20) T he sum of 751808112 and 2234184 is subtracted from 964218684. What is the difference obtained? Solution: I Explore (H.O.T.S.) Short Answer Question 21) B y how much is 14617862 less than 27700900? Solve this by rounding the numbers to the nearest thousands. Solution: Number Operations 47
Long Answer Question 22) In a group of primary schools, there are 178645128 students. Out of these 74536200 are in Grade 1, 2, 3. What is the number of students studying in Grade 4 and 5? Who are more in number and by how much? Round off the answer to the nearest hundred. Solution: 4.2 Multiply Large Numbers and Divide Numbers by 2-digit Numbers I Recall Multiple Choice Questions 1) For any three numbers ‘a’, ‘b’ and ‘c’, a × (b × c) = (a × b) × c is called the ______________. [] [] (A) subtraction property (B) associative property (C) identity property (D) both (B) and (C) 2) For any number ‘a’, a × 1 = 1 × a = a. This is also called the ________. (A) subtraction property (B) additive identity (C) multiplicative identity (D) both (B) and (C) 48
3) The multiplication fact for the division fact 4870 ÷ 5 = 974 is _____. [] (A) 5 × 974 = 4870 (B) 4870 ÷ 974 = 5 (C) 974 × 5 = 4870 (D) both (A) and (C) I Remember and Understand Multiple Choice Questions 4) The digit in the ones place of the product between 2222 and 222 is ______.[ ] ] (A) 1 (B) 8 (C) 4 (D) 2 ] 5) The digit in the ones place of the product between 11111 and 11 is ______.[ (A) 2 (B) 1 (C) 3 (D) 4 6) The quotient in the division of 3303 by 3 is ______________. [ (A) 1011 (B) 1110 (C) 111 (D) 1101 Fill in the Blanks 7) T he product of the largest 4-digit number and the largest 2-digit number has ____________ digits. 8) The remainder in the division of 1505 by 5 is _____. 9) The ones digit in the quotient of the division of 4250 by 5 is _______. Very Short Answer Questions 10) Find the product of 1000 and 100. Solution: 11) Find the product of 30000 and 200. Solution: 12) W hat is the equation to check the correctness of a division? Solution: Number Operations 49
Short Answer Questions 13) Multiply: 2568 × 15 Solution: 14) What is the quotient and the remainder of 75148 ÷ 14? Solution: Long Answer Questions b) 1234 × 106 15) Find the following products: a) 6609 × 218 Solution: 50
16) Divide 52725 by 22. Check the correctness of the division. Solution: I Apply Short Answer Questions 17) There are 5606 bags of rice in a warehouse. If each bag weighs 62 kg, what is the total weight of the bags? Solution: 18) ` 47869893 is distributed equally among 9 people. Check if any amount is left over. Number Operations 51
Solution: Long Answer Questions 19) Leena bought 536 electric ovens at ` 3920 each for her shop. How much money did she spend in all? Solution: 20) Keshav has 3125 plants. He planted them in rows, with each row having 25 plants. How many rows were there? Also check the correctness of the division. Solution: 52
I Explore (H.O.T.S.) Short Answer Question 21) F ind the missing numbers in these products. a) T Th Th H T O b) T Th Th H T O 3 4 17 2832 × 63 ×87 1 21 19 24 + 05 2 0 +2 65 21 2 71 4 384 Long Answer Question 22) I n a library, there are 52623 books. If the books are arranged equally in the following numbers of rows, how many books will remain in each case? 2 rows 5 rows 6 rows 9 rows 10 rows Solution: Number Operations 53
4.3 BODMAS [] [] I Recall [] Multiple Choice Questions [] 1) The sum of 20 and 32 is ___________. [] (A) 52 (B) 25 (C) 33 (D) 62 [] 2) The difference between 49 and 30 is ___________. (A) 79 (B) 29 (C) 19 (D) 11 3) The quotient in the division of 99 by 9 is ________. (A) 0 (B) 11 (C) 9 (D) 99 I Remember and Understand Multiple Choice Questions 4) The value of 4 × (2 + 6) is _________. (A) 16 (B) 14 (C) 32 (D) 60 5) The value of 16 – (3 + 9) is _________. (A) 4 (B) 22 (C) 17 (D) 10 6) The value of 4 × 4 ÷ 2 is _________. (A) 16 (B) 4 (C) 8 (D) 1 Fill in the Blanks 7) 15 + 6 – 3 = _______ 8) 2 × 2 + 1 = ______ 9) 3 ÷ 3 – 1 = _______ Very Short Answer Questions 10) What does ‘M’ stand for in BODMAS? Solution: 54
11) Which operation needs to be carried out first according to the BODMAS rule - Subtraction or Division? Solution: 12) What is the full form of ‘A’ in BODMAS? Solution: Short Answer Questions 13) Find the value of: a) 3 × 8 ÷ 4 b) 29 – 9 × 3 Solution: 14) What is the value of: a) 19 ÷ 1 + 19 b) 36 + 32 – 5 Solution: Number Operations 55
Long Answer Questions b) 9 + (9 – 9) 15) Find the values of: a) 13 + 13 × 2 d) 2 + 7 ÷ 1 c) 6 – 16 ÷ 4 Solution: 16) F ind the values of: a) 22 ÷ 11 + 8 b) 14 × (16 + 4) c) 9 + 9 ÷ 9 d) 15 – (9 + 3) Solution: 56
I Apply Short Answer Questions 17) Find the missing number in 4 × 4 + _____ = 26 Solution: 18) Spot the incorrect step and correct it for 7 + 3 × 2 – 1 Step 1: Solving from the left, 7 + 3 = 10 Step 2: Multiplying 10 by 2 = 10 × 2 = 20 Step 3: Subtracting 1 from 20, 20 – 1 = 19 Number Operations 57
Solution: Long Answer Questions b) 14 ÷ 2 + (9 × 3) 19) Solve: a) 5 × 3 + (20 ÷ 4 – 2) Solution: 58
20) Solve: a) 19 + 4 – (5 × 2) b) 8 × 6 – (40 ÷ 5) Solution: I Explore (H.O.T.S.) Short Answer Question 21) Reena had 6 water bottles. Her friend gave her 2 more. She then gave half of the total number of bottles to her sister. How many bottles is she left with? Solve using BODMAS rule. Solution: Number Operations 59
Long Answer Question 22) Solve the following: a) Sunny has 4 packets of pencils. There are 5 pencils in each packet. He lost 4 of the pencils. How many pencils are now left with him? b) There were 21 girls and 14 boys in a class. The group leader divided them into groups of 7. How many groups will thus be formed? Solution: 60
Number Operations 61
5Chapter Playing with Numbers 5.1 Prime and Composite Numbers I Recall Multiple Choice Questions [] 1) A prime number among the following is ____. [] (A) 4 (B) 18 (C) 20 (D) 2 [] 2) The number 9 is a multiple of _________. (A) 3 (B) 4 (C) 5 (D) 7 3) A composite number among these is _______. (A) 7 (B) 3 (C) 6 (D) 17 I Remember and Understand Multiple Choice Questions [ ] 4) The twin primes among these are _____. ] ] (A) 3 and 5 (B) 41 and 42 (C) 6 and 9 (D) 1 and 2 5) The number that is neither a prime nor a composite number is _____. [ (A) 2 (B) 1 (C) 19 (D) 4 6) The co-prime numbers among the following is _____. [ (A) 2 and 14 (B) 3 and 9 (C) 1 and 5 (D) 2 and 16 Fill in the Blanks 7) Twin prime numbers have a difference of _________________ between them. 8) Co-prime numbers have ______________ as their highest common factor. 9) For a number to be divisible by 5, the ones digit of the given number must be __________ or 5. 62
Very Short Answer Questions 10) Is the number 22 divisible by 3? Solution: 11) Which place of a given number must be 0 so that it is divisible by 10? Solution: 12) What is the prime factorisation of 4? Solution: Short Answer Questions 13) Write the prime factorisation of 76 using the division method. Solution: 14) Write the prime factorisation of 98 using the division method. Solution: Playing with Numbers 63
Long Answer Questions 15) Find whether the number 28294 is divisible by 2, 3, 4, 5, 6, 9, 10 and 11. Solution: 16) Carry out the prime factorisation of: a) 68 b) 88 Solution: 64
I Apply Short Answer Questions 17) A shop sells books of a particular subject in packs of 8. The shop has 10 Marathi, 12 Telugu, 13 Hindi, 16 Social Studies, 18 Science, 22 English and 24 Mathematics books. Which subject books make an incomplete pack? Solution: 18) Rahim sells eggs in crates. One crate can hold only 11 eggs. On which of the following days was he not able to pack all the eggs in crates? Monday : 4785 eggs; Tuesday: 2234 eggs; Wednesday: 5134 eggs; Thursday: 5841 eggs; Friday: 3344 eggs; Saturday: 4019 eggs; Sunday: 5001 eggs Solution: Playing with Numbers 65
Long Answer Questions 19) For a birthday party, Nisha bought 7 bottles of rose milkshake and 14 bottles of orange milkshake. She wants to have identical tables arranged without having any bottles of milkshake left over. What is the maximum number of tables that Nisha can arrange? Solution: 20) The principal of a school meets the parents of Class 1 students every 15 days. She meets the parents of the Class 2 students every 20 days. On which day will she have to meet the parents of both the classes? Solution: 66
I Explore (H.O.T.S.) Short Answer Question 21) Prime factorise 1880 using the division method. Solution: Long Answer Question b) 2222 22) Prime factorise using the division method. a) 4000 Solution: Playing with Numbers 67
5.2 H.C.F. and L.C.M. I Recall Multiple Choice Questions 1) 8990 is divisible by ______. [] (A) 7 (B) 5 (C) 3 (D) 9 2) For a number to be divisible by 2, the digit in the ones place must be [] _____________. (A) 0, 2, 4, 6 or 8 (B) 0, 3, 4, 7 or 9 (C) 2, 3, 4, 5 or 9 (D) 1, 2, 3, 7 or 9 3) For a number to be divisible by 6, the number must be divisible by both __________. [ ] (A) 8 and 3 (B) 8 and 2 (C) 2 and 5 (D) 2 and 3 I Remember and Understand Multiple Choice Questions 4) The complete list of all the factors of 36 is ________________. [] [ ] (A) 1, 2, 3, 4, 12, 18, 36 (B) 1, 2, 3, 4, 6, 9, 12, 18, 36 [] (C) 1, 2, 3, 4, 5, 6, 36 (D) 1, 2, 3, 4, 5, 9, 12, 18, 36 5) The list of the first five multiples of 12 is ________________. (A) 12, 24, 32, 40, 48 (B) 12, 24, 36, 48, 50 (C) 5, 10, 15, 20, 25 (D) 12, 24, 36, 48, 60 6) The number that is not a factor of 80 is ______________. (A) 14 (B) 2 (C) 10 (D) 16 Fill in the Blanks 7) The largest 2-digit composite number is ____. 8) Multiples of even numbers are _______ numbers. 9) The smallest 2-digit prime number is ____. 68
Very Short Answer Questions 10) How many prime numbers are there between 20 and 50? Solution: 11) Write all the factors of 48. Solution: 12) Write the prime factorisation of 6. Solution: Short Answer Questions 13) Find the H.C.F. of 12 and 18 using the common division method. Solution: 14) Find the L.C.M. of 10 and 15 using the listing method. Solution: Long Answer Questions 15) Find the H.C.F. and L.C.M. of the following numbers using the listing method. a) 36, 42 b) 75, 50 Solution: Playing with Numbers 69
16) W rite the factors and multiples of the given numbers. Then, find their H.C.F. and L.C.M. a) 36, 90 b) 12, 24 Solution: 70
I Apply Short Answer Questions 17) T he H.C.F. of two numbers is 8 and their L.C.M. is 96. If the first number is 24, find the second number. Solution: 18) The L.C.M. of two numbers is 48. If the two numbers are 16 and 24, what is their H.C.F.? Find out using the relation between L.C.M. and H.C.F. Solution: Long Answer Questions 19) Find the missing numbers. a) H.C.F. = 4; L.C.M. = 252; first number = 28; second number = ? b) H.C.F. = 2; L.C.M. = 1368; first number = ?; second number = 72 Playing with Numbers 71
Solution: 20) C omplete the following table. S.No. Numbers H.C.F. L.C.M. Product a) 18, 42 ? 126 ? b) 25, 75 25 ? ? Solution: 72
I Explore (H.O.T.S.) Short Answer Question 21) Find the L.C.M. of 18, 24 and 32 using the common division method. Solution: Playing with Numbers 73
Long Answer Question 22) Find the H.C.F. and L.C.M. of 20, 28 and 36 using the common division method. Solution: 74
Time6Chapter 6.1 Convert Time I Recall Multiple Choice Questions 1) The number of days in April is______. [ ] [ ] (A) 30 (B) 29 (C) 31 (D) 28 [ ] (D) 15 2) The number of minutes in an hour is ______. (A) 45 (B) 60 (C) 30 3) The time shown by the given clock is _____. (A) 2:30 (B) 6:08 (C) 6:10 (D) 1:30 I Remember and Understand [] (D) 1 s ÷ 60 Multiple Choice Questions [] 4) One minute is equal to ________. (D) 1 h ÷ 3600 (A) 6 s (B) 60 s (C) 1 s ÷ 6 [] (C) 3600 h (D) 1 day ÷ 24 5) One second is equal to ________. (C) 24 days 75 (A) 60 h (B) 1 h ÷ 60 6) One hour is equal to _______. (A) 60 days (B) 1 day ÷ 60
Fill in the Blanks 7) T here are ___________ seconds in two hours. 8) There are _________ minutes in a second. 9) A day has ______________ minutes. Very Short Answer Questions 10) How many hours are there in two days? Solution: 11) H ow many minutes are there in four hours? Solution: 12) How many hours are equal to 120 minutes? Solution: Short Answer Questions 13) Convert 2 weeks into days. Solution: 14) C onvert 4 days into seconds. Solution: Long Answer Questions 15) Convert the following: a) 90000 s into minutes, hours and days b) 200 min into hours Solution: 76
16) Convert the following: b) 270 min into hours a) 230 s into min d) 143 hours to days c) 540 min to hours Solution: I Apply Short Answer Questions 17) R ahul spends 240 minutes every week in dance class. How many hours does he spend there? Solution: 18) V eena exercises for 30 minutes every day. How many minutes does she exercise in two weeks? Solution: Time 77
Long Answer Questions 19) Jai’s shop was closed for 180 minutes on Friday. How many hours was the shop closed for? Also express the same time in seconds. Solution: 20) A bus from Pune to Mumbai took 9600 seconds to complete its journey. For how many minutes did it travel? Another bus took the same route and took 13200 seconds to complete the journey. For how many hours did the second bus travel? Solution: 78
I Explore (H.O.T.S.) Short Answer Question 21) Anil travels for 1 h 30 min and his brother travels for 3780 seconds. Who travels for a longer duration? Solution: Long Answer Question 22) Anita takes 3 days 4 hours and 10 minutes to complete her Maths assignment. How much time in seconds does she take to complete the assignment? Solution: 6.2 Add and Subtract Time I Recall Multiple Choice Questions 1) 3 hours = ________ minutes [ ] (A) 180 (B) 250 (C) 360 (D) 270 Time 79
2) 2 hours = _____ seconds [ ] [ ] (A) 3600 (B) 360 (C) 720 (D) 7200 (D) 360 3) 3600 seconds = ________ hour(s) (A) 1 (B) 3 (C) 30 I Remember and Understand Multiple Choice Questions 4) The sum of 3 hours 20 min and 4 hours 5 min is ___________. [ ] (D) 1 h 25 min ] (A) 7 h 25 min (B) 1 h 15 min (C) 7 h 15 min [ 5) The sum of 7 hours 25 min and 2 hours 20 min is ___________. (D) 10 h 5 min (A) 5 h 25 min (B) 10 h 15 min (C) 9 h 45 min 6) The difference between 2 hours 5 min and 10 hours 20 min is ___________. [ ] (A) 12 h 25 min (B) 8 h 25 min (C) 8 h 15 min (D) 12 h 15 min Fill in the Blanks 7) 5 hours 20 min + 3 hours 15 min = ______ hours 35 min 8) 9 hours 20 min − 3 hours 10 min = ______ hours 10 min 9) 4 hours 55 min − 1 hour 25 min = 3 hours ______ min Very Short Answer Questions 10) Subtract 5 hours 10 minutes from 15 hours 15 minutes. Solution: 11) Add 8 hours 42 minutes to 1 hour 12 minutes. Solution: 12) Add 3 hours 15 minutes and 5 hours 22 minutes. Solution: Short Answer Questions 13) Convert 60 minutes into hours and then add 1 hour 30 minutes to it. Solution: 80
14) Convert 60 seconds into minutes and add it to 3 hours 30 minutes. Solution: Long Answer Questions 15) Subtract 14 hours 15 minutes from 25 hours 10 minutes. Solution: 16) Subtract 2 h 42 min from 353 min. Solution: Time 81
I Apply Short Answer Questions 17) Raju ran on the race track for 1 hour 15 minutes. Viju ran for 1 hour 30 minutes. For how much more time did Viju run than Raju? Solution: 18) Piyush ate his lunch at 2:00 p.m. He has his dinner after a gap of 6 hours. At what time does Piyush have his dinner? Solution: Long Answer Questions 19) Sonali completed her Mathematics homework in 1 hour 10 minutes, History homework in 2 hours 20 minutes and Science homework in 1 hour 10 minutes. How long did she take to complete her homework for all three subjects? Solution: 82
20) It takes 48 minutes to wash 4 windows of a building. How much time in hours will it take to wash all 30 windows of the building? Solution: I Explore (H.O.T.S.) Short Answer Question 21) The scouts of a school began their practice for Republic Day parade 32 days in advance. On which date did they start practice? Solution: Time 83
Long Answer Question 22) S oham started his reading homework at 3:45 p.m. and finished it at 4:30 p.m. Then he practised Mathematics from 4:30 p.m. until 5:00 p.m. Finally, he studied for a Science test from 5:00 p.m. to 5:30 p.m. How much time did Soham spend in all on completing his homework and studying? Solution: 84
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