Passport-G3-FoundationMax-Maths-FY_opt

2) Add 4-digit numbers without regrouping Adding two 4-digit numbers is similar to adding two 3-digit numbers. Let us understand this through an example. Example 2: Add 1352 and 3603. Solution: Arrange the numbers one below the other. Solved Step 1: Add the ones. Step 2: Add the tens. Th H T O Th H T O 1 3 5 2 1 3 5 2 + 3 6 0 3 + 3 6 0 3 5 5 5 Step 3: Add the hundreds. Step 4: Add the thousands. Th H T O Th H T O 1 3 5 2 1 3 5 2 + 3 6 0 3 + 3 6 0 3 9 5 5 4 9 5 5 Solve these Th H T O Th H T O Th H T O 4 1 9 0 2 0 0 2 1 1 1 1 + 2 0 0 0 + 3 0 0 3 + 2 2 2 2 3) Add 4-digit numbers with regrouping We regroup the sum when it is equal to or more than 10. Example 3: Add 1456 and 1546. Solution: Arrange the numbers one below the other. Add and regroup if necessary. Addition 45 L04_V2_PPS_Maths_G1_TB_Addition.indd 45 1/12/2017 10:04:21 PM

Solved Step 1: Add the ones. Step 2: Add the tens. Th H T O Th H T O 1 1 1 1 4 5 6 1 4 5 6 + 1 5 4 6 + 1 5 4 6 2 0 2 Step 3: Add the hundreds. Step 4: Add the thousands. Th H T O Th H T O 1 1 1 1 1 1 1 4 5 6 1 4 5 6 + 1 5 4 6 + 1 5 4 6 0 0 2 3 0 0 2 Solve these Th H T O Th H T O Th H T O 1 7 5 8 2 6 7 8 4 5 9 2 + 5 6 6 2 + 1 3 3 2 + 1 4 5 6 Train My Brain Solve the following: a) 321 + 579 b) 725 + 215 c) 8837 + 1040 4.1 I Apply Look at some examples where we use the addition of 3-digit and 4-digit numbers. Example 4: Vinod had some stamps out of which he gave 278 stamps to his brother. Vinod now has 536 stamps left with him. How many stamps did he have in the beginning? 46 L04_V2_PPS_Maths_G1_TB_Addition.indd 46 1/12/2017 10:04:21 PM

Solution: Number of stamps Vinod has now = 536 H T O Number of stamps he gave his brother = 278 1 1 Number of stamps Vinod had in the 5 3 6 + 2 7 8 beginning = 536 + 278 = 814 8 1 4 Example 5: Ajit collected ` 2683 and Radhika collected ` 3790 for donating to an old age home. What is the total money collected? Th H T O Solution: Amount collected by Ajit = ` 2683 1 1 Amount collected by Radhika = ` 3790 2 6 8 3 Total amount collected for the donation + 3 7 9 0 6 4 7 3 = ` 2683 + ` 3790 = ` 6473 Example 6: The number of students in Class 3 of Heena’s school is 236. The number of students in Class 3 of Veena’s school is 289. How many students of Grade 3 were present in both the schools? Solution: Number of students present in Heena’s school = H T O 236 1 1 Number of students present in Veena’s school = 2 3 6 289 + 2 8 9 5 2 5 Total number of students present in Class 3 of both the schools = 236 + 289 = 525 4.1 I Explore (H.O.T.S.) Let us see a few more examples on the addition of 4-digit numbers. Example 7: Three pieces of ribbon of lengths 2134 cm, 1185 cm and 3207 cm are cut from a long ribbon. What was the length of the ribbon before the pieces were cut? Addition 47 L04_V2_PPS_Maths_G1_TB_Addition.indd 47 1/12/2017 10:04:22 PM

Solution: The pieces of ribbon are 2134 cm, 1185 cm Th H T O and 3207 cm long. 1 1 Length of the ribbon before the pieces were 2 1 3 4 cut = 2134 cm + 1185 cm + 3207 cm + 1 1 8 5 + 3 2 0 7 Therefore, the length of the ribbon before the 6 5 2 6 pieces were cut = 6526 cm Example 8: Payal, Eesha and Suma have 1284, 7523 and 5215 stamps respectively. Frame an addition problem. Solution: An addition problem contains words such as - in all, total, altogether and so on. So, the question can be ‘‘Payal, Eesha and Suma have 1284, 7523 and 5215 stamps respectively. How many stamps do they have altogether?” Maths Munchies How can we add faster? 2 3 1 Example: 546 + 678 First, round off the numbers to the closest multiple of 10. Thus, 546 becomes 550 and 678 become 680. 550 + 680 = 1230 We now determine how much we added to round off both the numbers. 546 + 4 = 550, 678 + 2 = 680 4 + 2 = 6, has been added to the original question. So, we subtract 6 from the sum obtained to get the final answer. Thus, 1230 – 6 = 1224 is the final answer. Concept 4.2: Estimate the Sum of Two Numbers I Think Neena has ` 450 with her. She wants to buy a toy car for ` 285 and a toy train for ` 150. Do you think she has enough money to buy them? To answer this question, we must learn to estimate the sum of two numbers. 48 L04_V2_PPS_Maths_G1_TB_Addition.indd 48 1/12/2017 10:04:22 PM

4.2 I Recall We have learnt addition of 2-digit and 3-digit numbers. Here is a quick recap of the steps. Step 1: We place the numbers one below the other, according to their places. Step 2: Start adding from the ones place. Step 3: Regroup the necessary sum and carry it forward to the next place. Step 4: Write the answer. 4.2 I Remember and Understand Many a times, knowing the exact number may not be needed. When we say there are about 50 students in class, we mean that the number is close to 50. Numbers which are close to the exact number can be rounded off. Rounding off numbers is also known as estimation. Let us now learn to round off or estimate the given numbers. Rounding to the nearest 10 Observe the number line given. The numbers on it are written in tens. If the digit in the ones place is equal to or greater than 5, we round off the number to the closest multiple of ten 12 is between 10 and 20 and is closer to 10. greater than the given So, we round off 12 down to 10. number. Addition 49 L04_V2_PPS_Maths_G1_TB_Addition.indd 49 1/12/2017 10:04:23 PM

35 is exactly in between 30 and 40. So, we round it off to 40. Let us now learn a step-wise procedure to round off numbers to the nearest 10. Example 9: Round off the following numbers to the nearest 10: a) 86 b) 42 Solution: Let us round off the given numbers using a step-wise procedure. Solved Solve these Steps 86 42 57 25 63 Step 1: Observe the digit in the 86 42 57 25 63 ones place of the number. Step 2: If the digit in the ones place is 6 > 5 2 < 5 ____ > 5 ____ = 5 ____ < 5 4 or less, round the number down to 42 is ____ is the previous ten. 86 is rounded ____ is ____ is rounded If it is 5 or more, rounded down to rounded rounded down to round the number up to 90 40 up to ____ up to ____ ____ up, to the next tens. Rounding off numbers is used to estimate the sum of two 2-digit and 3-digit numbers. Let us understand this through an example: Example 10: Estimate the sum: a) 64 and 15 b) 83 and 18 Solution: a) 64 + 15 Rounding off 64 to the nearest tens gives 60 (as 4 < 5). Rounding off 15 to the nearest tens gives 20 (as 5 = 5). So, the required sum is 60 + 20 = 80. b) 83 + 18 Rounding off 83 to the nearest tens gives 80 (as 3 < 5). Rounding off 18 to the nearest tens gives 20 (as 8 > 5). So, the required sum is 80 + 20 = 100. 50 L04_V2_PPS_Maths_G1_TB_Addition.indd 50 1/12/2017 10:04:23 PM

Example 11: Estimate the sum in the following: a) 245 and 337 b) 483 and 165 Solution: a) 245 + 337 Rounding off 245 to the nearest tens gives 250 (as 5 = 5). Rounding off 337 to the nearest tens gives 340 (as 7 > 5). So, the required sum is 250 + 340 = 590. b) 483 + 165 Rounding off 483 to the nearest tens gives 480 (as 3 < 5). Rounding off 165 to the nearest tens gives 170 (as 5 = 5). So, the required sum is 480 + 170 = 650. Train My Brain Estimate the sum of the following: a) 13 + 12 b) 824 + 295 c) 518 + 181 4.2 I Apply Here are some examples where the estimation of the sum can be used. Train My Brain his class. In Example 12: Arun wants to distribute sweets among two sections of Section A, there are 43 students and in Section B, there are 36 students. Estimate the number of sweets that Arun should take to the class. Solution: Number of students in Section A = 43 Rounding off 43 to the nearest tens, we get 40. Number of students in Section B = 36 Rounding off 36 to the nearest tens, we get 40. Their sum is 40 + 40 = 80. Therefore, Arun should take about 80 sweets to the class. Addition 51 L04_V2_PPS_Maths_G1_TB_Addition.indd 51 1/12/2017 10:04:23 PM

Example 13: Raj buys vegetables for ` 63 and fruits for ` 25. Estimate the amount of money he should give the shopkeeper. Solution: Amount spent on vegetables = ` 63 63 rounded to the nearest tens is 60. Amount spent on fruits = ` 25 25 rounded to the nearest tens is 30. Total amount to be paid = ` 60 + ` 30 = ` 90 Raj should give about ` 90 to the shopkeeper. 4.2 I Explore (H.O.T.S.) Observe some more situations where estimation of sum is used. Example 14: There are 416 walnut trees in a park. The park workers plant 574 more walnut trees. Estimate the number of walnut trees in the park after the workers finish planting. Solution: Number of trees in the park = 416 Rounding off 416 to the nearest tens, we get 420. Number of more trees the park workers plant = 574 Rounding off 574 to the nearest tens, we get 570. Their sum is 420 + 570 = 990. So, about 990 plants will be there after the workers finish planting. Example 15: Ramya has 26 cookies and 34 toffees. Renu has 42 cookies and 13 toffees. Estimate the total number of cookies and toffees. Solution: Number of cookies with Ramya = 26 Number of toffees with her = 34 Rounding off 26 and 34 to the nearest tens, we get 30 and 30 respectively. Number of cookies with Renu = 42 52 L04_V2_PPS_Maths_G1_TB_Addition.indd 52 1/12/2017 10:04:23 PM

Number of toffees with her = 13 Rounding off 42 and 13 to the nearest tens, we get 40 and 10 respectively. So, the sum of cookies = 30 + 40 = 70 Sum of toffees = 30 + 10 = 40 Therefore, altogether they have 70 cookies and 40 toffees. Maths Munchies Estimation is smart guessing. This important skill is used more than actual 2 3 1 calculation in real life. We use it to guess amount of money to carry while going to shop. We also use estimation to purchase material required to build houses. Our parents buy raw food for cooking by using estimation. Concept 4.3: Add 2-digit Numbers Mentally I Think Neena had 18 colour pencils. Her sister gave her 71 more. Neena wanted to know the total number of pencils mentally. Do you know how Neena could find it? To answer this question, we need to learn mental addition of two numbers. 4.3 I Recall We have already learnt to add two 1-digit numbers mentally. To do so, we keep the larger number in mind and add the smaller one to 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 Addition 53 L04_V2_PPS_Maths_G1_TB_Addition.indd 53 1/12/2017 10:04:24 PM

c) 1 + 4 = ________ [ ] (A) 3 (B) 4 (C) 6 (D) 5 d) 5 + 0 = ________ [ ] (A) 4 (B) 5 (C) 0 (D) 6 e) 6 + 3 = ________ [ ] (A) 4 (B) 6 (C) 3 (D) 9 4.3 I Remember and Understand Let us now learn to add two 2-digit numbers mentally, through these examples. 1) Add 2-digit numbers mentally without regrouping Example 16: Add mentally: 53 and 65 Solution: To add the given numbers mentally, follow these steps: Solved Solve this Steps 53 and 65 38 and 41 Step1: Add the digits in the ones place of the two numbers 3 + 5 = 8 ____ + ____ = ___ mentally. Step 2: Add the digits in the The digits in the tens The digits in the tens tens place of the two numbers place of the two place of the two mentally. numbers are 5 and 6. numbers are ___ and Keep 6 in your mind, count 5 forward as 7, ____. Keep ____ in your 8, 9, 10 and 11. mind, count ___ forward 5 + 6 = 11 as ____, ____and ____. ____ + ____ = ___ Step 3: Write sum of digits obtained So, 53 + 65 = 118. So, 38 + 41 = ___. in step 1 and sum of digits obtained in step 2 together. This is the sum of the given numbers. 54 L04_V2_PPS_Maths_G1_TB_Addition.indd 54 1/12/2017 10:04:24 PM

2) Add 2-digit numbers mentally with regrouping Example 17: Add mentally: 29 and 56 To mentally add two 1-digit Solution: To add the given numbers mentally numbers, keep the larger follow these steps. number in mind and the smaller on the fingers. Solved Solve this Steps 29 and 56 83 and 47 Step1: Split the two given 29 = 20 + 9 83 = ___ + ____ numbers as tens and ones 56 = 50 + 6 47 = ___ + ____ mentally. Step 2: Add the ones 9 + 6 = 15 ____ + ____ = ____ of the two numbers mentally. Step 3: Add the tens 20 + 50 = 70 ____ + ____ = ____ of the two numbers mentally. Step 4: Add the sums from 70 + 15 ____ + ___ = ____ steps 2 and 3 mentally = 70 + 10 + 5 (regroup if needed). = 85 Step 5: Write the sum of So, 29 + 56 = 85. So, 83 + 47 = ___. the given numbers. 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. Addition 55 L04_V2_PPS_Maths_G1_TB_Addition.indd 55 1/12/2017 10:04:24 PM

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. = 40 + 20 + 18 = 60 + 10 + 8 (Regroup and add) = 70 + 8 = 78 56 L04_V2_PPS_Maths_G1_TB_Addition.indd 56 1/12/2017 10:04:24 PM

4.3 I Explore (H.O.T.S.) We have seen mental addition of two 2-digit numbers. Let us now see some 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. Solved Solve this Steps 25, 37 and 19 40, 29 and 54 Step 1: Split the three given numbers 25 = 20 + 5 40 = ___ + ____ as tens and ones mentally. 37 = 30 + 7 29 = ___ + ____ 19 = 10 + 9 54 = ____+____ Step 2: Add the tens of the given 20 + 30 + 10 = 60 ____ + ____+ ____ numbers mentally. = ____ Step 3: Add the ones of the given 5 + 7 + 9 = 21 ____+___ + ____ = numbers mentally. ____ Step 4: Add the sums from steps 2 and 60 + 21 ____ + ___ = ____ 3 mentally, regroup again if needed. = 60 + 20 + 1 = 81 Step 5: Write the sum of the given So, 25 + 37 + 19 = 81. So, 40 + 29 + 54 = ___. numbers. Maths Munchies To estimate the sum of 2-digit numbers mentally: 2 3 1 Step 1: Add the tens place of the numbers. Step 2: Count the total digits in the ones place, which are 5 or more than 5. Step 3: Add the count to the tens place. Place ‘0‘ in the units place. Addition 57 L04_V2_PPS_Maths_G1_TB_Addition.indd 57 1/12/2017 10:04:24 PM

Connect the Dots Social Studies Fun Early humans had the basic idea of addition. Ancient Indians contributed to the concept of addition by inventing the number Zero. 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. A Note to Parent The concept of mental addition is one that we widely use 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. 58 L04_V2_PPS_Maths_G1_TB_Addition.indd 58 1/12/2017 10:04:33 PM

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) Shyam has 269 pens and Ritesh has 832 pens. How many pens do the boys have altogether? b) Ravi’s garden has 673 rose flowers and Rahul’s garden has 978 rose flowers. How many flowers are there in the two gardens? 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) Sonu has 46 red roses, Mona has 22 yellow roses. Estimate the total number of roses. b) Rakesh has 67 pencils and Mukesh has 43 pencils. Estimate the number of pencils both of them have in all. 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 57 b) 75 and 56 c) 82 and 19 d) 27 and 35 e) 17 and 37 Addition 59 L04_V2_PPS_Maths_G1_TB_Addition.indd 59 1/12/2017 10:04:34 PM

S Subtractionubtraction I Will Learn Concepts 5.1: Subtract 3-digit and 4-digit Numbers 5.2: Estimate the Difference between Two Numbers 5.2: Subtract 2-digit Numbers Mentally L05_V2_PPS_Maths_G3_TB.indd 60 1/12/2017 10:09:44 PM

Concept 5.1: Subtract 3-digit and 4-digit Numbers I Think Given below is the number of men and women in Neena’s town in the years 2013 and 2014. Years 2013 2014 Men 2020 2107 Women 1704 1882 How many more men than women lived in Neena's town in the years 2013 and 2014? To answer this question, we must learn subtraction of 4-digit numbers. 5.1 I Recall Recall that we can subtract numbers by writing one below the other. 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 = _________ d) 18 – 5 = _________ e) 47 – 1 = _________ f) 50 – 45 = _________ 5.1 I Remember and Understand We have learnt how to subtract two 3-digit numbers without regrouping. Let us now learn how to subtract them with regrouping. While subtracting, start from the ones place. Subtraction 61 L05_V2_PPS_Maths_G3_TB.indd 61 1/12/2017 10:09:46 PM

1) 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 through an example. Example 1: Subtract: 427 from 586 Solution: To subtract, write the smaller number below the larger number. Solved Step 1: Subtract the ones. But, 6 – 7 is not Step 2: Subtract the Step 3: Subtract possible as 6 < 7. So, regroup the digits in tens. the hundreds. the tens place. 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 T O H T O H T O 7 16 7 16 7 16 5 8 \ 6 \ 5 8 \ 6 \ 5 8 \ 6 \ – 4 2 7 – 4 2 7 – 4 2 7 9 5 9 1 5 9 Solve these H T O H T O H T O 6 2 3 5 5 2 4 5 3 – 3 7 6 – 2 6 3 – 2 6 4 2) 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. 62 L05_V2_PPS_Maths_G3_TB.indd 62 1/12/2017 10:09:47 PM

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 7 6 8 9 7 6 8 9 − 5 0 3 2 − 5 0 3 2 7 5 7 Step 3: Subtract the hundreds. Step 4: Subtract the thousands. Th H T O Th H T O 7 6 8 9 7 6 8 9 − 5 0 3 2 − 5 0 3 2 6 5 7 2 6 5 7 Solve these Th H T O Th H T O Th H T O 2 8 7 9 4 7 8 9 8 0 0 0 – 2 1 3 7 – 2 4 7 5 – 2 0 0 0 3) 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: Subtract: 4868 from 7437 Solution: Write the smaller number below the larger number. Subtraction 63 L05_V2_PPS_Maths_G3_TB.indd 63 1/12/2017 10:09:47 PM

Steps Solved Solve these Step 1: Subtract the ones. Th H T O Th H T O But, 7 − 8 is not possible as 7 < 8. So, regroup the tens digit, 2 17 3. 3 tens = 2 tens + 1 ten. Borrow 7 4 3 \ 7 \ 1 6 5 4 1 ten to the ones place. − 4 8 6 8 − 1 2 4 6 9 Step 2: Subtract the tens. But, Th H T O Th H T O 2 − 6 is not possible as 2 < 6. 12 So, regroup the hundreds digit, 4. 4 hundreds = 3 hundreds + 1 3 2 \ 17 5 6 7 4 hundred. Borrow 1 hundred to 7 4 \ 3 \ 7 \ − 2 3 8 2 the tens place. − 4 8 6 8 6 9 Step 3: Subtract the hundreds. Th H T O Th H T O But, 3 − 8 is not possible. So, 13 12 regroup the thousands digit, 7. 6 3 \ 2 \ 17 7 4 6 8 7 thousands = 6 thousands + 1 7 \ 4 \ 3 \ 7 \ − 4 8 3 7 thousand. Borrow 1 thousand to − 4 8 6 8 the hundreds place. 5 6 9 Step 4: Subtract the thousands. Th H T O Th H T O 13 12 6 3 \ 2 \ 17 9 2 7 6 7 \ 4 \ 3 \ 7 \ − 5 1 4 7 − 4 8 6 8 2 5 6 9 Train My Brain Solve the following: a) 719 – 320 b) 813 – 621 c) 3678 – 2466 64 L05_V2_PPS_Maths_G3_TB.indd 64 1/12/2017 10:09:47 PM

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 T O Number of marbles given to Sonu’s brother = 135 3 7 5 − 1 3 5 Number of marbles left with him = 375 – 135 = 240 2 4 0 Therefore, 240 marbles are left with Sonu. 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? Solution: Total number of stamps Vinod had = 536 H T O 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 = − 2 7 8 536 – 278 = 258 2 5 8 We can use subtraction of 4-digit numbers in real-life situations. Let us see some examples. Example 6: 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 6 4 3 6 Length of the piece cut = 3235 cm − 3 2 3 5 The length of the remaining piece of rope = 3 2 0 1 6436 cm – 3235 cm = 3201 cm Example 7: Mohan’s uncle stays 8630 m away from Mohan’s house. Mohan travelled 6212 m of the distance. What is the distance yet to be covered by Mohan to reach his uncle’s house? Subtraction 65 L05_V2_PPS_Maths_G3_TB.indd 65 1/12/2017 10:09:48 PM

Solution: Distance between Mohan’s house and his uncle’s house = 8630 m Distance travelled by Mohan = 6212 m Th H T O Remaining distance Mohan has to travel 2 10 8 6 3 ⁄ 0 ⁄ = 8630 m – 6212 m = 2418 m − 6 2 1 2 Therefore, Mohan has to travel 2418 m more to 2 4 1 8 reach his uncle’s house. 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. T O Solution: a) 36 – 27 2 16 3 \ 6 \ We can write 36 = 27 + 9 − 2 7 b) 364 – 145 9 364 – 145 = 219 H T O We can write 364 = 145 + 219 5 14 3 6 \ 4 \ − 1 4 5 2 1 9 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. 66 L05_V2_PPS_Maths_G3_TB.indd 66 1/12/2017 10:09:48 PM

a) Of the 37 students in class, 14 are girls. How many are boys? b) 37 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 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? Maths Munchies How can we subtract faster? 2 3 1 Let us look at the subtraction 62 – 36. Step 1: Split the values 62 and 36 as follows: 6 / 2 3 / 6 Step 2: Now, do simple subtraction as follows: 2 – 6 = – 4 and 6 – 3 = 3 Step 3: As we get negative result, we need to add 10 to the second digit and subtract 1 from the first digit obtained after subtraction. 3 and (–4) can be solved as 3 – 1 and 10 – 4 This gives us 2 and 6. Step 4: The answer obtained is 26. Therefore, 62 – 36 = 26. Subtraction 67 L05_V2_PPS_Maths_G3_TB.indd 67 1/12/2017 10:09:48 PM

Concept 5.2: Estimate the Difference between Two Numbers I Think Neena 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 Neena after buying them? To answer this question, we must learn to estimate the difference between two numbers. 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 Rounding off 69 to the nearest tens gives 70 (as 9 > 5) and rounding off 15 to the nearest tens, gives 20 (as 5 = 5). Estimation is finding a So, the required difference is 70 – 20 = 50. number that is close enough to the right answer. 68 L05_V2_PPS_Maths_G3_TB.indd 68 1/12/2017 10:09:49 PM

b) 86 – 12 Rounding 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 Rounding 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 Rounding 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 n 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). Number of pencils given to Parul’s sister = 32 32 rounded off to the nearest 10 is 30 (since 2 < 5). Subtraction 69 L05_V2_PPS_Maths_G3_TB.indd 69 1/12/2017 10:09:49 PM

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 school 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 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. 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 primary section, 416 are from the middle section, and the rest are from high school. How many high school students are there in the school? Solution: Total number of students = 976 H T O Number of students from the primary section = 325 1 Number of students from the middle section = 416 3 2 5 + 4 1 6 Total number of students in primary and middle school 7 4 1 sections = 325 + 416 = 741 Number of students in high school = Total number of H T O students – Number of students in primary and middle 9 7 6 school sections = 976 – 741 = 235 − 7 4 1 2 3 5 Therefore, the number of high school students is 235. 70 L05_V2_PPS_Maths_G3_TB.indd 70 1/12/2017 10:09:49 PM

Maths Munchies Sometimes, we can avoid regrouping in subtraction. 2 3 1 Let us look at 44 − 36. Step 1: Add '4' to both the numbers. So, 44 becomes 48 and 36 becomes 40. Step 2: Now, subtract 40 from 48. 48 − 40 = 8 Step 3: Thus, 44 − 36 = 8. Concept 5.3: Subtract 2-digit Numbers Mentally I Think Neena had 19 pens. She gave 12 pens to her sister. Can you find the number of pens remaining with Neena without using a paper and a pencil? To subtract two numbers mentally, we need to learn mental subtraction of two numbers. 5.3 I Recall Recall that to subtract two 1-digit numbers mentally, we keep the larger number in our 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 Subtraction 71 L05_V2_PPS_Maths_G3_TB.indd 71 1/12/2017 10:09:50 PM

d) 5 – 0 = ________ [ ] (A) 4 (B) 5 (C) 0 (D) 6 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. Subtracting 2-digit numbers mentally is similar to that. Let us understand this through an example. 1) Subtract 2-digit numbers mentally without regrouping Example 15: Subtract mentally: 52 from 76 Solution: Follow these steps to subtract mentally. Solved Solve this Steps 52 from 76 35 from 69 Step1: Subtract mentally the digits in the ones place 6 – 2 = 4 ______ – ______ = of the two numbers. Step 2: Subtract mentally The digits in the tens place The digits in the tens place of the digits in the tens place of the two numbers are 7 the two numbers are _______ of the two numbers. and 5. and _______. So, imagine that 7 fingers So, imagine that _____ fingers are open. Then imagine are open. closing 5 of them. Then imagine closing of 7 – 5 = 2 them. ____– ____ = ___ Step 3: Write the difference So, 76 – 52 = 24. So, 69 – 35 = ____. 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. 72 L05_V2_PPS_Maths_G3_TB.indd 72 1/12/2017 10:09:50 PM

2) Subtract 2-digit numbers mentally with regrouping Example 16: Subtract mentally: 29 from 56 Solution: Follow these steps to subtract mentally. Solved Solve this Steps 29 from 56 46 from 83 Step1: Split the two given 29 = 20 + 9 83 = ___ + ____ numbers as tens and ones. 56 = 50 + 6 46 = ___ + ____ Step2: 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. regroup the tens. Add 10 ones to 6 to get 16 If it 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. Step 3: Subtract the ones of 16 – 9 = 7 ____ – ____ = ____ the two numbers mentally. Step 4: Subtract the tens of 4 tens – 2 tens = 2 tens ____ – ____ = ____ the two numbers mentally. Step 5: Write the answers So, 56 – 29 = 27. ____ – ___ = ____ 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 some examples. Subtraction 73 L05_V2_PPS_Maths_G3_TB.indd 73 1/12/2017 10:09:50 PM

Example 17: Manoj has 64 notebooks. He has used 45 notebooks. How many notebooks are left with him? Solve mentally. Solution: Number of notebooks Manoj has = 64 Number of notebooks he has used = 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. 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 some real-life examples 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. 74 L05_V2_PPS_Maths_G3_TB.indd 74 1/12/2017 10:09:50 PM

Maths Munchies We can subtract 2 numbers easily by splitting the smaller number. 2 3 1 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 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! 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 everyday or even taking their help in making basic calculations for shopping or monthly expenses. There are many applications such as www.innovatemyschool.com that you could use for the same. Subtraction 75 L05_V2_PPS_Maths_G3_TB.indd 75 1/12/2017 10:09:55 PM

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 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 3 groups. 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 there in the class, who are in the blue group? b) Sneha has 77 balloons. She gives 42 balloons to her sister. About how many balloons remain with Sneha? 76 L05_V2_PPS_Maths_G3_TB.indd 76 1/12/2017 10:09:55 PM

Drill Time 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 9) Word problems a) Ram has 48 pencils. He has used 29 pencils. How many pencils are left with him? Solve mentally. b) Sejal travelled for 23 km on Day 1 and 76 km on Day 2. How much more distance (in km) did Sejal travel on Day 2 than on Day 1? Solve mentally. Subtraction 77 L05_V2_PPS_Maths_G3_TB.indd 77 1/12/2017 10:09:56 PM

M Multiplicationultiplication I Will Learn Concepts 6.1: Multiply 2-digit Numbers 6.2: Multiply 3-digit Numbers by 1-digit and 2-digit Numbers 6.3: Double 2-digit and 3-digit Numbers Mentally L06_V2_PPS_Math_G3_TB_07112016_V0.indd 78 1/12/2017 10:16:43 PM

Concept 6.1: Multiply 2-digit Numbers I Think Neena goes on a holiday to her hometown for 3 weeks. How many days would she spend in her hometown? To answer this question, we must learn the multiplication tables. 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. Let us recall the multiplication tables of numbers 1 to 6. Table of 1 Table of 2 Table of 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 Multiplication 79 L06_V2_PPS_Math_G3_TB_07112016_V0.indd 79 1/12/2017 10:16:52 PM

Table of 4 Table of 5 Table of 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. 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 multiplicand. • The number written to the right of the ‘×’ sign is called multiplier. • The number written to the right of the ‘=’ sign is called product. Multiplication Fact 5 × 6 = 30 ↓ ↓ ↓ Multiplicand Multiplier Product Note: (a) Representing the multiplicand, multiplier and product using the symbols ‘×’ and ‘=’ is called a multiplication fact. 80 L06_V2_PPS_Math_G3_TB_07112016_V0.indd 80 1/12/2017 10:16:52 PM

(b) The multiplicand and the multiplier are also called the factors of the product. For example, 2 × 7 = 14 = 7 × 2; 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. Table of 7 Table of 8 7 × 1 = 7 seven ones are seven 8 × 1 = 8 eight ones are eight 7 × 2 = 14 seven twos are fourteen 8 × 2 = 16 eight twos are sixteen 7 × 3 = 21 seven threes are twenty- 8 × 3 = 24 eight threes are twenty- one four 7 × 4 = 28 seven fours are twenty- 8 × 4 = 32 eight fours are thirty-two eight 7 × 5 = 35 seven fives are thirty-five 8 × 5 = 40 eight fives are forty 7 × 6 = 42 seven sixes are forty-two 8 × 6 = 48 eight sixes are forty-eight 7 × 7 = 49 seven sevens are forty-nine 8 × 7 = 56 eight sevens are fifty-six 7 × 8 = 56 seven eights are fifty-six 8 × 8 = 64 eight eights are sixty-four 7 × 9 = 63 seven nines are sixty-three 8 × 9 = 72 eight nines are seventy- two 7 × 10 = 70 seven tens are seventy 8 × 10 = 80 eight tens are eighty Table of 9 9 × 1 = 9 nine ones are nine 9 × 2 = 18 nine twos are eighteen 9 × 3 = 27 nine threes are twenty-seven Order Property: Changing 9 × 4 = 36 nine fours are thirty-six the order in which numbers 9 × 5 = 45 nine fives are forty-five are multiplied does not change the product. This 9 × 6 = 54 nine sixes are fifty-four is called order property of 9 × 7 = 63 nine seven are sixty-three multiplication. 9 × 8 = 72 nine eights are seventy-two 9 × 9 = 81 nine nines are eighty-one 9 × 10 = 90 nine tens are ninety Multiplication 81 L06_V2_PPS_Math_G3_TB_07112016_V0.indd 81 1/12/2017 10:16:52 PM

Multiplying 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. Steps Solved Solve these Step 1: Multiply the ones. 3 × 7 = 21 H T O Step 2: Regroup the 21 ones = 2 tens and product. 1 ones 1 7 × 9 Step 3: Write the ones T O H T O digit of the product in the product and carry the tens 2 digit to the tens place. 2 3 1 5 × 7 × 4 1 Step 4: Multiply tens. 2 × 7 = 14 Step 5: Add the carry from 14 + 2 = 16 step 3 to the product. H T O Step 6: Write the sum in the H T O tens place. 2 2 3 2 3 × 8 × 7 1 6 1 Train My Brain What is the product in each of the following? a) 17 × 7 b) 28 × 9 c) 19 × 8 82 L06_V2_PPS_Math_G3_TB_07112016_V0.indd 82 1/12/2017 10:16:53 PM

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 T O Number of classes in the school = 8 3 5 4 Number of students in the school = 54 × 8 × 8 Therefore, the total number of students in the school = 432 4 3 2 Example 3: Manoj travelled 7 km in a day. If he travels the same distance every day, what distance does he travel in 25 days? H T O Solution: The distance that Manoj travelled in a day = 7 km 3 He travels the same distance every day. The distance he 2 5 travels in 25 days = 25 × 7 × 7 1 7 5 Therefore, Manoj travels 175 km in 25 days. 6.1 I Explore (H.O.T.S.) Framing word problems: Using multiplication tables, we can frame word problems from the given clues. Let us now try to frame a few 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. Multiplication 83 L06_V2_PPS_Math_G3_TB_07112016_V0.indd 83 1/12/2017 10:16:55 PM

Example 5: Number of students in a row = 8 Number of rows = 2 Total rows = 16 Solution: Word problem: There are 2 rows with 8 students in each row. What is the total number of students? Maths Munchies Multiplication by Splitting 5 × (5+3) Multiplication can be made simple by splitting the larger number into two numbers. Consider 5 × 8. Split the larger number 8 and write it as a sum of two + 1 numbers. 2 3 8 = 5 + 3. Thus, 5 × 8 = 5 (5 + 3). Now multiply each of these numbers by the multiplier and add the products. 5 × (5 + 3) = 5 × 5 + 5 × 3 = 25 + 15 = 40 Recall that 5 × 8 = 40. (From multiplication tables of 5 or 8) As the two parts of the larger number are distributed to the multiplier, we call this as the distributive property of multiplication over addition. Concept 6.2: Multiply 3-digit Numbers by 1-digit and 2-digit Numbers I Think Neena collected some shells and put them into 9 bags. If each bag has 110 shells, how many shells did she collect? To answer this question, we must learn multiplication of 3-digit numbers. 84 L06_V2_PPS_Math_G3_TB_07112016_V0.indd 84 1/12/2017 10:16:56 PM

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. Let us answer these to revise the concept. a) 22 × 2 = _________ b) 42 × 1 = _________ c) 33 × 4 = _________ d) 11 × 7 = _________ e) 45 × 3 = _________ e) 50 × 2 = _________ Similarly, we can multiply a 3-digit number by a 1-digit number. 6.2 I Remember and Understand We multiply 3-digit numbers just as we multiply 2-digit numbers. 1) Multiplying 3-digit numbers by 1-digit numbers While multiplying, (without regrouping) always start multiplying Let us understand the step-by-step procedure the ones of the through a few examples. multiplicand by the Example 6: Multiply: 401 × 3 ones of the multiplier. Solution: Follow these steps to multiply the given numbers. Solved Step 1: Multiply the Step 2: Multiply the Step 3: Multiply the hundreds ones and write the tens and write the and write the product under product under ones. product under tens. hundreds. H T O H T O Th H T O 4 0 1 4 0 1 4 0 1 × 3 × 3 × 3 3 0 3 1 2 0 3 Multiplication 85 L06_V2_PPS_Math_G3_TB_07112016_V0.indd 85 1/12/2017 10:16:57 PM

Solve these H T O H T O H T O 2 2 0 1 3 0 2 3 2 × 4 × 2 × 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 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 the following examples. Example 7: Multiply: 513 × 5 Solution: Follow these steps to multiply the given numbers. Steps Solved Solve these Step 1: Multiply the ones and write the H T O product under ones. Regroup if the H T O product has two or more digits. 1 5 1 3 6 3 5 × 5 × 7 5 Step 2: Multiply the tens. Add the carry H T O H T O over (if any) to the product. Write the sum under tens. 1 Regroup if the product has two or more 5 1 3 4 4 4 digits. × 5 × 8 6 5 Step 3: Multiply the hundreds. Add the Th H T O H T O carry over (if any) to the product and write the sum under hundreds. Regroup if 1 the product has two or more digits. 5 1 3 3 4 2 × 5 × 5 2 5 6 5 86 L06_V2_PPS_Math_G3_TB_07112016_V0.indd 86 1/12/2017 10:16:57 PM

3) 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. Steps Solved Solve these Step 1: Arrange the numbers in H T O columns, as shown. 2 4 3 × 3 4 H T O Step 2: Multiply the ones by the ones H T O digit of the multiplier. 3 × 4 = 12. Write 2 in the ones place of the product. 1 1 4 1 Write 1 in the tens place as carry over. 2 4 3 × 2 2 × 3 4 2 Step 3: Multiply the tens digit by the H T O ones digit of the multiplier. 4 × 4 = 16. Add the carry over from the previous 1 1 step. So, 16 + 1 = 17. Write 7 in the tens 2 4 3 place of the product and 1 in the × 3 4 hundreds place as carry over. 7 2 Train My Brain T O H Step 4: Multiply the hundreds by the H T O ones digit of the multiplier. 2 × 4 = 8. Add the carry over from the previous 1 1 step. So, 8 + 1 = 9. Write 9 in the hundreds 2 4 3 4 5 3 place of the product. × 3 4 × 1 3 9 7 2 Step 5: Write 0 in the ones place before H T O multiplying ones by the tens digit of the multiplier. 1 1 Multiply the ones by the tens digit of 2 4 3 the multiplier. Write the product under × 3 4 7 2 9 tens place. 9 0 3 × 3 = 9 Multiplication 87 L06_V2_PPS_Math_G3_TB_07112016_V0.indd 87 1/12/2017 10:16:57 PM

Steps Solved Solve these Step 6: Multiply the tens by the tens H T O digit of the multiplier. 4 × 3 = 12 1 H T O Write 2 in hundreds place of the 1 1 product and 1 in hundreds place of 2 4 3 the multiplicand as carry over. × 3 4 9 7 2 2 6 3 2 9 0 × 2 3 Step 7: Multiply the hundreds by the Th H T O tens digit of the multiplier. 2 × 3 = 6 1 Add the carry over from the previous 1 1 step. So, 6 + 1 = 7. Write 7 in the thousands place of the multiplicand. 2 4 3 × 3 4 9 7 2 H T O 7 2 9 0 Step 8: Add the products and write the Th H T O sum. The sum is the required product. 3 5 2 1 × 2 3 1 1 2 4 3 × 3 4 9 7 2 7 2 9 0 8 2 6 2 Train My Brain Find the following product: a) 341 × 2 b) 156 × 4 c) 222 × 23 88 L06_V2_PPS_Math_G3_TB_07112016_V0.indd 88 1/12/2017 10:16:58 PM

6.2 I Apply Let us now see some real-life word problems. Example 9: Rohan ran 315 m every day for a week. How many metres did he run in that week? Solution: 1 week = 7 days Th H T O Distance run by Rohan in a day = 315 m 1 3 Distance he ran in a week = 315 m × 7 3 1 5 × 7 Therefore, the total distance run by him in 1 week = 2 2 0 5 2205 m Example 10: Payal saves ` 175 per month for a year. How much money will she have at the end of the year? Th H T O Solution: Amount saved by Payal per month = ` 175 1 1 Number of months in a year = 12 1 7 5 × 1 2 Total money saved in a year = 175 × 12 1 1 Therefore, total money Payal has at the end of a year 3 5 0 = ` 2100 1 7 5 0 2 1 0 0 6.2 I Explore (H.O.T.S.) Sometimes, we can find numbers that satisfy two or more conditions. Let us now see some 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. Multiplication 89 L06_V2_PPS_Math_G3_TB_07112016_V0.indd 89 1/12/2017 10:16:58 PM

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 × 9 and 36 = 6 × 6. Of 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. Maths Munchies Multiplying by 10 and 100 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. 1 2 3 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 90 L06_V2_PPS_Math_G3_TB_07112016_V0.indd 90 1/12/2017 10:16:59 PM

Concept 6.3: Double 2-digit and 3-digit Numbers Mentally I Think Neena has 23 red beads. Her friend has double the number of beads. Neena wants to know the number of beads her friend has. Do you know how to find that mentally? To answer this, we need to learn to double numbers 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. Calculating mentally makes problem solving faster and easier. For example, 5 × 2 = 10, 3 × 2 = 6, 10 × 2 = 20 and so on. 6.3 I Remember and Understand Let us now understand how to double a 2-digit number mentally through a few examples. Example 13: Double the given number: 53 Solution: To double the given number, follow these Doubling a number steps: means multiplying by 2. Multiplication 91 L06_V2_PPS_Math_G3_TB_07112016_V0.indd 91 1/12/2017 10:16:59 PM

Solved Solve this Steps 53 41 Step 1: Multiply the tens digit The tens digit is 5. The tens digit is ____. by 2. So, 5 × 2 = 10. So, ___ × 2 = ___. Step 2: If the ones digit is less The ones digit is 3. The ones digit is ___ than or equal to 4, write the 3 < 4 (True) ___ < ___ (True/ False) product in step 1 as it is. If not, add 1 to it and write. Step 3: Multiply the ones digit 3 × 2 = 6 ___ × 2 = ___ by 2. Step 4: Write the products in 53 × 2 = 106 ___ × 2 = ___ steps 1 and 3 together. This gives double of the given number. 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 some examples where we apply this concept. Example 14: Rohit has 14 shirts. His brother has double the number of shirts. How many shirts does Rohit’s brother have? Solution: Number of shirts Rohit has = 14 Number of shirts Rohit’s brother has = Double of that Rohit has = 14 × 2 = 28 Therefore, Rohit’s brother has 28 shirts. 92 L06_V2_PPS_Math_G3_TB_07112016_V0.indd 92 1/12/2017 10:16:59 PM

Example 15: Sony is 36 years old. Her aunt’s age is double that of Sony’s age. 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: Steps Solved Solve this 125 293 Step 1: Multiply the number The number formed The number formed formed by the two leftmost digits by the two leftmost by the two leftmost by 2. digits is 12. 12 × 2 = 24. digits is ____. So, ___ × 2 = ___. Step 2: If the ones digit of the The ones digit is 5. The ones digit is __ given number is less than or equal 5 < 4 (False) ___ < ___ (True/ False) to 4. If it is true, write the product 24 + 1 = 25 in step 1 as it is. If not, add 1 to it and write. Step 3: Multiply the ones digit by 5 × 2 = 10 ___ × 2 = ___. 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. Multiplication 93 L06_V2_PPS_Math_G3_TB_07112016_V0.indd 93 1/12/2017 10:17:00 PM

Maths Munchies Multiplying 3-digit Numbers by 11 Multiply 623 by 11. Step 1: Write down the number 623 and put a before 6 and another after * * 3. Here, the represents ‘0’ So, the number becomes 623 . * * * Step 2: Starting from the rightmost place, keep adding two digits, that is, 0 + 3 = 3 3 + 2 = 5 1 2 + 6 = 8 2 3 6 + 0 = 6 Step 3: Writing the digits from bottom to top, we get the answer. Therefore, 623 × 11 = 6853. Connect the Dots Social Studies Fun Four is considered the holiest number in Islam. For this reason, 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. 94 L06_V2_PPS_Math_G3_TB_07112016_V0.indd 94 1/12/2017 10:17:01 PM