one number are twin prime numbers. 17 and 19 are twin prime numbers. Exercise 3.7 1. Answer the following questions. a. Which even number is prime? b. What are the two factors of prime number? 2. Write all the prime numbers from 1 to 10. 3. Write all the prime numbers from 10 to 20. c. A number has two factors 1 and the number itself. What is the number called? d. If a number has more than two factors, what is it called? e. Which number is neither prime nor composite? f. Give an example of twin prime numbers. g. How many prime numbers are less than 10? h. How many even numbers are prime? i. What number is factor of every number? note: • 1 is neither a prime nor a composite number. • 2 is the only even number which is prime. • The smallest prime number is 2. 4. Write the number from 50 to 100. • circle 1 • circle all the numbers divisible by 2 • circle all the numbers divisible by 3 • circle all the numbers divisible by 4, 5, 6, 7, 8 and 9 a. Make the list of remaining numbers. b. What are the numbers called?
Oasis School Mathematics Book-5 66 5. Solve as directed a. Write the smallest prime number. b. Write five pairs of prime numbers whose sum is prime number. c. Write 5 composite numbers having 9 in the ones place. d. Write composite factors of 19. Is it prime number? e. Every composite number can be written as a product of two or more composite numbers. Is it true? 6. Write the following numbers as the product of two or more prime numbers. a. 57 b. 69 c. 42 d. 99 Answers Consult your teacher. 7. Give reason. a. 5 is a prime number. b. 8 is a composite number. 8. Separate prime and composite number from 50 to 100. 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
Oasis School Mathematics Book-5 67 Factors of the numbers 1 to 20. 20 19 18 17 16 15 14 13 12 11 10 10 9 9 8 8 7 7 6 6 6 5 5 5 5 4 4 4 4 4 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Activity
Oasis School Mathematics Book-5 68 • Make the table of 20 × 20 grid. • In the bottom row, write 1 in all the box. • In the second last row, write 2 in the gap of 1 boxes. • In third last low, write 3 in the gap of 2 boxes. • In the fourth last row, write 4 in the gap of 4 boxes. To find the factor 4, see the number 4 on the grid. Under 4 in the same column there are 4, 2, 1. \ Factors of 4 are 4, 2, 1. Similarly, complete the table. From the given table the factors of the number are: 6 11 16 7 12 17 8 13 18 9 14 19 10 15 20 The prime numbers from 1 to 20 are ...................................................................... Let's take any two numbers 18 and 24. The possible factors of 18 are 1, 2, 3, 6, 9, and 18. The possible factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24. The common factor of 18 and 24 are 1, 2, 3 and 6. Here, the greatest common factors of 18 and 24 is 6. Hence, the highest common factor (H.C.F.) of two or more than two numbers is the greatest number that is the factor of all the numbers. Finding h.c.F. by prime factorisation method: Let's find the H.C.F. of two numbers using prime factorisation method. The greatest common factor is the highest common factor. Highest Common Factor (H.C.F.)
Oasis School Mathematics Book-5 69 Steps: • Break each of the given numbers into their prime factors. • Take out the common prime factors. • Multiply the common prime factors obtained from the second step. • The product so obtained is H.C.F. Find the H.C.F. of 24 and 54. Solution: Now, 24 = 2 × 2 × 2 × 3 54 = 2 × 3 × 3 × 3 H.C.F. = 2 × 3 (Taking common factors) = 6 example : 2 24 2 12 2 6 3 2 54 3 27 3 9 3 note: H.C.F. of two prime numbers = 1. Let’s take any two numbers 6 and 8. The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48 etc. The multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64 etc. The common multiples are 24, 48, .... etc., smallest common multiple is 24. \ L.C.M. of 6 and 8 is 24. H.C.F. of 5 and 7 is 1. Finding of l.c.m. by prime factorisation method: Let's take any two numbers 12 ans 18. Here, Now, 12 = 2 × 2 × 3 18 = 2 × 3 × 3 \ L.C.M. = 2 × 3 × 2 × 3 = 36 2 12 2 6 3 2 18 3 9 3 Steps: • Resolve each of the given numbers into its factors. • Select all the common factors. • Select rest of the factors which are not common. • Multiply these factors. • The product so obtained is L.C.M. 2 and 3 are common factors and rest of the factors are 2 and 3. L.C.M. = 2 × 3 × 2 × 3 Lowest Common Multiple (L.C.M.)
Oasis School Mathematics Book-5 70 note: L.C.M. of two prime numbers = their product L.C.M. of 5 and 7 = 5 × 7 = 35 Finding l.c.m. by division method: If the given numbers are large, we use division method to find the L.C.M. Find the L.C.M. of 12, 16 and 24: \ L.C.M = 2 × 2 × 2 × 3 × 1 × 2 × 1 = 48 2 12, 16, 24 2 6, 8, 12 2 3, 4, 6 3 3, 2, 3 1, 2, 1 Steps: • Write all the numbers in a line. • Divide the given numbers by a prime factors if it divides at least two of them. • Write down the quotient and the undivided number side by side in the next line. • Proceed in this way until you get all the numbers prime in a row. • Find the product of divisors and the numbers in the last row. • The product so obtained is L.C.M. L.C.M. of 3 and 11 is 3 × 11 = 33. 1. Write all the possible factors of the following numbers. list the common factors and then find h.c.F. a. 9, 12 b. 15, 18 c. 15, 20 d. 16, 24 e. 20, 25 f. 36, 60 g. 48, 64 2. Find the twelve multiples of the following numbers. list the common multiples and then find l.c.m. a. 2, 5 b. 4, 6 c. 3, 5 d. 6, 8 e. 4, 8 f. 6, 12 g. 6, 10 3. using prime factorisation method, find the h.c.F. of: a. 6, 8 b. 8, 12 c. 6, 16 d. 9, 12 e. 12, 16 f. 18, 27 g. 12, 15 h. 27, 45 i. 24, 28 j. 36, 48 k. 10, 15, 20 l. 18, 24, 36 m. 12, 15, 18 n. 28, 42, 56 o. 36, 18, 12 4. using division method, find the l.c.m. of: a. 6, 16, 24 b. 9, 12, 18 c. 15, 25, 35 d. 20, 30, 40 e. 36, 48, 60 f. 40, 45, 60 g. 48, 72, 96 h. 28, 42, 84 i. 26, 52, 65 j. 28, 36, 42 Exercise 3.8
Oasis School Mathematics Book-5 71 Let's observe the following statements, out of 100 full marks, Santosh obtained 62 marks: In general, we say he obtained around 60 marks. In general we say, • I have Rs. 68. • I have around Rs. 70. There are 56 students in a class. In general we say There are around 60 students in a class. 10, 20, 30, 40, 50, etc. are tens In above three examples we have replaced a number into tens which is closer to the given number. 5. a. Find the greatest number which exactly divides 12 and 21? b. Find the greatest number which exactly divides 15, 20 and 25? 6. a. Find the smallest number which is exactly divisible by 8, 12 and 18. b. Find the smallest number which is exactly divisible by 12, 18 and 24. 7. a. If ‘a’ and ‘b’ are the prime numbers, find their H.C.F. and L.C.M. b. What is the H.C.F. of 5 and 11? c. What is the L.C.M. of 2 and 3? Answers 1. a) 3 b) 3 c) 5 d) 4 e) 5 f) 12 g) 16 2. a) 10 b) 12 c) 15 d) 24 e) 8 f) 12 g) 30 3. a) 2 b) 4 c) 2 d) 3 e) 4 f) 9 g) 3 h) 9 i) 4 j) 12 k) 5 l) 6 m) 3 n) 14 o) 6 4. a) 48 b) 36 c) 525 d) 120 e) 720 f) 360 g) 288 h) 84 i) 260 j) 252 5. a) 3 b) 5 6. a) 72 b) 72 7. a) H.C.F.=1, L.C.M. = ab, b) H.C.F. = 1, L.C.M. = 55, c) H.C.F. = 1, L.C.M. = 6. Rounding off Whole Numbers
Oasis School Mathematics Book-5 72 Rounding off to the nearest 100. 200 210 220 230 240 250 260 270 280 290 300 Take a number 240. Number 240 lies between 200 and 300. 240 is closer to 200 than 300. \ We round off 240 to 200. Again, take a number 278. • 100, 200, 300, 400, etc. are hundred 278 lies closer to 300 than 200. We round off 278 to 300. Again, 250 is halfway between 200 and 300. We round off 250 to higher number. 250 rounded off to the nearest hundred is 300. Hence, rounding off means replacing the given number by another convenient number which is easy to understand but close to the original number. Remember ! To round off the number to the nearest 100 • Look at the digit in the tens place. • If the digit at tens place is 0, 1, 2, 3 or 4, replace each of the tens and ones digit by 0 and keep the other digit same. • If the digit at tens place is 5, 6, 7, 8, or 9, then increase the hundreds digit by 1 and replace each of the tens and ones digit by 0. Rounding off to the nearest 1000. 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 3000
Oasis School Mathematics Book-5 73 Here, 2300 lies between 2000 and 3000. It is closer to 2000 than 3000. \ We round off 2300 to 2000. Again, 2600 is closer to 3000 than 2000. \ We round off 2600 to 3000. Again, 2500 is halfway between 2000 and 3000. We round off to the higher number. \ 2500 rounded off to the nearest ten is 3000. Observe the above number line and answer the question given below: • To which number 2000 or 3000 closer from 2300? • To which number 2000 or 3000 closer from 2600? • To which number 2000 or 3000 closer from 2500? Remember ! To round off the number to the nearest 1000 • Look at the digit in the hundred place. • If the digit at the hundreds place is 1, 2, 3, or 4, replace the hundreds digit by 0 and write digit in tens and ones also 0. • If the digit at the hundreds place is 5, 6, 7, 8 or 9, replace the hundreds, tens and ones digit by 0 and increase the thousands digit by 1. cRemember ! lass Assignment 1. Round off the given numbers to the nearest hundred. 900 910 920 930 940 950 960 970 980 990 100 910 930 990 980 920 960
Oasis School Mathematics Book-5 74 Let's convert some statements rounding off to its nearest hundred. Ramesh has Rs. 570. ⇒ Ramesh has around Rs. 600. There are 716 students in a school. ⇒ There are around 700 students in a school. Lochan won the election by the majority of 1583 votes. ⇒ Lochan won the election by the majority of around 1600 votes. Again, here are some statements, rounding off to the nearest thousands. I have Rs. 1372. ⇒ I have around Rs. 1000. The are 15762 voters in a municipality. ⇒ There are around 16,000 voters in a municipality. Monthly salary of Sangita is Rs. 22635. ⇒ Monthly salary of Sangita is around Rs. 23,000. 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 3000 2 Round off the given numbers to the nearest thousand. 2100 2400 2800 2600 2300 2900 1. Observe the given number line and round off the circled numbers to the nearest hundred. 200 210 220 230 240 250 260 270 280 290 300 a. Exercise 3.8
Oasis School Mathematics Book-5 75 b. 500 510 520 530 540 550 560 570 580 590 600 c. 700 710 720 730 740 750 760 770 780 790 800 2. Round off the following numbers to the nearest hundred. a. 226 b. 387 c. 524 d. 694 e. 836 f. 792 3. convert the given statement after rounding off to the nearest hundred. a. There are 668 people in a community. b. 432 people in a community get vaccinated against Covid-19 c. There are 473 students in a school. d. I have 322 friends in facebook. 4. Observe the given number line and round off the circled numbers to the nearest thousand. 5000 5100 5200 5300 5400 5500 5600 5700 5800 5900 6000 a. 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900 3000 c. 7000 7100 7200 7300 7400 7500 7600 7700 7800 7900 8000 b. 5. round off the following numbers to the nearest thousand. a. 3200 b. 4100 c. 28200 d. 59100 e. 38200 f. 46700
Oasis School Mathematics Book-5 76 6. convert the given statement after rounding off to nearest thousands. a. There are 38642 voters in a municipality. b. 50138 people in a municipality were vaccinated against Covid-19. c. There are 27782 audience in a stadium. d. 96382 examiners attempt an examination. 1. a. What are the first 9 places of local place value system of numeration? b. Display the number 237642104 in the place value chart according to local place value system. c. Put comma according to this system and write its number name. 2. a. What are periods of 9 digits number according to International Place Value System. b. Display the number 306542096 in the place value chart according to International place value system. c. Put comma according to this system d. Write its number name. 3. a. ( cf]6f cª\sn] ag]sf ;+Vofsf :yfg / lk6Lo8x? s] s] x'g< n]Vg'xf];\ . b. $%^@#&$!@ nfO{ :yfgLo k4tLcg';f/ :yfgdfg tflnsfdf k|:t't ug'{xf];\ . c. :yfgLo k4tLcg';f/ sdf -,_ k|of]u u/L pQm ;ª\Vofsf] gfd n]Vg'xf];\ . 4. a. Find the odd and even numbers from 10 to 20. b. Separate these numbers into prime and composite. c. Write the multiplies of 2 between 1 to 20. d. Write the multiplies of 3 between 1 to 20. e. Write the multiples of 5 between 1 to 20. f. Factorize the number 20 using factor tree method. Miscellaneous Exercise
Oasis School Mathematics Book-5 77 5. From the multiplication fact 2 × 9 = 18. a. What are the factors of 18 and what is the multiple of 2 and 9? b. From the another multiplication fact and write 3 statements amount factor and multiple. c. Write all possible multiplication fact of 18. d. From the above example, make the list of all possible factors of 18. 6. a. Identify whether 178 is nearer to 100 or 200. b. Round off 178 to its nearest hundred. c. Identify whether 2768 is nearer to 2000 or 3000. d. Round off 2768 to its nearest thousands. 7. a. There are 1684 students in a school. Convert this information rounding off to its nearest hundred. b. Convert this statement rounding off to its nearest thousand. Answers Consult your teacher. Project Work • Collect 5/5 different statement in our daily life where the rounding off the number to its nearest hundred and to its nearest thousand are applied. • From different sources. Find the population of SAARC countries. Put comma according to local place value system and write their number name in Devanagari and local place value system. Express the population by rounding off the its nearest thousands: Similarly, using International place value system put comma and write the number name using International place value system.
Oasis School Mathematics Book-5 78 choose the correct alternatives. 1. One hundred thousand is equal to (i) one lakh (ii) ten lakh (iii) one crore 2. One million is equal to (i) one lakh (ii) ten lakh (iii) one crore 3. Which of the following number is neither prime nor composite? (i) 2 (ii) 1 (iii) 3 4. One crore sixty lakh three thousand eighty two is (i) 16203082 (ii) 1623082 (iii) 1620382 5. two hundred thirty two million, sixty two thousand ninety two is (i) 2326212 (ii) 232062012 (iii) 23206212 6. rounding off 23573 is its nearest thousand is (i) 23570 (ii) 23600 (iii) 24000 7. rounding of 56823 to its nearest hundred is (i) 56820 (ii) 56800 (iii) 56900 8. the possible factors of 8 are (i) 2 and 4 (ii) 2, 4 and 8 (iii) 1, 2, 4 and 8 9. Which of the following statement is not true? (i) 2 is only one prime number which is even. (ii) Every even number is composite. (iii) Two factors of prime numbers are 1 and the number itself. 10. Which of the following number is not a prime number (i) 17 (ii) 13 (iii) 12
Oasis School Mathematics Book-5 79 11. What are the factors of 12? (i) 1, 2, 3, 6, 12 (ii) 1, 2, 3, 4, 6 (iii) 1, 2, 3, 4, 6, 12 12. Which one of the following is not a period? (i) Lakh (ii) Ten thousand (iii) Thousand 13. Which one of the following is not a factor of 8? (i) 2 (ii) 4 (iii) 3 14. Which one of the following is not a multiple of 7? (i) 21 (ii) 35 (c) 40 15. Select the best answer for each problem. a. Prithvi Narayan Shah was born on 1779 B.S. About how many years ago was he born? (i) About 300 years (ii) About 200 years (iii) About 400 years b. The zipper was invented on 1891A.D. About how many years ago was that data? Select the answer in tens. (i) About 140 years (ii) About 130 years (iii) About 200 years c. The total audience in a football match is 89,376. It is (i) About 90,000 (ii) About 91,000 (iii) About 89,000.
Oasis School Mathematics Book-5 80 Unit Test Full marks – 30 Attempt all the questions. 1. a. Show the number 5265913062 in the place value chart. 1 b. Put comma in a appropriate place. 1 c. Write its number name using Local place value system. 2 2. a. Show the number 560186307 in place value chart. b. Put comma in appropriate place using International Place Value System. c. Write its number using International place value system. 2 3. a. Write the all prime numbers between 1 to 20. 2 b. Write the following Hindu Arabic numbers in Devanagari numbers and write their number name. 3 (i) 567128 (ii) 1265102 4. round off the following numbers 2 a. 561237 (to its nearest thousand) b. 650815 (to its nearest hundreds) 5. a. Write all the possible factors of 12. 2 b. Write first 5 multiplies of 3. 2 c Factorise 30 using factor tree. 2 6. rewrite the following statements by rounding off: 2 a. There are 1683 students in a school. (nearest hundred) b. Monthly salary of Aasma is Rs. 56582. (nearest thousand) 7. a. Write the number if its name is Three hundred forty two million, sixty three thousand four hundred twenty six. 1 b. Put comma using International place value system. 1 c. Put comma using Local place value system. 1 d. Write in number name according to Local place value system. 2 e. Write this number in Devanagari and its number name in Devanagari. 2
Oasis School Mathematics Book-5 81 Review • When the numbers are added, the result is the sum: 7 + 5 = 12 (sum) • When the numbers are subtracted, the result is the difference: 12 - 8 = 4 (difference) In the relation 7 + 5 = 12, 12 is the sum of 7 and 5. 12 – 8 = 4, 4 is the difference between 12 and 8. 1. complete the following as above: a. 12 + 7 + 8 = ........ + ........ = ........ b. 25 + 6 + 5 = ........ + ........ = ........ c. 13 + 7 + 6 = ........ + ........ = ........ d. 27 + 3 + 8 = ........ + ........ = ........ e. 14 + 18 + 2 = ........ + ........ = ........ f. 53 + 17 + 5 = ........ + ........ = ........ 2. a. What should be added to 18 to make 25? b. What should be subtracted from 12 to make 7? c. What should be subtracted from the sum of 12 and 18 to get 20? d. What should be added to the difference of 18 and 12 to make 15? e. What should be subtracted from the difference of 18 and 6 to make 8? class Assignment Four Fundamental Operations UNIT 4 Add: 7 + 9 + 3 = 10 + 9 = 19 14 + 8 + 6 = 20 + 8 = 28 7 + 3 = 10, 10 + 9 = 19 14 + 6 = 20, 20 + 8 = 28 23 + 6 + 7 = 30 + 6 = 36
Oasis School Mathematics Book-5 82 4. A set of numbers is given 12, 18, 16, 20, 25, 30 Take any three numbers from the above set whose sum is 50. + + = 50 Take any two numbers from the above set whose sum is 50. + + = 50 Take any three numbers from the above set whose sum is 75. + + = 75 Take any four numbers from the above set whose sum is 80 + + + = 80 Review on Addition and Subtraction of Large Numbers Addition: Addition of very large numbers is same as the addition of smaller numbers. Start to add from ones and regroup if necessary. Add: Look at one more example, 3746489 + 589642 + 57829 1 1 1 1 1 1 3 4 7 6 4 8 7 + 2 9 4 5 7 6 3 6 4 2 2 2 5 0 1 1 2 1 1 2 3 7 4 6 4 8 9 + 5 8 9 6 4 2 + 5 7 8 2 9 4 3 9 3 9 6 0 Carry over Carry over I understand, while adding I have to add the digits of same place. 3. complete the given table: 25 57 + 32 –..... 38 –..... 18 +..... 42
Oasis School Mathematics Book-5 83 Subtraction: Subtraction of very large numbers is same as the subtraction of the smaller numbers. Start subtracting from ones and regroup if necessary. 4 12 11 15 13 8 14 5 3 2 6 3 9 4 - 2 6 5 7 6 8 7 2 6 6 8 7 0 7 7 9 9 9 9 9 10 8 0 0 0 0 0 0 - 2 5 6 3 8 2 7 5 4 3 6 1 7 3 Alternative method 7 9 9 9 9 9 9 - 2 5 6 3 8 2 6 5 4 3 6 1 7 3 Subtract 1 from 8000000 = 7999999 Subtract 1 from 2563827 = 2563826 Subtract them Look at one more example. 8000000 - 2563827 Addition and subtraction together: 23576408 + 57146374 - 21857431 Solution: 1 1 1 1 2 3 5 7 6 4 0 8 + 5 7 1 4 6 3 7 4 8 0 7 2 2 7 8 2 First Add two numbers having positive sign. Again, 7 9 16 11 12 8 0 7 2 2 7 8 2 - 2 1 8 5 7 4 3 1 5 8 8 6 5 3 5 1 Subtract the numbers having negative sign from the sum. 1. Add: 45 879 2 3 + 5 694 6 7 + 859 2 6 c. 3 4 7 6 8 7 9 + 8 2 7 4 9 6 7 3 2 0 8 9 6 4 9 + 5 8 6 9 4 7 3 6 a. b. Exercise 4.1
Oasis School Mathematics Book-5 84 2. Add the following: a. 2387641 + 586435 + 287637 + 4873 b. 4587326 + 38645731 + 56473 + 678 3. Subtract the following: 5 6 8 7 3 4 2 - 2 1 6 5 9 7 3 4 7 6 3 5 2 1 - 2 8 7 4 7 6 5 3 2 0 4 3 7 0 - 6 4 2 1 7 5 a. b. c. 4. Subtract the following: a. 3257639 - 1283768 b. 5365042 - 876358 c. 63577804 - 29765496 d. 72548692 - 379689 5. Simplify: a. 2368407 + 5346218 – 1423857 b. 58324604 – 2304325 + 28410842 There are many situations in our daily life where addition and subtraction takes place. Observe the following events and identify which mathematical operations is to be applied here. • There are 6520kg apples and 7820kg oranges in a store. How many kg fruits are there altogether? • If 2625kg apples are sold. How much kg apples are left to sell? If 6284 kg oranges are sold, how many kg oranges are left to sell? In first case, we have to operate addition and in next two cases we have to operate subtraction. Answers Consult your teacher. Verbal Problems on Addition and Subtraction
Oasis School Mathematics Book-5 85 The male and female population of a town are 1,56,97,642 and 1,37,14,572 respectively. Find the total population of the town. Solution: example 1 Male population = 1 5 6 9 7 6 4 2 Female population = + 1 3 7 1 4 5 7 2 Total population = 2 9 4 1 2 2 1 4 \ Total population of the town is 2,94,12,214. Read the questions properly and decide what you have to do, addition or subtraction. The cost of a piece of land is Rs. 45,25,742 and the cost of another piece is Rs.35,46,827. By how much is the cost of first piece more than the second? Solution: example 2 The cost of first piece of land = Rs 4 5 2 5 7 4 2 The cost of second piece of land = - Rs 3 5 4 6 8 2 7 Their difference = Rs 9 7 8 9 1 5 \ The cost of first piece of land is Rs 9, 78, 915 more than that of the second. 2. a. Find the number that is 3,852 greater than 18,296? b. Find the number which is 5625 more than 12,682? 1. a. There are 56,692 men, 78,342 women and 22,683 children in a town. Find the total population of the town. b. A man earns Rs 32,635 in the month of Baishakh, Rs 45,645 in the month of Jestha and Rs 56205 in the month of Asad. What is his total income in three months? 3. a. What is the sum of the greatest number of 7 digits and the smallest number of 8 digits? b. What is the sum of the greatest number of 7 digits and the greatest number formed by the digits 3, 8, 9, 2, 6, 0? Exercise 4.2
Oasis School Mathematics Book-5 86 Answers Consult your teacher. When two numbers are multiplied, the result is called the product and the numbers are its factors. multiplication of a number by 10, 20, 30, etc. 45 × 30 = 1350 55 × 40 = 2200 45 × 3 = 135, write one zero after 135 55 × 4 = 220, write one zero after 220 5 × 7 = 35 factors product multiply: 24 × 30 = 32 × 20 = 46 × 40 = 52 × 50 = 56 × 30 = 83 × 60 = Project Work Prepare a short story on a fruit seller where addition and subtraction take place. 5. a. What is the difference of the greatest number of 6 digits and the smallest number of 6 digits? b. What is the difference between the greatest number of 7 digits and the smallest number formed by the digits 2, 3, 6, 4, 2, 1, 5? 6. a. The sum of two numbers is 57,28,631. If one of the numbers is 27,81,624, find the other number. b. Which number should be subtracted from 74,26,817 to make 34,08,962? 4. a. Find the number that is 12,632 less than 24,864? b. Find the number which is 14,696 less than 18,782? Multiplication
Oasis School Mathematics Book-5 87 multiplication of a number by 100, 200, 300, etc. Study the given multiplications, 48 × 300 = 14400 35 × 200 = 7000 Multiply 48 and 3 48 × 3 = 144 Write 2 zeros at the end = 144000 35 × 2 = 70 \ 35 × 200 = 7000 multiply: 42 × 10 = 46 × 20 = 82 × 30 = 96 × 40 = 57 × 50 = 84 × 60 = 12 × 100 = 32 × 200 = 56 × 300 = 43 × 400 = 38 × 500 = 45 × 600 = 15 × 1000 = 17 × 2000 = 28 × 3000 = 36×4000 = 42 × 6000 = 45 × 5000 = class Assignment multiplication of large numbers We have already learnt the multiplication of 4 digit numbers by 3 digit numbers. Let's revise it. Let's see an example, Multiply 4263 × 524. Solution: 4 2 6 3 × 5 2 4 1 7 0 5 2 8 5 2 6 0 + 2 1 3 1 5 0 0 2 2 3 3 8 1 2 Multiply by ones 4 2 6 3 × 4 1 7 0 5 2 Multiply by tens 4 2 6 3 × 2 0 8 5 2 6 0 Multiply by hundreds 4 2 6 3 × 5 0 0 2131500 \ 4263 × 524 = 2233812
Oasis School Mathematics Book-5 88 4 2 6 3 × 5 2 4 1 7 0 5 2 8 5 2 6 0 2 1 3 1 5 0 0 2 2 3 3 8 1 2 + 1. multiply: a. 62 × 20 b. 363 × 30 c. 462 × 200 d. 568 × 400 e. 637 × 6000 f. 882 × 7000 g. 498 × 5000 h. 3254 × 4000 2. multiply: a. 2315 × 54 b. 9621 × 36 c. 3402 × 45 d. 2315 × 54 e. 1968 × 305 f. 5021 × 412 g. 8093 × 265 h. 5264 × 374 Exercise 4.3 Answers Consult your teacher. When a number is divided by the other, Divisor 5) 36 (7 Quotient - 35 1 Remainder Again, 400 ÷ 20 = 40 ÷ 2 = 20 600 ÷ 40 = 60 ÷ 4 = 15 900 ÷ 30 = 90 ÷ 3 = 30 Cancel same number of zeros from the dividend and divisor. Division of a number by 10, 20, 30, 100, 200, 300, etc. 50 ÷ 10 = 5 60 ÷ 20 = 6 ÷ 2 = 3 80 ÷ 40 = 8 ÷ 4 = 2 When the dividend ending with zeros is divided by another number ending with zeros cancel the same number of zeros from the end of both dividend and divisor. In short method, Division
Oasis School Mathematics Book-5 89 200 ÷ 20 = 400 ÷ 10 = 300 ÷ 30 = 600 ÷ 30 = 600 ÷ 20 = 500 ÷ 50 = 400 ÷ 20 = 60 ÷ 20 = 80 ÷ 40 = 900 ÷ 30 = 800 ÷ 40 = 600 ÷ 20 = 80 ÷ 10 = 400 ÷ 80 = 600 ÷ 40 = class Assignment Divide: We have already learnt about the division of four digit numbers by two digit numbers. Let's divide a 6 digit number by a 3 digit number. Division of larger numbers Remember ! • 0 ÷ any number = 0 • any number ÷ 1 = the number itself. Divide: 475286 ÷ 125 Solution: 125) 4 7 5 2 8 6 (3802 Quotient - 3 7 5 1 0 0 2 - 1 0 0 0 2 8 6 - 2 5 0 3 6 Remainder \ Quotient = 3802 Remainder = 36 Steps: • 125 is a three digit number. So take three digits 475 from the dividend. • 125 × 3 = 375, write 3 as the quotient • 475 - 375 = 100, bring down 2, now the new dividend is 1002. 125 × 8 = 1000, write 8 as the quotient • 1002 - 1000 = 2, bring down 8, now the new dividend is 28. • 28 is not divisible by 125, write 0 as the quotient. • Bring down 6. Now, the new dividend is 286. • 125 × 2 = 250, write 2 as the quotient. • 286 - 250 = 36 (Remainder)
Oasis School Mathematics Book-5 90 1. Divide: a. 140 ÷ 20 b. 270 ÷ 90 c. 840 ÷ 40 d. 950 ÷ 50 e. 2800 ÷ 70 f. 1600 ÷ 400 g. 35000 ÷ 7000 h. 54000 ÷ 9000 i. 7200000 ÷ 80000 2. Divide: a. 2225 ÷ 15 b. 3325 ÷ 25 c. 4618 ÷ 35 d. 2275 ÷ 25 e. 3360 ÷ 35 f. 5832 ÷ 84 g. 12686 ÷ 51 h. 49872 ÷ 68 i. 18468 ÷ 22 j. 4650 ÷ 265 k. 37654 ÷ 365 l. 67632 ÷ 575 There are many situations in our daily life where multiplication and division take place. There are 315 students in a school. Each student pays Rs. 3750 every month. Other expense except salary of teacher is Rs. 1,50,000.Each teacher gets the monthly salary of Rs. 22540. Net profit made by the school is to be divided equally among 15 shareholders. Study the above paragraph properly and answer the questions given below. a. What is the total monthly income of the school? b. What is the income of the school after deducting other expenses? c. What amount of salary is to paid to the teacher? d. What is the net profit of school? e. How much does each shareholder get? Identify which mathematical operations is used in above cases? Exercise 4.5 Answers Consult your teacher. Word Problems on Multiplication and Division
Oasis School Mathematics Book-5 91 While solving the word problems, follow the following steps: Steps: • Understand the questions • Decide what to do. (+, –, ×, ÷) • Solve the problem. A train travels 3696 km in 24 hours. How many kilometers does it travel in one hour? Solution: Distance covered by train in 24 hours = 3696 km Distance covered by train in 1 hour = 3696 24 km \ Distance covered by a train in 1 hour = 154 km example 2 Now, 24 ) 3 6 9 6 (154 - 2 4 1 2 9 - 1 2 0 9 6 - 9 6 0 The cost of a refrigerator is Rs 15,875. What is the cost of 12 refrigerators? Solution: The cost of a refrigerator = Rs 15875 The cost of 12 refrigerators = Rs 15,875 × 12 Now, \ The cost of 12 refrigerators = Rs 1,90,500. example 1 1 5 8 7 5 × 1 2 3 1 7 5 0 1 5 8 7 5 1 9 0 5 0 0 In 1 hour a train travels less distance than in 24 hours. So, I have to divide. Cost of 12 refrigerators is more than the cost of one. So I have to multiply. +
Oasis School Mathematics Book-5 92 1 Solve the following problems: a. The cost of a mobile set is Rs 1,875. What will be the cost of 18 mobile sets? b. There are 346 chocolates in a packet. How many chocolates are there in 525 packets? c. A dealer bought 3,465 meters of cloths at a rate of Rs 425 per metre. How much did he pay altogether? d. A man earns Rs 2,235 a day. How much does he earn in 365 days? 2. a. How many times can a number 36 be subtracted from 7344? b. The product of two numbers is 14,875. If one number is 425, find the other number. c. Yearly income of a man is Rs 1,65,710. How much does he earn in 1 day? d. A school needs 24,500 pencils in a year. How many boxes of 25 must the school buy? Exercise 4.5 Activity Multiplication using doubling and halving skills. multiply: 35 × 27 Steps: • Write two numbers in two columns. • Double the first column and half the second column. Ignore the remainder while halving. • Keep finding halves until you reach 1. • Cross both the numbers if there are even numbers in both column. • Add the remaining numbers from the column where you double the numbers. Answers Consult your teacher. 35 + 70 + 280 + 560 = 945 First column Second column 35 70 140 280 560 27 13 6 3 1
Oasis School Mathematics Book-5 93 Using this method, multiply: (a) 42 × 24 (b) 21 × 35 (c) 52 × 23 checking: 3 5 × 2 7 2 4 5 + 7 0 0 9 4 5 game of addition and division • Take any three single digit numbers 3 5 and 6 • Make all the possible 2 digit numbers 35 36 53 56 63 and 65 • Add these numbers. 35 + 36 + 53 + 56 + 63 + 65 = 308 • Add the first 3 single digit numbers. 3 + 5 + 6 = 14 • Divide : 308 by 14 308 ÷ 14 = 22 Let's try this, with three single digit numbers. a. 3, 5, 9 b. 2, 4, 8 c. 3, 6, 8 It's interesting! Every time final result is 22.
Oasis School Mathematics Book-5 94 Addition rule: • The addition of two numbers with positive sign gives the sum with positive sign. (+ number) + (+ number) = (+ sum) Example : (+8) + +5) = 13, (+9) + (+2) = + 11, etc. • The addition of two numbers with negative sign gives the sum with negative sign. (- number) + (- number) = (- sum) Examples: (-3) + (-5) = (-8), (-6) +(-7) = (-13), etc. Two numbers with same signs are always added. + 5 + 3 = + 8 (-3)+ (-6) = (-9) • The addition with two numbers with a positive and negative gives the sum with the sign of larger number. (+ number) + (- number) = (+ sum) if (+ number) > (- number) (+ number) + (- number) = (- sum) if (+ number) < (- number) multiplication rule: • Multiplication of two numbers with positive sign each gives the product with positive sign. (+number) × (+ number) = (+ product) Examples: (+6) × (+7) = + 42, (+5) × (+2) = (+10), etc. Two numbers with different signs are always subtracted. Sign of the result is the sign of the greater number. (+6) + (-5) = (+1) (+3) + (-7) = (-4) (+2) × (+3) = ( +6) + 5 is a positive number. 5 is a positive number. - 5 is a negative number. The mathematical operations (addition, subtraction, multiplication and division) follow the following rules to use + or - sign. The number with no sign just before it is a positive number. Sign rules of Plus (+), Minus (-), Multiplication (×) and Division (÷)
Oasis School Mathematics Book-5 95 • Multiplication of two numbers with negative sign each gives the product with positive sign. (- number) × (- number) = (+ product) Examples: (+-5) × (-3) = (+15), (-7) × (-2) = (+14), etc. (-4) × (-5) = (+20) • Multiplication of two numbers with different signs gives the product with negative sign. (+ number) × (- number) = (- product) (- number) × (+ number) = (- product) Example: (+6) × (–5) = (–30), (–3) × (+9) = –27, etc. (+3) × (-5) = (-15) (-4) × (+6) = (-24) Division rule: • The division of two numbers with positive sign each gives the quotient with positive sign. (+ number) ÷ (+ number) = (+ quotient) Examples: (+6) ÷ (+2) = + 3, (+18) ÷ (+3) = +6, etc. • The division of two numbers with negative sign each gives the quotient with positive sign. (- number) ÷ (- number) = (+ quotient) Examples: (–24) ÷ (–4) = +6, (–33) ÷ (–3) = + 11, etc. • The division of two numbers with different signs gives the quotient with negative sign. (-number) ÷ (+ number) = (- quotient) (+number) ÷ (- number) = (- quotient) Examples: (–12) ÷ (+3) = (–4), (+20) ÷ (–5) = –4, etc. (+6) ÷ (-2) = (-3) (-12) ÷ (+3) = (-4) (+6) ÷ (+2) = ( +3)
Oasis School Mathematics Book-5 96 1. Simplify: a. (+6) + (+8) b. (+5) + (+7) + (+3) c. (+6) + (+9) + (+3) d. (-7) + (-6) e. (-8) + (+3) f. (-6) + (+9) g. (+7) + (-3) h. (-9) + (+5) i. (+7) + (-9) + (+3) j. (+9) + (-8) + (+3) k. (-8) + (-3) l. (-7) + (-6) m. (-5) + (-9) n. (-3) + (-7) + (+6) o. (-6) + (-7) + (+8) Exercise 4.7 2. Simplify: a. (+6) × (+3) b. (+8) × (+4) c. (+7) × (-3) d. (+5) × (-6) e. (+7) × (-2) f. (-9) × (+3) g. (-3) × (+4) h. (-3) × (-4) i. (-6) × (-2) j. (-7) × (-4) k. (-2) × (+6) × (+3) l. (+3) × (-6) × (-8) m. (-6) × (+3) × (-2) n. (+8) × (-3) × (-2) o. (-2) × (+3) × (-4) 3. Simplify: a. (+20) ÷ (+4) b. (–24) ÷ (-6) c. (–32) ÷ (+4) d. (+40) ÷ (–8) e. (–50) ÷ (+10) f. (–48) ÷ (–6) g. (–56) ÷ (+7) h. (–42) ÷ (–7) i. (+60) ÷ (–4) j. (–28) ÷ (–7) k. (–36) ÷ (+4) Answers Consult your teacher. (+) × (+) = (+) (+) ÷ (+) = (+) (+) × (-) = (-) (+) ÷ (-) = (-) (-) × (+) = (-) (-) ÷ (+) = (-) (-) × (-) = (+) (-) ÷ (-) = (+) Summary
Oasis School Mathematics Book-5 97 An expression may contain two or more mathematical operations. Such expressions can be solved by following these operations in proper order. This process is called simplification. Addition, subtraction, multiplication and division are four fundamental operations. Such mixed operations in a problem are performed in the following order. Division (D) Operate first Multiplication (M) Operate second Addition (A) Operate third Subtraction (S) Operate last Simplify: 49 ÷ 7 × 4 - 6 + 15. Solution: 49 ÷ 7 × 4 - 6 + 15 = 7 × 4 - 6 + 15 [operating ÷ sign] = 28 - 6 + 15 [operating × sign] = 43 - 6 [operating + sign] = 37 [operating - sign] Simplify: 15 – 18 + 16 – 17 Solution: 15 – 18 + 16 – 17 = 15 + 16 – 18 – 17 = 31 – 35 [Add two +ve terms and two -ve terms] = –4 example 2 example 1 I have to operate ÷, ×, + and - in order. Order of Operations
Oasis School Mathematics Book-5 98 Divide 75 by 5, then subtract 10 from the quotient. Solution: Mathematical expression for the given statement is 75 ÷ 5 - 10 = 15 - 10 = 5 From the sum Rs. 400, a man spent Rs. 60 and Rs. 130 in two successive days, how much money is left? Solution: Let's convert the above statement into mathematical form. Now, 400 – 60 – 130 = 400 – 190 [Adding two negative numbers] = 110 example 3 example 4 1. Simplify: a. + 3 – 2 b. – 7 + 6 + 8 c. 18 – 7 – 6 + 8 - 2 d. 15 – 5 + 6 – 8 – 2 e. – 20 + 6 - 3 + 15 - 7 f. -50 + 20 - 80 + 40 2. Simplify: a. 6 × 3 – 2 b. –6 + 3 × 7 - 5 c. 5 × 7 – 3 + 2 d. 20 × 2 – 3 – 5 e. 25 + 13 × 3 + 4 f. 7 × 2 – 3 × 5 g. 15 × 5 – 13 × 3 + 9 h. 6 × 7 – 3 × 2 i. 5 × 4 – 6 + 8 3. Simplify: a. 20 - 6 ÷ 3 b. 35 ÷ 5 - 2 × 3 c. 15 ÷ 3 + 12 ÷ 4 d. 25 + 20 ÷ 5 - 8 Exercise 4.8 e. 18 ÷ 3 - 15 ÷ 5 + 2 × 3 - 2 f. 3 × 6 + 15 ÷ 5 - 2 × 5 + 65 g. 18 × 3 - 5 × 6 - 35 ÷ 7 + 10 h. 32 + 99 ÷ 9 × 3 - 14 × 4 - 11 i. 20 ÷ 4 + 3 × 7 - 8 × 6 j. 18 × 3 - 20 × 2 - 8 × 200 ÷ 25 + 10
Oasis School Mathematics Book-5 99 5. Start with the number given and perform the operations in order shown by arrows: 6. convert the following statement into mathematical expression and simplify. Answers 1. a) 1 b) 7 c) 11 d) 6 e) -9 (f) -70 2. a) 16 b) 10 c) 34 d) 32 e) 68 f) 68 g) -1 (h) 36 (i) 32 3. a) 18 b) 1 c) 8 d) 21 e) 7 f) 76 g) 29 h) -2 i) -22 j) -40 4. a) 19 b) 22 c) 8 d) 26 e) 32 f) 2 g) 55 5. Consult your teacher. 6. a) Rs. 12, 695 b) Rs. 75 Project Work Collect 5 different problems of simplification in our daily life. Present that in your classroom. 4. translate the following statements into mathematical expression and simplify: a. 12 is subtracted from the sum of 13 and 18. b. 7 is added to the product 3 and 5. c. The product of 2 and 7 is added to 9 and 15 is subtracted. d. The product of 4 and 5 is added to the product of 2 and 3. e. 24 is divided by 3 and the quotient is multiplied by 4. f. 95 is divided by 19 and 3 is subtracted from the quotient. g. The quotient of 120 divided by 6 is added to the product of 5 and 7. a. From the monthly salary Rs. 22350 a man spent Rs. 3120 on food and Rs. 6535 in cloths, find how much money is left with him. b. A man earns Rs. 65 per day. From the saving of 6 days, he spent Rs. 250 to buy cloths and Rs. 65 to buy pen. How much money is left with him?
Oasis School Mathematics Book-5 100 i. cross number puzzle. (a) Use +, or – in the circle to get the given result. (b) Use +, × or ÷ sign in the circle to get given result. (c) Put +, × and ÷ once in a circle to get the given result. (d) Put +, – and ÷ once in the circle to get the given result. 132 45 67 8 8 = 100 1 6 2 3 8 11 5 7 9 10 4 Across: 1. 20 × 8 – 48 ÷ 3 1. 123 × 9 + 4 3. 1000 – 25 × 4 + 8 2. 100 ÷ 2 – 1 4. 4 × 100 + 7 3. 200 × 5 - 1 7. 20 × 3 – 18 ÷ 3 4. 8 × 5 8. 265 + 332 – 90 5. 11445 ÷ 15 10. 15 is subtracted from 48 6. product of 40 and 4 is increased by the product of 10 and 3 7. 50 × 100 8. 14 multiplied by 4 9. 125 × 35 11. 3321 + 12 Down: 33 3 3 3 = 100 45 3 2 10 = 40 80 20 2 5 = 7 ii. Find the target. Activity