4.3 Mental Maths Techniques: Addition Mental Maths Let us now learn to add two 2-digit numbers, 29 and 56, mentally. Steps Solved Solve this 29 and 56 83 and 47 Step 1: Split the two given numbers as tens and ones 29 = 20 + 9 83 = ___ + ____ mentally. 56 = 50 + 6 47 = ___ + ____ 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 Train My Brain steps 2 and 3 mentally = 70 + 10 + 5 c) 42 + 98 (regroup if needed). = 85 Step 5: Write the sum of the So, 29 + 56 = 85. given numbers. ? Train My Brain Solve the following mentally: a) 21 + 39 b) 44 + 57 d) 82 + 19 e) 17 + 37 Addition 47 NR_BGM_9789388700627 TRAVELLER G03 MATHS TEXTBOOK PART 1_Text.pdf 51 12/14/2018 5:03:12 PM
Maths Munchies 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: Count the digits in the ones place, which are 5 or more than 5. Here, only one digit is equal to 5. So, the total count is 1. Step 3: Add 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 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. Social Studies Fun Early humans had the basic idea of addition. Aryabhatta contributed to the concept of addition by inventing the number ‘0’. 48 12/14/2018 5:03:12 PM NR_BGM_9789388700627 TRAVELLER G03 MATHS TEXTBOOK PART 1_Text.pdf 52
Drill Time 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) Word problems a) S hyam has 269 pens and Ritesh has 832 pens. How many pens do they have altogether? b) R avi’s garden has 673 flowers and Rahul’s garden has 978 flowers. How many flowers are there in their gardens? 4.2 Estimate the Sum of Two Numbers 4) 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 5) Word problems a) Sunil has 56 red roses, Sona has 32 yellow roses. Estimate the total number of roses they have. b) R ahul has 66 pencils and Vinod has 34 pencils. Estimate the number of pencils both of them have in all. A Note to Parent We use mental addition in our day-to-day lives especially to calculate the total amount of money. Encourage your child to practise the concept by taking his or her help in calculating the amount of bills, tendering change, buying groceries and so on. Addition 49 NR_BGM_9789388700627 TRAVELLER G03 MATHS TEXTBOOK PART 1_Text.pdf 53 12/14/2018 5:03:12 PM
5Chapter Subtraction I Will Learn About • using subtraction of 3-digit numbers in real-life. • subtracting numbers with and without regrouping. 5.1 Subtract 3-digit and 4-digit Numbers I Think The given grid shows the number of men and women in Neena’s town in the years 2013 and 2014. Years 2013 2014 How can Neena find the number of men Men 2254 2187 more than that of women living in her town in the two years? Women 2041 2073 I Recall Recall that we can subtract numbers by writing them one below the other. We subtract a 2-digit number from a larger 2-digit number or a 3-digit number. Similarly, we subtract a 3-digit number from a larger 3-digit number. 50 12/14/2018 5:03:12 PM NR_BGM_9789388700627 TRAVELLER G03 MATHS TEXTBOOK PART 1_Text.pdf 54
Let us answer these to revise the concept. a) 15 – 0 = _________ b) 37 – 36 = _________ c) 93 – 93 = _________ d) 18 – 5 = _________ e) 47 – 1 = _________ f) 50 – 45 = _________ I Remember and Understand We have learnt to subtract two 3-digit numbers without While subtracting, regrouping. Let us now learn to subtract them with start from the ones regrouping. place. Subtract 3-digit numbers with regrouping When we subtract a larger digit from a smaller digit, we regroup the digit in the next higher place and borrow. Let us understand this through an example. Example 1: Subtract: 427 from 586 Solution: To subtract, write the smaller number below the larger number. Solved Step 3: Subtract the hundreds. Step 1: Subtract the ones. But, 6 – 7 is Step 2: Subtract the not possible as 6 < 7. So, regroup the tens. digits in the tens place. 8 tens = 7 tens + 1 ten. 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 5 –4 8\\ \\6 –4 \\8 \\6 5 \\8 6\\ 27 27 –4 2 7 9 59 15 9 Subtraction 51 NR_BGM_9789388700627 TRAVELLER G03 MATHS TEXTBOOK PART 1_Text.pdf 55 12/14/2018 5:03:13 PM
H TO Solve these H TO 623 H TO 453 –376 –264 552 –263 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 example helps you understand this better. Example 2: Subtract: 5032 from 7689 Solution: To subtract, write the smaller number below the larger number. Step 1: Subtract the ones. Solved Step 2: Subtract the tens. Th H T O 7689 Th H T O –5032 7689 –5032 7 57 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 52 12/14/2018 5:03:13 PM NR_BGM_9789388700627 TRAVELLER G03 MATHS TEXTBOOK PART 1_Text.pdf 56
Th H T O Solve these Th H T O 8000 4789 – 2000 Th H T O –2475 2879 –2137 ? Train My Brain c) 3678 – 2466 Solve the following: a) 719 – 320 b) 813 – 621 I Apply We very often use the subtraction of 3-digit and 4-digit numbers in real life. Here are a few examples. Example 3: Sonu bought 375 marbles. He gave 135 marbles to his brother. How many marbles does he have now? Solution: Total number of marbles Sonu bought = 375 H TO Number of marbles he gave his brother = 135 375 Number of marbles left with him = 375 – 135 = 240 –1 3 5 Therefore, Sonu has 240 marbles left with him. 240 Example 4: Vinod had 536 stamps. He gave some stamps to his brother and then Vinod was left with 278 stamps. How many stamps did Vinod Solution: give his brother? H TO Total number of stamps Vinod had = 536 12 Number of stamps Vinod had after giving 4 2\\ 16 some to his brother = 278 \\5 \\3 \\6 Number of stamps he gave his brother –278 = 536 – 278 = 258 258 Example 5: A rope is 6436 cm long. A 3235 cm long piece is cut from it. How much of the rope is left? Subtraction 53 NR_BGM_9789388700627 TRAVELLER G03 MATHS TEXTBOOK PART 1_Text.pdf 57 12/14/2018 5:03:13 PM
Solution: Length of the rope = 6436 cm Th H T O Length of the piece cut = 3235 cm 6436 The length of the remaining piece of rope –3 2 3 5 = 6436 cm – 3235 cm = 3201 cm 3201 I Explore (H.O.T.S.) We can check the correctness of a subtraction problem using addition. Consider an example. Example 6: 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\\ –1 4 5 –2 7 9 9 21 We can write 36 = 27 + 9. 364 – 145 = 219 We can write 364 = 145 + 219. Therefore, to check if a subtraction is correct, we add the subtrahend and the difference. If this sum is the same as the minuend, the subtraction is correct. Note: (a) Subtrahend = The number being subtracted (b) Minuend = The number from which a number is subtracted Subtraction Fact ↓ ↓ ↓ Minuend Subtrahend Difference 54 12/14/2018 5:03:13 PM NR_BGM_9789388700627 TRAVELLER G03 MATHS TEXTBOOK PART 1_Text.pdf 58
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. The following are some examples. a) Of the 37 students in a class, 14 are girls. How many are boys? b) 3 7 children are playing on the ground. 23 of them are girls. How many boys are playing on the ground? Similarly, we can frame some interesting problems using subtraction facts of 3-digit numbers. Let us see an example. Example 7: 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 basket, there are 706 mangoes. 234 of them were rotten. How many good fruits are there in the basket? b) 461 people booked a train for a trip to Goa. 110 people cancelled the trip. How many people went on the trip? 5.2 Estimate the Difference between Two Numbers I Think ` 185 ` 135 Neena had ` 350 with her. She wanted to buy a toy truck for ` 185 and a toy train for ` 135. Can Neena buy both the items with the money she has? I Recall 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. Subtraction 55 NR_BGM_9789388700627 TRAVELLER G03 MATHS TEXTBOOK PART 1_Text.pdf 59 12/14/2018 5:03:13 PM
a) 87 = ______ b) 53 = ______ c) 65 = ______ d) 41 = ______ e) 76 = ______ I Remember and Understand Rounding off numbers can be used to estimate the Estimation is finding difference between two 2-digit numbers and between a number that is two 3-digit numbers. Let us understand this through close enough to examples. the right answer. Example 8: Estimate the difference: a) 69 – 15 b) 86 – 12 Solution: a) 69 – 15 Rounding off 69 to the nearest tens gives 70 (as 9 > 5). Rounding off 15 to the nearest tens, gives 20 (as 5 = 5). So, the estimated difference is 70 – 20 = 50. b) 86 – 12 Rounding off 86 to the nearest tens gives 90 (as 6 > 5). Rounding off 12 to the nearest tens, gives 10 (as 2 < 5). So, the estimated difference is 90 – 10 = 80. Example 9: Estimate the difference: a) 593 – 217 b) 806 – 124 Solution: a) 593 – 217 Rounding off 593 to the nearest tens gives 590 (as 3 < 5). Rounding off 217 to the nearest tens, gives 220 (as 7 > 5). So, the estimated difference is 590 – 220 = 370. b) 806 – 124 Rounding off 806 to the nearest tens gives 810 (as 6 > 5). Rounding off 124 to the nearest tens, gives 120 (as 4 < 5). So, the estimated difference is 810 – 120 = 690. ? Train My Brain Estimate these differences: a) 25 – 9 b) 135 – 112 c) 64 – 35 56 12/14/2018 5:03:13 PM NR_BGM_9789388700627 TRAVELLER G03 MATHS TEXTBOOK PART 1_Text.pdf 60
I Apply Estimation of differences can be used in real-life situations. Let us see a few examples. Example 10: 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). 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 11: Ram has 94 sweets. He distributes 46 sweets among his school friends. Estimate the number of sweets that 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 school 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. 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 12: In a school, there are 976 students. 325 are from primary school and 416 are from middle school. The rest are from high school. How many high school students are there in the school? Solution: Total number of students = 976 Subtraction 57 NR_BGM_9789388700627 TRAVELLER G03 MATHS TEXTBOOK PART 1_Text.pdf 61 12/14/2018 5:03:13 PM
Number of primary school students = 325 HTO Number of middle school students = 416 1 Total number of primary and middle school 3 2 5 students +4 1 6 = 325 + 416 = 741 741 Number of high school students = Total number HTO of students – Number of students in primary and 976 middle schools = 976 – 741 = 235 –7 4 1 Therefore, the number of high school students is 235 235. 5.3 Mental Maths Techniques: Subtraction Mental Maths Let us now learn to subtract two 2-digit numbers, 29 from 56, mentally. Steps Solved Solve this 29 from 56 46 from 83 Step 1: Split the two given 29 = 20 + 9 83 = ______ + ______ numbers as tens and ones. 56 = 50 + 6 46 = ______ + ______ Step 2: Check if ones can 6 – 9 is not possible. So, ____ – ____ is possible (True/ be subtracted. If not, regroup the tens. False) If it is true, subtract. If regroup the tens. it is false, regroup. Add ten ones to ones and Add 10 ones to 6 to Add 10 ones to ___ to get reduce 1 ten from tens. get 16 and subtract 1 ____ and subtract 1 ten ten from 5 tens to get from ____ tens to get ____ Step 3: Subtract the 4 tens. tens. ones of the two numbers mentally. 16 – 9 = 7 ______ – ______ = ______ Step 4: Subtract the tens of 4 tens – 2 tens = 2 tens ______ – ______ = ______ the two numbers mentally. Step 5: Write the answers from steps 3 and 4 So, 56 – 29 = 27. ______ – ______ = ______ together as the difference. 58 12/14/2018 5:03:13 PM NR_BGM_9789388700627 TRAVELLER G03 MATHS TEXTBOOK PART 1_Text.pdf 62
? Train My Brain d) 81 – 42 e) 20 – 11 Solve the following mentally: a) 53 – 34 b) 65 – 26 c) 65 – 16 Maths Munchies We can subtract 2 numbers easily by splitting the smaller number. Let us consider 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 Connect the Dots Science Fun n 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! Subtraction 59 NR_BGM_9789388700627 TRAVELLER G03 MATHS TEXTBOOK PART 1_Text.pdf 63 12/14/2018 5:03:13 PM
Drill Time 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 3) Word problems a) T here are 8745 people at a cricket match. 4313 people leave. How many people are left? b) A factory made 5786 pencils. 3625 pencils were lost in a fire. How many pencils were saved? 5.2 Estimate the Difference between Two Numbers 4) Estimate these differences: a) 65 – 15 b) 48 – 16 c) 67 – 32 d) 896 – 432 e) 679 – 387 5) Word problems a) In a school, there are 562 students of 3 groups. Of them, 118 are from the red group. 321 are from the green group. The rest are from the blue group. About how many students in the school are in the blue group? b) A aliya has 77 balloons. She gives 42 balloons to her sister. About how many balloons remain with Sneha? A Note to Parent You can help your child develop the ability to calculate mentally with speed and precision. Give him or her small problems to solve everyday. Let them help with your monthly expense calculations. 60 12/14/2018 5:03:13 PM NR_BGM_9789388700627 TRAVELLER G03 MATHS TEXTBOOK PART 1_Text.pdf 64
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