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 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 51 12/17/2018 4:06:38 PM
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 12/17/2018 4:06:38 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 52
= 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 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 53 12/17/2018 4:06:38 PM
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 12/17/2018 4:06:38 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 54
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 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 55 12/17/2018 4:06:38 PM
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 12/17/2018 4:06:38 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 56
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: 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? 5.1 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 = ______ 5.1 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. 53 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 57 12/17/2018 4:06:39 PM
Example 1: Estimate the difference: a) 69 – 15 b) 86 – 12 Solution: a) 69 – 15 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 2: 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 5.1 I Apply Estimation of differences can be used in real-life situations. Let us see a few examples. Example 3: 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). 54 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 58 12/17/2018 4:06:39 PM
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 4: 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. 5.1 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 5: 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? Solution: Total number of students = 976 HTO Number of students from the pre-primary section = 325 1 Number of students from the primary section = 416 Total number of students in pre-primary and primary 325 school sections = 325 + 416 = 741 +4 1 6 741 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 55 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 59 12/17/2018 4:06:39 PM
Concept 5.2: 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 2017 and 2018. Years 2017 2018 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 5.2 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. Let us answer these to revise the concept. a) 15 – 0 = _________ b) 37 – 36 = _________ c) 93 – 93 = _________ f) 50 – 45 = _________ d) 18 – 5 = _________ e) 47 – 1 = _________ 5.2 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 6: Subtract 427 from 586. Solution: To subtract, write the smaller number below the larger number. 56 12/17/2018 4:06:39 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 60
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. H TO 7 16 8 tens = 7 tens + 1 tens. Borrow 1 ten to the ones place. Reduce the tens by 1 5 \\8 \\6 ten. Now subtract 7 ones from 16 ones. –4 2 7 H TO H TO 15 9 7 16 7 16 5 –4 8\\ 6\\ 5 \\8 \\6 27 –4 2 7 9 59 H TO Solve these H TO H TO 6 23 5 52 4 53 – 3 76 – 2 63 – 2 64 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 7: Subtract: 5032 from 7689 Solution: To subtract, write the smaller number below the larger number. Step 1: Subtract the ones. O Solved O 9 9 Th H T 2 Step 2: Subtract the tens. 2 768 7 7 −503 Th H T 768 −503 5 Subtraction 57 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 61 12/17/2018 4:06:39 PM
Step 3: Subtract the hundreds. Solved Step 4: Subtract the thousands. Th H T O 7689 Th H T O −5032 7 68 9 − 5 03 2 657 2 65 7 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 8: What is the difference 7437 and 4868? Solution: Write the smaller number below the larger number. Steps Solved O Solve these Step 1: Subtract the ones. Th H T O Th H T 17 But, 7 − 8 is not possible as 2 1654 \\7 −1 2 4 6 7 < 8. So, regroup the tens digit, 7 4 3\\ 8 3. 3 tens = 2 tens + 1 ten. Borrow −4 8 6 9 1 ten to the ones place. Step 2: Subtract the tens. But, Th H T O 2 − 6 is not possible as 2 < 6. 12 So, regroup the hundreds digit, 3 \\2 17 4. 4 hundreds = 3 hundreds + − 7 4\\ 3\\ \\7 1 hundred. Borrow 1 hundred to 4 8 6 8 the tens place. 69 58 12/17/2018 4:06:39 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 62
Steps Solved Solve these Th H T O Step 3: Subtract the hundreds. Th H T O But, 3 − 8 is not possible. So, 13 12 5674 regroup the thousands digit, −2 3 8 2 7. 7 thousands = 6 thousands + 6 \\3 \\2 17 1 thousand. Borrow 1 thousand \\7 4\\ 3\\ \\7 to the hundreds place. −4 8 6 8 569 Step 4: Subtract the thousands. Th H T O Th H T O 13 12 7468 6 \\3 \\2 17 −4 8 3 7 \\7 4\\ 3\\ \\7 −4 8 6 8 2569 Train My Brain Solve the following: a) 719 – 320 b) 813 – 621 c) 3678 – 2466 5.2 I Apply Subtraction of 3-digit numbers is very often used in real life. Here are a few examples. Example 9: 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 Subtraction 59 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 63 12/17/2018 4:06:39 PM
Example 10: 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 11: 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. Example 12: 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. 5.2 I Explore (H.O.T.S.) We can check the correctness of a subtraction problem using addition. Consider an example. 60 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 64 12/17/2018 4:06:39 PM
Example 13: 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 −1 4 5 7 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? 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 14: Frame a word problem using: a) 706 – 234 = 472 b) 461 − 110 = 351 Solution: A few possible word problems 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? Subtraction 61 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 65 12/17/2018 4:06:39 PM
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 12/17/2018 4:06:39 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 66
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_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 67 12/17/2018 4:06:39 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 12/17/2018 4:06:39 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 68
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 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 69 12/17/2018 4:06:39 PM
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 12/17/2018 4:06:39 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 70
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 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 71 12/17/2018 4:06:39 PM
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 12/17/2018 4:06:40 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 72
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. NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 73 69 12/17/2018 4:06:40 PM
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 12/17/2018 4:06:40 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 74
Multiplication Fact ↓↓ ↓ Multiplicand Multiplier Product Note: (a) R epresenting the multiplicand, multiplier and product using the symbols ‘×’ and ‘=’ is called a multiplication fact. (b) T he multiplicand and the multiplier are also Order Property: Changing called the factors of the product. the order in which the numbers are multiplied (c) The 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 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 75 12/17/2018 4:06:40 PM
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 54 Therefore, the total number of students in the school = 432 ×8 432 72 12/17/2018 4:06:40 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 76
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 25 travels in 25 days = 25 × 7. ×7 Therefore, Manoj travels 175 km in 25 days. 175 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 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 77 12/17/2018 4:06:40 PM
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 12/17/2018 4:06:40 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 78
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 444 product has two or more digits. 1 3 ×8 5 51 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 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 79 12/17/2018 4:06:40 PM
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 453 1 ×13 Write 2 in the ones place of the product. Write 1 in the tens place as the carry over. 243 H TO ×34 263 Step 3: Multiply the tens by the ones digit ×23 of the multiplier. 4 × 4 = 16 2 12/17/2018 4:06:40 PM 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 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 80
Steps Solved Solve these Step 7: Multiply the hundreds by the tens digit of the multiplier. Th H T O H TO 2×3=6 1 352 ×23 Add the carry over from the previous 11 step. So, 6 + 1 = 7. Write 7 in the thousands 243 place of the multiplicand. ×34 972 7290 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 Solution: that week? Th H T O 1 week = 7 days Distance run by Rohan in a day = 315 m 13 Distance he ran in a week = 315 m × 7 = 2205 m 315 So, Rohan covered a total distance of 2205 m in one ×7 week. 2205 Multiplication 77 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 81 12/17/2018 4:06:40 PM
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 12/17/2018 4:06:40 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 82
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_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 83 12/17/2018 4:06:41 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 12/17/2018 4:06:41 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 84
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 ___. So, ___ × 2 = ___. Step 4: Write the products in steps So, 125 × 2 = 250 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 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 85 12/17/2018 4:06:41 PM
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 12/17/2018 4:06:41 PM Compose a poem on multiplication as: Six times six. Magic tricks. Abracadabra. Thirty-six. 82 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 86
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 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 Multiplication 83 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 87 12/17/2018 4:06:41 PM
Drill Time 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? 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 12/17/2018 4:06:41 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 88
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