Passport-G3-Textbook-Maths-FY

Steps Solved Solve this 53 and 65 38 and 41 Step 1: Add the digits in the ones place of the two 3+5=8 _____ + _____ = _____ numbers mentally. Step 2: Add the digits in The digits in the tens The digits in the tens place the tens place of the two place of the two of the two numbers are ___ numbers mentally. numbers are 5 and 6. and ____. Keep ____ in your Keep 6 in your mind, mind, count ___ forward as Step 3: Write sum of count 5 forward as 7, 8, ____, ____and ____. the digits obtained in 9, 10 and 11. ____ + ____ = ___ step 1 and sum of the 5 + 6 = 11 digits obtained in step 2 So, 53 + 65 = 118. So, 38 + 41 = ___. together. This is the sum of the given numbers. Add 2-digit numbers mentally with regrouping To mentally add two 1-digit numbers, keep the larger Example 17: Add mentally: 29 and 56 number in mind and the smaller on the fingers. Solution: To add the given numbers mentally follow these steps. Steps Solved 29 and 56 Solve this 83 and 47 Step 1: Regroup the two 29 = 20 + 9 83 = ___ + ____ given numbers as tens and 56 = 50 + 6 47 = ___ + ____ ones mentally. ____ + ____ = ____ Step 2: Add the ones of the 9 + 6 = 15 ____ + ____ = ____ two numbers mentally. ____ + ___ = ____ Step 3: Add the tens of the 20 + 50 = 70 two numbers mentally. So, 83 + 47 = ___. Step 4: Add the sums from 70 + 15 steps 2 and 3 mentally = 70 + 10 + 5 (regroup if needed). = 85 So, 29 + 56 = 85. Step 5: Write the sum of the given numbers. Addition 47

Train My Brain Solve the following mentally. a) 21 + 30 b) 42 + 57 c) 42 + 98 4.3 I Apply We have seen how easy it is to add two 2-digit numbers mentally. Let us see some real-life situations in which mental addition of 2-digit numbers is useful. Example 18: Suraj has 34 sheets and Kamal has 27 sheets of paper. How many sheets of paper do they have in all? Solve mentally. Solution: Number of sheets of paper Suraj has = 34 Number of sheets of paper Kamal has = 27 Total number of sheets they have together = 34 + 27 Regrouping the given numbers in tens and ones and adding, we get 30 + 4 + 20 + 7 To add two 1-digit numbers mentally, keep the larger number in mind and add the smaller one to it. Add tens and ones accordingly. = 50 + 11 = 50 + 10 + 1 (Regroup and add) = 60 + 1 = 61 Therefore, Suraj and Kamal have 61 sheets of paper. Example 19: Vivek has 49 bags and Shyam has 29 bags. How many bags do they have in total? Solve mentally. Solution: Number of bags Vivek has = 49 Number of bags Shyam has = 29 Total number of bags they have together = 49 + 29 Regrouping the given numbers in tens and ones and adding, we get 40 + 9 + 20 + 9 To add two 1-digit numbers, keep the larger number in mind and add the smaller one to it. Add tens and ones accordingly. 48

= 40 + 20 + 18 = 60 + 10 + 8 (Regroup and add) = 70 + 8 = 78 So, they have 78 bags in total. 4.3 I Explore (H.O.T.S.) We have seen mental addition of two 2-digit numbers. Let us now see a few examples to add three 2-digit numbers mentally. Example 20: Add mentally: 25, 37 and 19 Solution: To add the given numbers mentally follow these steps. Steps Solved Solve this 25, 37 and 19 40, 29 and 54 Step 1: Regroup the three given 25 = 20 + 5 40 = ___ + ____ numbers as tens and ones mentally. 37 = 30 + 7 29 = ___ + ____ 19 = 10 + 9 54 = ____+____ Step 2: Add the tens mentally. 20 + 30 + 10 = 60 ____ + ____+ ____ = ____ Step 3: Add the ones mentally. 5 + 7 + 9 = 21 ____+___ + ____ = ____ Step 4: Add the sums from steps 2 60 + 21 ____ + ___ = ____ and 3 mentally, regroup again if = 60 + 20 + 1 = 81 needed. So, 25 + 37 + 19 = 81. So, 40 + 29 + 54 = ___. Step 5: Write the sum of the given numbers. Addition 49

Maths Munchies 213 Steps to estimate the sum of 2-digit numbers mentally: Step 1: T ake any two numbers, say 75 and 12. Add the tens digit which gives 8. Step 2: C ount the digits in the ones place. Here, only one digit is equal to 5. So, the total count is 1. Step 3: A dd this count to the tens place. So, the sum in the tens place becomes 9. Place ‘0‘ in the ones place. So, the estimated sum is 90. Connect the Dots Social Studies Fun Early humans had the basic idea of addition. Aryabhatta contributed to the concept of addition by inventing the number ‘0’. English Fun To remember the rules for rounding off numbers, let us read a poem in English. We will, we will round you. Find the place, look next door Five or more, you raise the score Four or Less, you let it rest Look to right, put zeroes in sight We will, we will round you. 50

Drill Time Concept 4.1: Add 3-digit and 4-digit Numbers 1) Add 3-digit numbers with regrouping. a) 481 + 129 b) 119 + 291 c) 288 + 288 d) 346 + 260 e) 690 + 110 2) Add 4-digit numbers without regrouping. a) 1234 + 1234 b) 1000 + 2000 c) 4110 + 1332 d) 5281 + 1110 e) 7100 +1190 3) Add 4-digit numbers with regrouping. a) 5671 + 1430 b) 3478 + 2811 c) 4356 + 1753 d) 2765 + 1342 e) 4901 + 2222 4) Word problems a) There are 142 people riding in Train A and 469 people in Train B. How many people rode in both the trains altogether? b) Ali scored 272 points in one level of a computer game. His friend, Jenny, scored 538 points in the next level. What is their total score in both the levels? Concept 4.2: Estimate the Sum of Two Numbers 5) Estimate the sum of the following: a) 211 and 115 b) 549 and 120 c) 385 and 190 d) 222 and 524 e) 672 and 189 6) Word problems a) Susan has 46 red roses and Mukesh has 22 yellow roses. Estimate the total number of roses. b) Rakesh has 67 pencils and Mona has 43 pencils. Estimate the number of pencils both of them have in all. Addition 51

Drill Time Concept 4.3: Add 2-digit Numbers Mentally 7) Add 2-digit numbers mentally without regrouping. a) 31 and 22 b) 22 and 42 c) 45 and 51 d) 11 and 34 e) 32 and 61 8) Add 2-digit numbers mentally with regrouping. a) 45 and 47 b) 25 and 56 c) 12 and 19 d) 27 and 35 e) 17 and 37 A Note to Parent We widely use the concept of mental addition in day-to-day life especially to calculate the amount of money. Encourage your child to practise the concept by taking their help in calculating bills, tendering change, buying groceries and so on. 52

Chapter Subtraction 5 I Will Learn About • Subtracting 3-digit numbers with regrouping. • Subtracting 4-digit numbers with and without regrouping. • rounding off numbers. • estimating the difference between numbers. • subtracting two numbers mentally. Concept 5.1: Subtract 3-digit and 4-digit Numbers I Think The given grid shows the number of men and women in Farida’s town in the years 2016 and 2017. Years 2016 2017 Men 2254 2187 How can Farida find out how may more men than women lived in her town in the two years. Women 2041 2073 5.1 I Recall Recall that we can subtract numbers by writing the smaller number below the greater number. A 2-digit number can be subtracted from a larger 2-digit number or a 3-digit number. Similarly, a 3-digit number can be subtracted from a larger 3-digit number. 53

Let us answer these to revise the concept. c) 93 – 93 = _________ a) 15 – 0 = _________ b) 37 – 36 = _________ f) 50 – 45 = _________ d) 18 – 5 = _________ e) 47 – 1 = _________ 5.1 I Remember and Understand We have learnt how to subtract two 3-digit numbers without While subtracting, regrouping. Let us now learn how to subtract them with always start from regrouping. the ones place. Subtract 3-digit numbers with regrouping When a larger number is to be subtracted from a smaller number, we regroup the next higher place and borrow. Let us understand this with an example. Example 1: Subtract 427 from 586. Solution: To subtract, write the smaller number below the larger number. Step 1: Subtract the ones. But, 6 – 7 is Solved Step 3: Subtract the not possible as 6 < 7. So, regroup the hundreds. digits in the tens place. Step 2: Subtract the tens. 8 tens = 7 tens + 1 tens. Borrow 1 ten to the ones place. Reduce the tens by 1 ten. Now subtract 7 ones from 16 ones. H TO H TO H TO 7 16 7 16 7 16 5 –4 8\\ 6\\ 5 \\8 \\6 5 \\8 \\6 27 –4 2 7 –4 2 7 9 59 15 9 H TO Solve these H TO H TO 6 23 5 52 4 53 – 3 76 – 2 63 – 2 64 54

Subtract 4-digit numbers without regrouping Subtracting a 4-digit number from a larger 4-digit number is similar to subtracting a 3-digit number from a larger 3-digit number. The following examples help you understand this better. Example 2: Subtract: 5032 from 7689 Solution: To subtract, write the smaller number below the larger number. Solved Step 1: Subtract the ones. Step 2: Subtract the tens. Th H T O Th H T O 76 8 9 76 8 9 −50 3 2 −50 3 2 7 5 7 Step 3: Subtract the hundreds. Step 4: Subtract the thousands. Th H T O Th H T O 7689 7 68 9 −5032 − 5 03 2 2 65 7 657 Th H T O Solve these Th H T O 2879 8000 –2137 Th H T O –2000 4789 –2475 Subtract 4-digit numbers with regrouping In subtraction of 4-digit numbers, we can regroup the digits in thousands, hundreds and tens places. Let us see an example. Example 3: What is the difference 7437 and 4868? Solution: Write the smaller number below the larger number. Subtraction 55

Steps Solved Solve these Step 1: Subtract the ones. Th H T O Th H T O But, 7 − 8 is not possible as 1654 74 2 17 −1 2 4 6 7 < 8. So, regroup the tens digit, −4 8 3. 3 tens = 2 tens + 1 ten. Borrow 3\\ \\7 Th H T O 1 ten to the ones place. 6 8 9 5674 −2 3 8 2 Step 2: Subtract the tens. But, Th H T O Th H T O 2 − 6 is not possible as 2 < 6. 12 7468 So, regroup the hundreds digit, 3 \\2 17 −4 8 3 7 4. 4 hundreds = 3 hundreds + − 7 4\\ 3\\ \\7 1 hundred. Borrow 1 hundred to 4 8 6 8 the tens place. 69 Step 3: Subtract the hundreds. Th H T O But, 3 − 8 is not possible. So, 13 12 regroup the thousands digit, 7. 7 thousands = 6 thousands + 6 \\3 \\2 17 1 thousand. Borrow 1 thousand to the hundreds place. \\7 4\\ 3\\ \\7 −4 8 6 8 569 Step 4: Subtract the thousands. Th H T O 13 12 6 \\3 \\2 17 \\7 4\\ 3\\ \\7 −4 8 6 8 2569 Train My Brain Solve the following: a) 719 – 320 b) 813 – 621 c) 3678 – 2466 56

5.1 I Apply Subtraction of 3-digit numbers is very often used in real life. Here are a few examples. Example 4: Sonu bought 375 marbles. He gave 135 marbles to his brother. How many marbles are left with him? Solution: Total number of marbles Sonu bought = 375 H TO Number of marbles given to Sonu’s brother = 135 375 Number of marbles left with him = 375 – 135 = 240 −1 3 5 Therefore, 240 marbles are left with Sonu. 240 Example 5: Vinod had 536 stamps. He gave some stamps to his brother and then Vinod was left with 278 stamps. How many stamps did Vinod give his brother? H TO Solution: Total number of stamps Vinod had = 536 12 Number of stamps Vinod had after giving some 4 2\\ 16 to his brother = 278 \\5 \\3 \\6 Number of stamps he gave his brother = −278 536 – 278 = 258 258 Therefore, Vinod gave 258 stamps to his brother. We can use subtraction of 4-digit numbers in real-life situations. Let us see some examples. Example 6: Mohan’s uncle stays 8630 m away from Mohan’s house. Mohan travelled Solution: 6212 m of the distance. What is the distance yet to Th H T O be covered by Mohan to reach his uncle’s house? 2⁄ 1⁄0 Distance between Mohan’s house and his uncle’s 8 630 house = 8630 m − 6 212 Distance travelled by Mohan = 6212 m 2 418 Remaining distance Mohan has to travel = 8630 m – 6212 m = 2418 m Therefore, Mohan has to travel 2418 m more to reach his uncle’s house. Subtraction 57

Example 7: A rope is 6436 cm long. A 3235 cm long piece is cut from it. How much of the rope is left? Solution: Length of the rope = 6436 cm Th H T O 6436 Length of the piece cut = 3235 cm −3 2 3 5 The length of the remaining piece of rope 3201 = 6436 cm – 3235 cm = 3201 cm Therefore, 3201 cm of the rope is left. 5.1 I Explore (H.O.T.S.) We can check the correctness of a subtraction problem using addition. Consider an example. Example 8: Subtract: a) 27 from 36 b) 145 from 364. Solution: a) 36 – 27 b) 364 – 145 TO HT O 2 16 5 14 \\3 \\6 3 \\6 4\\ −2 7 −1 4 5 9 21 9 We can write 36 = 27 + 9 364 – 145 = 219 We can write 364 = 145 + 219 We can conclude that to check if the subtraction is correct, we add the subtrahend (the number being subtracted) and the difference. If this sum is the same as the minuend (the number from which a number is subtracted), the subtraction is correct. Framing word problems Let us consider these subtraction facts. a) 37 – 14 = 23 b) 37 – 23 = 14 We can try to frame some interesting situations and problems using these subtraction facts. a) Of the 37 students in class, 14 are in the green house. How many students are in the red house? 58

b) 37 children are playing on the ground. 23 of them are playing football. How many are playing basketball? Similarly, we can frame some interesting problems using subtraction facts of 3-digit numbers. Let us see an example. Example 9: Frame a word problem using: a) 706 – 234 = 472 b) 461 − 110 = 351 Solution: One of the many possible different answers are: a) In a school, there are 706 students. 234 students were absent on Monday. How many students were present? b) 461 people booked the train for a trip to Goa. 110 people cancelled the trip. How many people went on the trip? Concept 5.2: Estimate the Difference between Two Numbers I Think Farida had ` 450 with her. She wanted to buy a toy car for ` 185 and a toy train for ` 150. How much money will remain with Farida after buying the toys? 5.2 I Recall We know that in some situations where we do not need the exact number, we use estimation. Estimation can be done by rounding off numbers to a given place. Let us answer these to revise the concept of rounding off to the nearest 10. a) 87 = ______ b) 53 = ______ c) 65 = ______ d) 42 = ______ e) 33 = ______ 5.2 I Remember and Understand Rounding off numbers can be used to estimate the difference between two 2-digit numbers and between two 3-digit numbers. Let us understand this through examples. Example 10: Estimate the difference: a) 69 – 15 b) 86 – 12 Solution: a) 69 – 15 Subtraction 59

Rounding off 69 to the nearest tens gives 70 Estimation is finding a number that is (as 9 > 5) and rounding off 15 to the nearest close enough to the tens, gives 20 (as 5 = 5). So, the required difference is 70 – 20 = 50. right answer. b) 86 – 12 R ounding off 86 to the nearest tens gives 90 (as 6 > 5) and rounding off 12 to the nearest tens, gives 10 (as 2 < 5). So, the required estimated difference is 90 – 10 = 80. Example 11: Estimate the difference: a) 593 – 217 b) 806 – 124 Solution: a) 593 – 217 R ounding off 593 to the nearest tens gives 590 (as 3 < 5) and rounding off 217 to the nearest tens, gives 220 (as 7 > 5). So, the required estimated difference is 590 – 220 = 370. b) 806 – 124 R ounding off 806 to the nearest tens gives 810 (as 6 > 5) and rounding off 124 to the nearest tens, gives 120 (as 4 < 5). So, the required estimated difference is 810 – 120 = 690. Train My Brain Estimate these differences: a) 25 – 9 b) 135 – 112 c) 64 – 35 5.2 I Apply Estimation of differences can be used in real-life situations. Let us see a few examples. Example 12: Parul has 83 pencils. She gives 32 pencils to her sister. Estimate the number of pencils that remain with Parul. Solution: Number of pencils Parul has = 83 83 rounded off to the nearest tens is 80 (since 3 < 5). 60

Number of pencils given to Parul’s sister = 32 32 rounded off to the nearest 10 is 30 (since 2 < 5). So, the estimated number of pencils left with Parul = 80 − 30 = 50 Therefore, Parul has about 50 pencils. Example 13: Ram has 94 sweets. He distributes 46 sweets among his friends. About how many sweets remain with Ram? Solution: Number of sweets Ram has = 94 94 rounded off to the nearest tens is 90 (since 4 < 5). Number of sweets distributed among Ram's friends = 46 46 rounded off to the nearest tens is 50 (since 6 > 5). So, the estimated number of sweets left with Ram = 90 − 50 = 40 Therefore, Ram has about 40 sweets. 5.2 I Explore (H.O.T.S.) In some situations, we may need to carry out both addition and subtraction. In such cases, we need to identify which operation is to be carried out first. Example 14: In a school, there are 976 students. Of them, 325 are from the pre-primary section, 416 are from the primary section, and the rest are from high school. How many high school students are there in the school? HTO Solution: Total number of students = 976 1 Number of students from the pre-primary section = 325 325 Number of students from the primary section = 416 +4 1 6 741 Total number of students in pre-primary and primary school sections = 325 + 416 = 741 Number of students in high school = Total number of HTO students – Number of students in pre-primary and 976 primary school sections = 976 – 741 = 235 −7 4 1 Therefore, there are 235 high school students. 235 Subtraction 61

Concept 5.3: Subtract 2-digit Numbers Mentally I Think Farida had 19 pens. She gave 12 pens to her sister. Can you find the number of pens remaining with Farida without using a paper and a pencil? 5.3 I Recall Recall that to subtract two 1-digit numbers mentally, we keep the larger number in mind and subtract the smaller one from it. Let us answer these to revise the concept. a) 5 – 4 = ________ [ ] (A) 5 (B) 4 (C) 1 (D) 9 b) 3 – 3 = ________ [ ] (A) 3 (B) 6 (C) 0 (D) 5 c) 4 – 1 = ________ [ ] (A) 3 (B) 4 (C) 6 (D) 8 d) 5 – 0 = ________ (C) 0 (D) 6 [ ] (A) 4 (B) 5 n e) 6 – 3 = ________ [ ] (A) 4 (B) 6 (C) 3 (D) 9 5.3 I Remember and Understand We have learnt to subtract 1-digit numbers mentally. Let us understand subtraction of 2-digit numbers mentally through an example. Subtract 2-digit numbers mentally without regrouping Example 15: Subtract mentally: 52 from 76 Solution: Follow these steps to subtract mentally. 62

Steps Solved Solve this 52 from 76 35 from 69 Step 1: Subtract mentally ______ – ______ = the digits in the ones 6–2=4 place of the two numbers. The digits in the tens place The digits in the tens place of of the two numbers are 7 the two numbers are _______ Step 2: Subtract mentally and 5. and _______. the digits in the tens place So, imagine that 7 fingers So, imagine that _____ fingers of the two numbers. are open. Then imagine are open. closing 5 of them. Then imagine closing ___ of 7–5=2 them. ____– ____ = ___ Step 3: Write the So, 76 – 52 = 24. So, 69 – 35 = ____. difference obtained in steps 1 and 2 together as the difference of the given numbers. Sometimes regrouping is necessary in subtraction. Let us see an example to understand this. Subtract 2-digit numbers mentally with regrouping Regroup the sum Example 16: Subtract mentally: 29 from 56 if it is equal to or Solution: Follow these steps to subtract mentally. more than 10. Steps Solved Solve this 29 from 56 46 from 83 Step 1: Regroup the two 29 = 20 + 9 83 = ___ + ____ given numbers as tens and ones. 56 = 50 + 6 46 = ___ + ____ Step 2: Check if the ones 6 – 9 is not possible. So, ____ - ____ is possible (True/ can be subtracted. If not, regroup the tens. False). If it is true, subtract. If it regroup the tens. Add 10 ones to 6 to get 16 is false, regroup. Add ten ones to ones and and subtract 1 ten from 5 Add 10 ones to ___ to get reduce 1 ten from tens. tens to get 4 tens. ____ and subtract 1 ten from ____ tens to get ____ tens. Subtraction 63 NR_BGM_182110020_Passport-G3-Textbook-Maths-FY_Corrected page.pdf 3 12/22/2017 4:16:48 PM

Steps Solved Solve this 29 from 56 46 from 83 Step 3: Subtract the 16 – 9 = 7 ____ – ____ = ____ ones of the two numbers mentally. 4 tens – 2 tens = 2 tens ____ – ____ = ____ Step 4: Subtract the So, 56 – 29 = 27. ____ – ___ = ____ tens of the two numbers mentally. Step 5: Write the answers from steps 3 and 4 together as the difference. Train My Brain Solve the following mentally. a) 53 – 31 b) 65 – 23 c) 65 – 14 5.3 I Apply We have seen that it is easy to subtract two 2-digit numbers mentally. In some real-life situations, we use mental subtraction of numbers. Let us see a few examples. Example 17: Manoj has 64 notebooks. He sold 45 notebooks. How many notebooks are left with him? Solve mentally. Solution: Number of notebooks Manoj has = 64 Number of notebooks he sold = 45 The number of notebooks remaining with him = 64 – 45 = 19 Therefore, Manoj has 19 notebooks left with him. Example 18: Alisha went to school for 49 days in Term I and 65 days in Term II. For how many more days did Alisha go to school in the Term II than in the Term I? Solve mentally. 64

Solution: Number of days Alisha went to school in Term I = 49 Number of days she went to school in Term II = 65 Difference in number of days = 65 – 49 = 16 Therefore, Alisha went to school 16 days more in Term II than in Term I. 5.3 I Explore (H.O.T.S.) We have seen mental subtraction of two 2-digit numbers. Let us now see a real-life example where we might have to add and subtract numbers mentally. Example 19: Renu had ` 80. She bought guavas for ` 25 and bananas for ` 17. Calculate mentally the money that Renu has to pay the fruit seller. Also calculate mentally the money left with her. Solution: Total money Renu had = ` 80 Money she spent on guavas = ` 25 Money she spent on bananas = ` 17 To find the money she has to give the fruit seller, Renu has to add the prices of guavas and bananas. That is, ` 25 + ` 17 = ` 42. To find the money remaining with her, Renu has to subtract this sum from the total money she had. So, ` 80 – ` 42 = ` 38. Therefore, ` 38 is left with Renu. Maths Munchies 213 We can subtract 2 numbers easily by splitting the smaller number. Let us look at 54 − 28. Step 1: Split the number 28 as 24 and 4. Step 2: Subtract the number 24 from 54. 54 − 24 = 30 Step 3: Now, subtract 4 from 30; 30 − 4 = 26. Step 4: 54 − 28 = 26 Subtraction 65

Connect the Dots Science Fun The human body has 206 bones in all. If both hands have 54 bones, then how many bones are there in the other parts of the body? English Fun Let us read a poem to learn subtraction. More on top? No need to stop! More on the floor? Go next door and get 10 more! Number the same? Zero's the game! Drill Time Concept 5.1: Subtract 3-digit and 4-digit Numbers 1) Subtract 3-digit numbers with regrouping. a) 254 – 173 b) 678 – 619 c) 147 – 129 d) 781 – 682 e) 356 – 177 2) Subtract 4-digit numbers without regrouping. a) 2341 – 1230 b) 7632 – 5120 c) 9763 – 2311 d) 7629 – 1318 e) 7589 – 1268 66

Drill Time 3) Subtract 4-digit numbers with regrouping. a) 7632 – 1843 b) 4391 – 2482 c) 9843 – 7943 d) 8325 – 5436 e) 6893 – 3940 4) Word problems a) A stick is 8745 cm long. A 4313 cm long piece is cut from it. What part of the stick is remaining? b) Raj stays 5786 m away from Matin’s house. Raj travelled 3825 m of the distance. What is the distance yet to be covered by Raj to reach Matin’s house? Concept 5.2: Estimate the Difference between Two Numbers 5) Estimate these differences: a) 65 – 15 b) 48 – 16 c) 67 – 32 d) 896 – 432 e) 679 – 387 6) Word problems a) In a class, there are 562 students. Of them, 118 are from the red group, 321 are from the green group, and the rest are from the blue group. How many students are in the blue group? b) Sneha has 77 balloons. She gives 42 balloons to her sister. About how many balloons remain with Sneha? Concept 5.3: Subtract 2-digit Numbers Mentally 7) Subtract 2-digit numbers mentally without regrouping. a) 43 from 84 b) 24 from 76 c) 52 from 87 d) 34 from 75 e) 14 from 38 8) Subtract 2-digit numbers mentally with regrouping. a) 42 from 81 b) 28 from 84 c) 11 from 20 d) 23 from 51 e) 76 from 81 Subtraction 67

Drill Time 9) Word problems a) Rehmat has 48 pencils. He has used 29 pencils. How many pencils are left with him? b) Sam travelled for 23 km on Day 1 and 76 km on Day 2. How much more distance (in km) did Sam travel on Day 2 than on Day 1? A Note to Parent You can help your child develop the ability to calculate mentally with speed and precision, by giving him or her small problems every day or even taking their help in making basic calculations during shopping or calculating monthly expenses. 68

Chapter Multiplication 6 I Will Learn About • using repeated addition to construct multiplication tables. • multiplying 2-digit numbers with and without regrouping. • doubling the numbers mentally. Concept 6.1: Multiply 2-digit Numbers I Think Farida bought 2 boxes of toffees to distribute among her classmates on her birthday. Each box has 25 toffees inside it. If there are 54 students in her class, do you think she has enough toffees? 6.1 I Recall In Class 2, we have learnt that multiplication is repeated addition. The symbol ‘×’ indicates multiplication. Multiplication means having a certain number of groups of the same size. 69

Let us recall the multiplication tables of numbers from 1 to 6. 1 2 3 1×1=1 2×1=2 3×1=3 1×2=2 2×2=4 3×2=6 1×3=3 2×3=6 3×3=9 1×4=4 2×4=8 3 × 4 = 12 1×5=5 2 × 5 = 10 3 × 5 = 15 1×6=6 2 × 6 = 12 3 × 6 = 18 1×7=7 2 × 7 = 14 3 × 7 = 21 1×8=8 2 × 8 = 16 3 × 8 = 24 1×9=9 2 × 9 = 18 3 × 9 = 27 1 × 10 = 10 2 × 10 = 20 3 × 10 = 30 4 5 6 4×1=4 5×1=5 6×1=6 4×2=8 5 × 2 = 10 6 × 2 = 12 4 × 3 = 12 5 × 3 = 15 6 × 3 = 18 4 × 4 = 16 5 × 4 = 20 6 × 4 = 24 4 × 5 = 20 5 × 5 = 25 6 × 5 = 30 4 × 6 = 24 5 × 6 = 30 6 × 6 = 36 4 × 7 = 28 5 × 7 = 35 6 × 7 = 42 4 × 8 = 32 5 × 8 = 40 6 × 8 = 48 4 × 9 = 36 5 × 9 = 45 6 × 9 = 54 4 × 10 = 40 5 × 10 = 50 6 × 10 = 60 Let us now construct multiplication tables of 7, 8 and 9. We can then learn to multiply 2-digit numbers. 6.1 I Remember and Understand In multiplication of two numbers: • The number written to the left of the ‘×’ sign is called the multiplicand. • The number written to the right of the ‘×’ sign is called the multiplier. • The number written to the right of the ‘=’ sign is called the product. 70

Multiplication Fact ↓↓ ↓ Multiplicand Multiplier Product Note: (a) R epresenting the multiplicand, multiplier and product using the symbols ‘×’ and ‘=’ is called a multiplication fact. (b) The multiplicand and the multiplier are also Order Property: Changing called the factors of the product. the order in which the numbers are multiplied (c) T he product is also called the multiple of both does not change the the multiplicand and the multiplier. product. This is called order For example, 2 × 7 = 14 = 7 × 2; property of multiplication. 4 × 5 = 20 = 5 × 4 and so on. Using multiplication facts and order property, let us now construct the multiplication tables of 7, 8 and 9. 7 8 9 7×1=7 8×1=8 9×1=9 7 × 2 = 14 8 × 2 = 16 9 × 2 = 18 7 × 3 = 21 8 × 3 = 24 9 × 3 = 27 7 × 4 = 28 8 × 4 = 32 9 × 4 = 36 7 × 5 = 35 8 × 5 = 40 9 × 5 = 45 7 × 6 = 42 8 × 6 = 48 9 × 6 = 54 7 × 7 = 49 8 × 7 = 56 9 × 7 = 63 7 × 8 = 56 8 × 8 = 64 9 × 8 = 72 7 × 9 = 63 8 × 9 = 72 9 × 9 = 81 7 × 10 = 70 8 × 10 = 80 9 × 10 = 90 Multiply 2-digit numbers by 1-digit numbers Now, let us learn to multiply a 2-digit number by a 1-digit number. Consider the following example. Example 1: Find the product: 23 × 7 Solution: Follow these steps to find the product. Multiplication 71

Steps Solved Solve these Step 1: Multiply the ones. 3 × 7 = 21 H TO Step 2: Regroup the product. 21 ones = 2 tens and 1 ones 17 Step 3: Write the ones digit of ×9 the product in the product TO and carry over the tens digit 2 H TO to the tens place. 23 15 ×7 ×4 Step 4: Multiply the tens. Step 5: Add the carry over 1 from step 3 to the product. Step 6: Write the sum in the 2 × 7 = 14 tens place. 14 + 2 = 16 H TO 2 23 ×7 161 Train My Brain Solve: a) 17 × 7 b) 28 × 9 c) 19 × 8 6.1 I Apply Let us now see some real-life situations where we use multiplication of 2-digit numbers. Example 2: There were 54 students in a class of a school. The school had 8 such classes. How many students were there in the entire school? Solution: Number of students in one class = 54 students H TO Number of classes in the school = 8 3 Number of students in the school = 54 × 8 25 Therefore, the total number of students in the school = 432 ×7 175 72

Example 3: Manoj travelled 7 km in a day. If he travels the same distance every day, how much distance does he travel in 25 days? H TO Solution: The distance that Manoj travelled in a day = 7 km 3 He travels the same distance every day. The distance he 54 travels in 25 days = 25 × 7. ×8 Therefore, Manoj travels 175 km in 25 days. 432 6.1 I Explore (H.O.T.S.) Let us now try to frame a few multiplication word problems using multiplication. Example 4: Number of chocolates in a box = 9 Number of such boxes = 5 Total chocolates = 45 Solution: Word problem: A box contains 9 chocolates. There are 5 such boxes. Find the total number of chocolates. Example 5: Frame a word problem with the given fact. 8 × 2 = 16 Solution: Word problem: There are 2 rows with 8 students in each row. What is the total number of students? Concept 6.2: Multiply 3-digit Numbers by 1-digit and 2-digit Numbers I Think Farida collected some shells and put them into 9 bags. If each bag has 110 shells, how many shells did she collect? 6.2 I Recall We have learnt to multiply a 2-digit number with a 1-digit number. We have also learnt to regroup the ones in multiplication. Multiplication 73

Let us answer these to revise the concept. a) 22 × 2 = _________ d) 33 × 4 = _________ b) 42 × 1 = _________ e) 50 × 2 = _________ c) 11 × 7 = _________ f) 45 × 3 = _________ 6.2 I Remember and Understand We multiply 3-digit numbers just as we multiply 2-digit numbers. Multiply 3-digit numbers by 1-digit numbers without regrouping Let us understand the step-by-step procedure through a While multiplying, few examples. always start multiplying the ones of the Example 6: Multiply: 401 × 3 multiplicand by the ones of the multiplier. Solution: Follow these steps to multiply the given numbers. Step 1: Multiply the ones Solved Step 3: Multiply the hundreds Step 2: Multiply the tens H TO Th H T O 401 H TO 401 401 ×3 ×3 3 ×3 1203 03 H TO Solve these H TO 220 232 HTO ×4 13 0 ×3 ×2 Multiply 3-digit numbers by 1-digit numbers with regrouping When a 3-digit number is multiplied by a 1-digit number, we may get a 2-digit product in any or all of the places. We regroup these products and carry over the tens digit of the product to the next place. Let us understand this better through an example. 74

Example 7: Multiply: 513 × 5 Solution: Follow these steps to multiply the given numbers. Steps Solved Solve these H TO Step 1: Multiply the ones and write the H TO product under ones. Regroup if the 1 444 product has two or more digits. ×8 513 ×5   5 Step 2: Multiply the tens. Add the carry H TO H TO over (if any) to the product. Write the sum under tens. 1 342 ×5 Regroup if the product has two or more 513 digits. ×5 65 Step 3: Multiply the hundreds. Add the Th H T O H TO carry over (if any) to the product and write the sum under hundreds. Regroup if 1 635 the product has two or more digits. ×7 513 ×5 2 565 Multiply 3-digit numbers by 2-digit numbers Multiplication of 3-digit numbers by 2-digit numbers may sometimes involve regrouping too. Let us understand this concept through step-by-step procedure. Consider the following examples. Example 8: Multiply: 243 × 34 Solution: Follow these steps to multiply the given numbers. Multiplication 75

Steps Solved Solve these Step 1: Arrange the numbers in columns, H TO as shown. H TO 141 243 ×22 Step 2: Multiply the ones of the ×34 multiplicand by the ones digit of the H TO multiplier. 3 × 4 = 12 H TO 1 453 Write 2 in the ones place of the product. ×13 Write 1 in the tens place as the carry over. 243 ×34 H TO Step 3: Multiply the tens by the ones digit of the multiplier. 4 × 4 = 16 2 263 ×23 Add the carry over from the previous H TO step. So, 16 + 1 = 17. Write 7 in the tens 11 place of the product and 1 in the 243 hundreds place as the carry over. ×34 Step 4: Multiply the hundreds by the ones digit of the multiplier. 2 × 4 = 8 72 Add the carry over from the previous H TO step. So, 8 + 1 = 9. Write 9 in the hundreds 11 place of the product. 243 ×34 Step 5: Write 0 in the ones place. 972 Multiply the ones of the multiplicand by HTO the tens digit of the multiplier. Write the 11 product under the tens place. 243 ×3 4 3×3=9 972 Step 6: Multiply the tens by the tens digit 90 of the multiplier. H TO 4 × 3 = 12 1 Write 2 in the hundreds place of the 11 product and 1 in hundreds place of the 243 multiplicand as the carry over. ×34 972 290 76

Step 7: Multiply the hundreds by the tens Th H TO H TO digit of the multiplier. 1 1 352 2×3=6 43 ×23 1 34 Add the carry over from the previous 2 72 step. So, 6 + 1 = 7. Write 7 in the thousands × 90 place of the multiplicand. 9 72 Step 8: Add the products and write the Th H T O sum. The sum is the required product. 1 11 243 ×34 972 7290 8262 Train My Brain c) 222 × 23 Find the following products: a) 341 × 2 b) 156 × 4 6.2 I Apply Let us now solve some word problems that have real-life applications. Example 9: Rohan ran 315 m every day for a week. How many metres did he run in that week? Th H T O Solution: 1 week = 7 days 13 Distance run by Rohan in a day = 315 m Distance he ran in a week = 315 m × 7 = 2205 m 315 So, Rohan covered a total distance of 2205 m in one ×7 2205 week. Multiplication 77

Example 10: Payal saves ` 175 per month for a year. How much money will she have Solution: at the end of the year? Th H T O Amount saved by Payal per month = ` 175 11 Number of months in a year = 12 175 Total money saved in a year = 175 × 12 × 12 Therefore, Payal has ` 2100 at the end of the year. 11 350 1750 2100 6.2 I Explore (H.O.T.S.) Sometimes, we can find numbers that satisfy two or more conditions. Let us now see a few examples. Example 11: Find two numbers whose sum is 13 and product is 6 more than 30. Solution: The two conditions in this problem are: a) The sum of the numbers is 13 b) The product of the numbers is 6 more than 30 From condition b), 6 more than 30 = 30 + 6 = 36. So, the product of the numbers is 36. Now, let us find the two numbers whose product is 36 and sum is 13. 36 = 1 × 36; 36 = 2 × 18; 36 = 3 × 12; 36 = 4 × T9raanidn36M=y6 ×B6r.aOinf these, the numbers whose sum is 13 are 9 and 4 (since 9 + 4 = 13). Therefore, the required numbers are 9 and 4. Example 12: Find two numbers whose difference is 1 and product is 2 more than 40. Solution: The two conditions in this problem are: a) The difference of the numbers is 1. b) The product of the numbers is 2 more than 40 which is 42. Now, let us find two numbers whose product is 42 and difference is 1. 42 × 1 = 42; 21 × 2 = 42; 14 × 3 = 42; 7 × 6 = 42. Of these the numbers whose difference is 1 are 7 and 6. Therefore, the required numbers are 7 and 6. 78

Concept 6.3: Double 2-digit and 3-digit Numbers Mentally I Think Farida has 23 red beads. Her friend has double the number of beads. Farida wants to know the number of beads her friend has. Do you know how to find that mentally? 6.3 I Recall We have learnt mental addition and subtraction in the previous chapters. Let us now learn to double a given number mentally. To double a number, we must be thorough with the multiplication table of 2. For example, 5 × 2 = 10, 3 × 2 = 6, 10 × 2 = 20 and so on. 6.3 I Remember and Understand Let us now understand to double a 2-digit number mentally through a few examples. Example 13: Double the number 53. Doubling a Solution: To double the given number, follow these steps. number means multiplying by 2. Steps Solved 53 Solve this 41 The tens digit is ____. Step 1: Multiply the tens digit by 2. The tens digit is 5. So, ___ × 2 = ___. The ones digit is ___ So, 5 × 2 = 10. ___ < ___ (True/ False) Step 2: If the ones digit is less than The ones digit is 3. ___ × 2 = ___ or equal to 4, write the product in 3 < 4 (True) ___ × 2 = ___ step 1 as it is. If not, add 1 to it and write. Step 3: Multiply the ones digit by 2. 3 × 2 = 6 Step 4: Write the products in steps 53 × 2 = 106 1 and 3 together. This gives us the double of the given number. Multiplication 79 NR_BGM_182110020_Passport-G3-Textbook-Maths-FY_Corrected page.pdf 4 12/22/2017 4:16:48 PM

Train My Brain Double the given numbers mentally. a) 22 b) 36 c) 51 6.3 I Apply We have learnt to double 2-digit numbers mentally. Let us now see a few examples where we apply this concept. Example 14: Rohit has 14 shirts. His brother has double the number of shirts than he has. How many shirts does Rohit’s brother have? Solution: Number of shirts Rohit has = 14 Number of shirts Rohit’s brother has = Double the number of shirts that Rohit has = 14 × 2 = 28 Therefore, Rohit’s brother has 28 shirts. Example 15: Sony is 36 years old. Her aunt’s age is double the age of Sony. How old is Sony’s aunt? Solution: Sony’s age = 36 years Age of Sony’s aunt = Double that of Sony’s age = 36 years × 2 = 72 years Therefore, Sony’s aunt is 72 years old. 6.3 I Explore (H.O.T.S.) Doubling a 3-digit number is similar to doubling a 2-digit number. Let us now see some examples. Example 16: Double the number 125. Solution: To double the given number, follow these steps. 80

Steps Solved Solve this 125 293 Step 1: Multiply the number formed by the two leftmost digits by 2. The number formed by The number formed by the two leftmost digits the two leftmost digits is is 12. 12 × 2 = 24. ____. So, ___ × 2 = ___. Step 2: If the ones digit of the given The ones digit is 5. The ones digit is __ number is less than or equal to 4. 5 < 4 (False) ___ < ___ (True/ False) write the product in step 1 as it is. If 24 + 1 = 25 not, add 1 to it and write. Step 3: Multiply the ones digit by 2. 5 × 2 = 10 ___ × 2 = ___. Its ones digit is 0. Its ones digit is ___. Step 4: Write the products in steps So, 125 × 2 = 250 So, ___ × 2 = ___. 1 and 3 together. This gives the double of the given number. Maths Munchies Multiplying by 10 and 100 213 When numbers are multiplied by 10, the products are the numbers followed by ‘0’. That is, the ones digit in the product is 0. Similarly, when numbers are multiplied by 100, the products are the numbers followed by ‘00’. That is, the ones and the tens digit in the product are 0. For example: a) 5 × 10 = 50 b) 9 × 10 = 90 5 × 100 = 500 9 × 100 = 900 c) 6 × 10 = 60 d) 4 × 10 = 40 6 × 100 = 600 4 × 100 = 400 Multiplication 81

Connect the Dots Social Studies Fun All the arrangements of Charbagh Garden of Taj Mahal are based on four or its multiples. The entire garden is divided into four parts. There are 16 flowerbeds. It is said that each of the flowerbeds is planted with 400 plants. English Fun Compose a poem on multiplication as: Six times six. Magic tricks. Abracadabra. Thirty-six. Drill Time Concept 6.1: Multiply 2-digit Numbers 1) Multiply 2-digit numbers by 2, 3, 4, 5 and 6. a) 56 × 3 b) 23 × 2 c) 77 × 6 d) 50 × 5 e) 62 × 4 82

Drill Time 2) Multiply 2-digit numbers by 7, 8 and 9. a) 23 × 9 b) 12 × 7 c) 76 × 8 d) 84 × 8 e) 83 × 9 3) Word problems a) There were 23 students in one group. The school had 4 such groups. How many students were there in all the groups? b) Viraj travelled for 30 km in one day. He travelled the same distance everyday for 7 days. How many kilometres did he travel in 7 days? Concept 6.2: Multiply 3-digit Numbers by 1-digit and 2-digit Numbers 4) Multiply 3-digit numbers by 1-digit number without regrouping. a) 101 × 8 b) 212 × 4 c) 414 × 2 d) 111 × 5 e) 323 × 3 5) Multiply 3-digit numbers by 1-digit numbers (with regrouping). a) 225 × 7 b) 762 × 4 c) 868 × 8 d) 723 × 5 e) 429 × 2 6) Multiply 3-digit numbers by 2-digit numbers. a) 769 × 21 b) 759 × 10 c) 578 × 42 d) 619 × 66 e) 290 × 30 7) Word problems a) Susan drove 462 km every day for a week. What distance did she drive in that week? b) Sohail spends ` 616 for a set of books. How much will he spend on 24 such sets? Concept 6.3: Double 2-digit and 3-digit Numbers Mentally 8) Double the given numbers mentally. a) 23 b) 52 c) 61 d) 10 e) 74 9) Word problems a) Rohan bought 42 books in Year I and double the number in Year II. How many books did he buy in Year II? b) Sonal earned ` 28 on Monday. She earned double the amount on Tuesday. How much did she earn on Tuesday? Multiplication 83

A Note to Parent Multiplication is used in many situations in our day-to-day activities for calculating time, distance, money to be paid in a departmental store, the area of a room and so on. Encourage your child to actively engage in these scenarios and help you with the calculations. 84

Chapter Time 7 I Will Learn About • identifying a day and a date on a calendar • reading the time correctly to the hour. Concept 7.1: Read a Calendar I Think Farida and her friends are playing a game using a calendar. They split into two groups. Each group says a date or a day of a particular month. The other group answers with the corresponding day or date of another month. Can you also play such a game? 7.1 I Recall 4) Wednesday Let us recall the days in a week and the months in a year. There are 7 days in a week. They are: 1) Sunday 2) Monday 3) Tuesday 5) Thursday 6) Friday 7) Saturday 85

There are 12 months in a year. They are: 1) January 2) February 3) March 4) April 8) August 5) May 6) June 7) July 12) December 9) September 10) October 11) November 7.1 I Remember and Understand While reading a calendar we can find the day of a given date. We can also find dates that fall on a particular day of the month. Let us do an activity to understand this concept better. The calendar that we use Activity: is called the Gregorian 1) List out the birthdays of your parents, grandparents, brothers and calendar. sisters. 2) Arrange them in a table as they appear in a calendar month-wise. 3) Note the days on which the birthdays appear. Stick this on your writing table. This will remind you to wish your family members “HAPPY BIRTHDAY” on their birthdays. Your tables could be similar to the one given below. Birthdays of my family members Birthday (2018) Member of the family Day 08-January Brother Sunday 10-March Mother Friday 16-June MINE Friday 03-August Father Thursday 04-October Wednesday Grand father Tuesday 12-December Grand mother Example 1: Observe the given calendar and answer the questions that follow. a) How many days are there in this month? b) How many Sundays are there in this month? c) Which day appears 5 times? 86

d) O n which day is the Republic day? JANUARY 2019 Solution: e) On which date is the second Saturday? SUN MON TUE WED THU FRI SAT a) There are 31 days in this month. 12345 6 7 8 9 10 11 12 b) There are four Sundays in this month. 13 14 15 16 17 18 19 c) Tuesday, Wednesday and Thursday 20 21 22 23 24 25 26 27 28 29 30 31 appear five times. d) The Republic day is on a Saturday. e) The second Saturday is on 12th. Example 2: From the calendar for the year 2018, write the days of the following events. a) Independence Day - ____________ b) Republic Day - _____________ c) Christmas - ____________ d) Teacher’s Day - _____________ e) Children’s Day - _____________ Solution: a) Independence Day - Wednesday b) Republic Day - Friday c) Christmas - Tuesday d) Teacher’s Day - Wednesday e) Children’s Day - Wednesday Train My Brain Answer the following questions. a) When is your father’s birthday? b) On which day is your birthday this year? c) When do you have summer vacation for school? Time 87

7.1 I Apply We use the calendar on a daily basis. Events like planning holidays, conducting sports and examinations in school are a few examples. October 2018 Example 3: Renu wants to plan her holiday in October SUN MON TUE WED THU FRI SAT from Friday to Wednesday to New Delhi. 1 23456 On the calendar, mark the days when 7 8 9 10 11 12 13 Renu can plan her holiday. 14 15 16 17 18 19 20 21 22 23 24 25 26 27 Solution: Renu’s trip will start on a Friday and end 28 29 30 31 on a Wednesday. Fridays in this month: 5, 12, 19, 26 October 2018 SUN MON TUE WED THU FRI SAT Wednesdays in this month: 3, 10, 17, 24, 31 1 2 3 456 7 8 9 10 11 12 13 Renu’s trip could be planned for 5th to 14 15 16 17 18 19 20 10th, 12th to 17th, 19th to 24th or 26th to 31st as 21 22 23 24 25 26 27 marked on the calendar. 28 29 30 31 Example 4: Use the January 2019 calendar shown to answer the question. Rupali is a clerk in a bank. She has January 2019 Solution: holidays on Sundays and on the first and the third Saturdays of the month. She also SUN MON TUE WED THU FRI SAT has holidays on the New Year’s Day and 12345 Republic Day. How many holidays does she have in the month of January? 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Republic day is on 26th January. 20 21 22 23 24 25 26 27 28 29 30 31 New Year day is on 1st January. The first and the third Saturday falls on 5th and 19th January respectively. Sundays fall on 6th, 13th, 20th and 27thJanuary. Rupali has holidays on 1st, 5th, 6th, 13th, 19th, 20th, 26th and 27th January. Therefore, she has 8 holidays in January. 88

7.1 I Explore (H.O.T.S.) Observe the calendar for February of different years. February 2009 February 2010 February 2011 SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT 1234567 123456 12345 8 9 10 11 12 13 14 7 8 9 10 11 12 13 6 7 8 9 10 11 12 15 16 17 18 19 20 21 14 15 16 17 18 19 20 13 14 15 16 17 18 19 22 23 24 25 26 27 28 21 22 23 24 25 26 27 20 21 22 23 24 25 26 28 27 28 February 2012 February 2013 February 2014 SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT 1234 12 1 5 6 7 8 9 10 11 3456789 2345678 12 13 14 15 16 17 18 10 11 12 13 14 15 16 9 10 11 12 13 14 15 19 20 21 22 23 24 25 17 18 19 20 21 22 23 16 17 18 19 20 21 22 26 27 28 29 24 25 26 27 28 23 24 25 26 27 28 February 2015 February 2016 February 2017 SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI SAT 1234567 123456 123 4 11 8 9 10 11 12 13 14 7 8 9 10 11 12 13 5 6 7 8 9 10 18 25 15 16 17 18 19 20 21 14 15 16 17 18 19 20 12 13 14 15 16 17 22 23 24 25 26 27 28 21 22 23 24 25 26 27 19 20 21 22 23 24 28 29 26 27 28 We observe that February has 29 days in the years 2012 and 2016. In the other years, February has 28 days. Every four years, an extra day is added to the month of February. This is due to the revolution of the Earth around the Sun. The Earth takes 365 days and 6 hours to go around the Sun. An ordinary year is taken as 365 days only. 6 hours put together four times make an extra day for every four years. This is added on to get the leap year. So, there are 365 + 1 = 366 days in a leap year. Time 89

Example 5: Find the leap years in the following years. 2020, 2021, 2022, 2024, 2025 Solution: In a leap year, the number formed by the last two digits is an exact multiple of 4. In 2020, the number formed by the last two digits is 20, which is a multiple of 4. In 2021, the number formed by the last two digits is 21, which is not a multiple of 4. In 2022, 22 is not a multiple of 4. In 2024, 24 is a multiple of 4. In 2025, 25 is not a multiple of 4. Thus, 2020 and 2024 are the leap years. Example 6: How many days were there from Christmas 2010 to Christmas 2011? Solution: 2011 was not a leap year. So, the number of days from Christmas 2010 to Christmas 2011 was 365. Concept 7.2: Read Time Correct to the Hour I Think Farida’s teacher taught her to read time. She now knows the units of time. Farida reads time when her father moves the hands of a clock to different numbers. Can you also read time from a clock? 7.2 I Recall We learnt that the long hand on the clock shows minutes and the short hand shows hours. In some clocks, we see another hand, thinner than the hour and the minute hands. This is the seconds hand. Let us recall reading time from a clock. 90

a) 7 o’clock is _______________ hours more than 4 o’clock. b) The _______________ hand takes one hour to go around the clock. c) The _______________ hand is the shortest hand on the clock. d) The time is _______________ when both the hour hand and the minute hand are on 12. e) 2 hours before 10 o’clock is _______________. 7.2 I Remember and Understand We see numbers 1 to 12 on the clock. These numbers are for counting hours. There are 60 parts or small lines between these numbers. They stand for minutes. The minute hand takes 1 hour to go around the clock 1 hour = 60 minutes face once. The minute hand takes 5 minutes to go from one number to the next number on the clock face. We multiply the number to which the minute hand points by 5 to get the minutes. For example, the minute hand in the figure is at 6. So, it denotes 6 × 5 = 30 minutes past the hour (here, after 3). Therefore, the time is read as 3:30. The hour hand takes one hour to move from one number to the other. Let us now read the time shown by these clocks. Fig. (a) Fig. (b) Fig. (c) Fig. (d) In figure (a), the minute hand is at 9. The hour hand is in between 5 and 6 . The number of minutes is 9 × 5 = 45. Thus, the time shown is 5:45. In figure (b), the minute hand is at 6. The number of minutes is 6 × 5 = 30. Time 91

The hour hand is between 7 and 8. Therefore, the time shown is 7:30. In figure (c), the minute hand is at 3. The number of minutes is 3 × 5 = 15. The hour hand has just passed 9. Therefore, the time shown is 9:15. In figure (d), the minute hand is at 4. So, the number of minutes is 4 × 5 = 20. The hour hand has just passed 2. Therefore, the time shown is 2:20. Example 7: On which number is the minute hand if the time is as given? a) 35 minutes b) 15 minutes c) 40 minutes d) 30 minutes Solution: To find minutes when the minute hand is at a number, we multiply by 5. So, to get the number from the given minutes, we must divide it by 5. a) 35 ÷ 5 = 7. So, the minute hand is at 7. b) 15 ÷ 5 = 3. So, the minute hand is at 3. c) 40 ÷ 5 = 8. So, the minute hand is at 8. d) 30 ÷ 5 = 6. So, the minute hand is at 6. Quarter past, half past and quarter to the hour We know that, ‘quarter’ means 1 . 4 In Fig (a), the minute hand of the clock has travelled a quarter of an hour. So, we call it quarter past the hour. The time shown is 2:15 or 15 minutes past 2 or quarter past 2. Fig. (a) ‘Half’ means 1 2 In Fig. (b), the minute hand has travelled half the clock after an hour. So, we call it half past the hour. The time shown is 2:30 or 30 minutes past 2 or half past 2. Fig. (b) In Fig. (c), the minute hand has to travel a quarter of the clock before it completes one hour. We call it quarter to the hour. The time shown is 7:45 or 45 minutes past 7 or quarter to 8. Example 8: Read the time in each of the given clocks and write it in Fig. (c) two different ways. 92

Solved Solve this Fig. (a) Fig. (b) Fig. (c) Fig. (d) The hour hand is The hour hand is The hour hand is The hour hand is between 3 and 4. between _____ and between _____ and between _____ and _____. The minutes _____. The minutes _____. The minutes So, the minutes are are after ____hours. are after ____hours. are after ____hours. after 3 hours. The The minute hand The minute hand The minute hand minute hand is at is at _____. So, is at _____. So, is at _____. So, 6. So, the time is 30 the time is _____ the time is _____ the time is _____ minutes after 3. We minutes after _____. minutes after _____. minutes after _____. write it as 3:30 or We write it as _____ We write it as _____ We write it as _____ half past 3. or _____. or _____. or _____. Train My Brain Answer the following questions. a) Write the time: quarter past 7. b) How many numbers do you see on the clock? c) H ow much time does the hour hand take to move from one number to the next? 7.2 I Apply We have learnt how to read the time. Now let us draw hands on the clocks when the time is given. Example 9: Draw the hands of a clock to show the given time. a) 1:15 b) 6:15 c) 7:30 d) 9:45 Time 93

Solution: To draw the hands of a clock, first note the minutes. If the minutes are between 1 and 30, draw the hour hand between the given hour and the next. But care should be taken to draw it closer to the given hour. If the minutes are between 30 and 60, draw the hour hand closer to the next hour. Then, draw the minute hand on the number that shows the given minutes. a) b) c) d) Example 10: Draw the hands of a clock to show the given time. a) Quarter to 7 b) Half past 4 Solution: Train My Brain b) a) 7.2 I Explore (H.O.T.S.) We have learnt to read and show time, exact to minutes and hours. Let us now learn to find the length of time between two given times. Example 11: The clocks given show the start time and the end time of the Maths class. How long was the class? 94

Solution: The start time is 10:00 and the end time is 10:45. The difference in the given times = 10:45 – 10:00 = 45 minutes Therefore, the length of the Maths class was 45 minutes. Example 12: Sanjay spends an hour between 4:30 and 5:30 for different activities. The start time for each activity is as shown. playing drinking milk homework TV on TV off Read the clocks and answer the following questions. a) When did Sanjay begin drinking milk? b) For how long did he play? c) For how long did he watch TV? d) When did he switch off the TV? Solution: From the given figures, a) Sanjay began drinking milk at 4:45. b) Sanjay began playing at 4:30 and ended at 4:45. So, he played for a quarter hour (15 minutes) as 4:45 – 4:30 = 15 minutes. c) The time for which he watched TV was 5:30 – 5:20 = 10 minutes. d) Sanjay switched off the TV at 5:30. The time between two given times is called the length of time. It is also called time duration or time interval. It is given by the difference of end time and start time. Time 95

Maths Munchies 213 A year with its last two digits as a multiple of 4 is a leap year. The rule is different for century years. Century years are the years which have 0 in the ones and tens places. Years such as 1300, 1400 and so on are century years. For century years to be leap years, the number formed by the digits in their thousands and hundreds places must be a multiple of 4. For example, the years 1600 and 2000 are leap years whereas the years 2100 and 2200 are not. Connect the Dots Science Fun How you noticed that you start feeling hungry between 12 noon to 2 o’clock? Why don’t you feel hungry before that? It is because our body gets used to a sequence of events. This sequence of events is called our ‘body cycle’. Another example of the body cycle is that if you sleep daily by 10:00 p.m. then you will feel sleepy at that time even when you are not in your bed. English Fun Here is a poem to remember what a calendar tells us. When we see the calendar we learn the month, the date, the year. Every week day has a name there are lots of numbers that look the same. So let’s begin to show you how we see the calendar right now. 96