Connect the Dots Science 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. A Note to Parent We widely use the concept of mental addition in day-to-day life especially to calculate amounts of money. Encourage your child to practise the concept by taking their help in calculating bills, tendering change, buying groceries and so on. Addition 45 Ascend_G3_Maths_Book_TB_Part1.indb 45 8/3/2023 11:37:34 AM
5 Subtraction I Will Learn estimating the difference between two numbers About rounding off numbers subtracting 3-digit numbers with regrouping subtracting 4-digit numbers with and without regrouping subtracting two numbers mentally 5.1: Estimate the Difference between Two Numbers Now that you’ve learned how to round off numbers and estimate the sum of two numbers, you can apply the same rules to estimate the difference between two numbers. But first, can you quickly explain to your partner what estimating and rounding off are? (If you want to revise, look at Concept 4.1.) How do we estimate the difference between two numbers? Just like estimating the sum of two 2-digit numbers, you first round off both numbers to the nearest tens and then subtract the smaller number from the bigger one. 46 8/3/2023 11:37:36 AM Ascend_G3_Maths_Book_TB_Part1.indb 46
Let’s say you need to estimate the difference between 86 and 12, these are the steps: 1) You round off 86 to the nearest tens which gives you 90 and round off 12 to the nearest tens which gives you 10. 2) Then you subtract them to get the estimated difference: 90 – 10 = 80. Imagine that your mother gave you 94 sweets on your birthday. What will you round off 94 to? Now imagine that you have to distribute 46 sweets among your friends. What will you round off 46 to? After distributing the sweets, how many are remaining with you? What is the estimated difference of 94 and 46? C an you think of a similar problem using 3-digit or 4-digit numbers and estimate the difference between the numbers with your partner? Work on it and share it with the class. Hints: To estimate the difference between two 3-digit numbers, we round off the numbers to the nearest 100. To estimate the difference between two 4-digit numbers, we round off the numbers to the nearest 1000. Represent the numbers on a number line to round off correctly. Round off 256 to the nearest 100s. 100 150 200 250 300 350 400 256 Far Near 256 is nearer to 300 than 200. So, it is rounded up to 300. Reflection Time! 1) Why do you think a number line helps in understanding the rounding off concept easily? 2) When you are travelling long distances by road or on a train, estimate the distance and the time taken to reach different milestones and note them in your book. 3) Think of any two situations where you can use your estimation skills. Subtraction Round off 4358 to the nearest 1000s. 47 Ascend_G3_Maths_Book_TB_Part1.indb 47 8/3/2023 11:37:37 AM
Drill Time 5.1: Estimate the Difference between Two Numbers 1) Estimate these differences: a) 65 – 15 b) 48 – 16 c) 67 – 32 d) 896 – 432 e) 679 – 387 f) 795 – 564 2) 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. About 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? c) Ajit bought 38 new books from a book fair. Now he has 74 books. About how many books did he have before he bought the new books? 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. 48 Subtraction Ascend_G3_Maths_Book_TB_Part1.indb 48 8/3/2023 11:37:37 AM
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 1: Subtract 427 from 586. Solution: To subtract, write the smaller number below the larger number. Step 1: Subtract the ones. But, 6 – 7 is Solved Step 3: Subtract the not possible as 6 < 7. So, regroup the hundreds. digits in the tens place. Step 2: Subtract the tens. 8 tens = 7 tens + 1 tens. Borrow 1 ten to the ones place. Reduce the tens by 1 ten. Now subtract 7 ones from 16 ones. H TO H TO H TO 7 16 7 16 7 16 5 5 –4 8\\ 6\\ 5 \\8 \\6 –4 \\8 \\6 27 –4 2 7 1 27 9 59 59 H TO Solve these H TO H TO 6 23 5 52 4 53 – 3 76 – 2 63 – 2 64 Subtraction 49 Ascend_G3_Maths_Book_TB_Part1.indb 49 8/3/2023 11:37:38 AM
Subtract 4-digit numbers without regrouping Subtracting a 4-digit number from a larger 4-digit number is similar to subtracting a 3-digit number from a larger 3-digit number. The following examples help you understand this better. Example 2: Subtract: 5032 from 7689 Solution: To subtract, write the smaller number below the larger number. Solved Step 1: Subtract the ones. Step 2: Subtract the tens. Th H T O Th H T O 768 9 76 8 9 −503 2 −50 3 2 7 5 7 Step 3: Subtract the hundreds. Step 4: Subtract the thousands. Th H T O Th H T O 7689 7 68 9 −5032 − 5 03 2 2 65 7 657 Th H T O Solve these Th H T O 2879 8000 –2137 Th H T O –2000 4789 –2475 Subtract 4-digit numbers with regrouping In subtraction of 4-digit numbers, we can regroup the digits in the thousands, hundreds and tens places. Let us see an example. Example 3: What is the difference between 7437 and 4868? Solution: Write the smaller number below the larger number. 50 Subtraction Ascend_G3_Maths_Book_TB_Part1.indb 50 8/3/2023 11:37:38 AM
Steps Solved Solve these Step 1: Subtract the ones. Th H T O Th H T O But, 7 − 8 is not possible as 1654 7 4 2 17 −1 2 4 6 7 < 8. So, regroup the tens digit, −4 8 3. 3 tens = 2 tens + 1 ten. Borrow 3\\ \\7 Th H T O 1 ten to the ones place. 6 8 9 5674 −2 3 8 2 Step 2: Subtract the tens. But, Th H TO 12 Th H T O 2 − 6 is not possible as 2 < 6. 7 So, regroup the hundreds digit, −4 3 \\2 17 7468 4. 4 hundreds = 3 hundreds + 4\\ 3\\ \\7 −4 8 3 7 1 hundred. Borrow 1 hundred to 868 the tens place. 69 Step 3: Subtract the hundreds. Th H T O But, 3 − 8 is not possible. So, 13 12 regroup the thousands digit, 7. 7 thousands = 6 thousands + 6 \\3 \\2 17 1 thousand. Borrow 1 thousand to the hundreds place. \\7 4\\ 3\\ \\7 −4 8 6 8 569 Step 4: Subtract the thousands. Th H T O 13 12 6 \\3 \\2 17 \\7 4\\ 3\\ \\7 −4 8 6 8 2569 Train My Brain Solve the following: a) 719 – 320 b) 813 – 621 c) 3678 – 2466 Subtraction 51 Ascend_G3_Maths_Book_TB_Part1.indb 51 8/3/2023 11:37:38 AM
5.2 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. Solution: How many marbles are left with him? H T O Total number of marbles Sonu bought = 375 3 7 5 Number of marbles given to Sonu’s brother = 135 −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 was left with 278 stamps. How many stamps did Vinod give to his brother? Solution: Total number of stamps Vinod had = 536 H TO 12 Number of stamps Vinod had after giving some to his brother = 278 4 2\\ 16 \\5 \\3 \\6 Number of stamps he gave to his brother = −278 536 – 278 = 258 258 Therefore, Vinod gave 258 stamps to his brother. We can use subtraction of 4-digit numbers in real-life situations. Let us see some examples. Example 6: Mohan’s uncle stays 8630 m away from Mohan’s house. Mohan travels Solution: 6212 m of the distance. What is the distance yet to Th H TO be covered by Mohan to reach his uncle’s house? 8 6 23⁄ 10⁄0 Distance between Mohan’s house and his uncle’s −6 house = 8630 m 2 12 2 4 18 Distance Mohan travels = 6212 m 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 7: A rope is 6436 cm long. A 3235 cm long piece is cut from it. How much of the rope is left? Solution: Length of the rope = 6436 cm Th H T O 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 Therefore, 3201 cm of the rope is left. 52 Subtraction Ascend_G3_Maths_Book_TB_Part1.indb 52 8/3/2023 11:37:39 AM
5.2 I Explore We can check the correctness of a subtraction problem using addition. Consider an example. Example 8: Subtract: a) 27 from 36 b) 145 from 364. Solution: a) 36 – 27 b) 364 – 145 TO HT O 2 16 5 14 \\3 \\6 3 \\6 4\\ −2 7 −1 4 5 9 21 9 36 - 27 = 9 364 – 145 = 219 We can write 36 = 27 + 9 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 9: 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? Subtraction 53 Ascend_G3_Maths_Book_TB_Part1.indb 53 8/3/2023 11:37:39 AM
b) 461 people booked a train for a trip to Goa. 110 people cancelled the trip. How many people went on the trip? Drill Time 5.2: 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 f) 543 – 267 2) Subtract 4-digit numbers without regrouping. a) 2341 – 1230 b) 7632 – 5120 c) 9763 – 2311 d) 7629 – 1318 e) 7589 – 1268 f) 8657 – 4320 3) Subtract 4-digit numbers with regrouping. a) 7632 – 1843 b) 4391 – 2482 c) 9843 – 7943 d) 8325 – 5436 e) 6893 – 3940 f) 9746 – 5859 4) Word problems a) A shopkeeper has 481 juice bottles. If he sells 177 bottles in a week, find the number of remaining bottles. b) 372 students participated in the annual day celebration of a school. If 199 of them were boys, find the number of girl participants. c) A stick is 8745 cm long. A 4313 cm long piece is cut from it. What length of the stick is remaining? d) Raj stays 5786 m away from Matin’s house. Raj travels 3825 m of the distance. What is the distance yet to be covered by Raj to reach Matin’s house? e) A van transported 6454 milk packets on a particular day. 3224 milk packets were sent to shop A and the remaining to shop B. How many packets were sent to shop B? 54 Subtraction Ascend_G3_Maths_Book_TB_Part1.indb 54 8/3/2023 11:37:39 AM
5.3: Subtract 2-digit Numbers Mentally Do you recall how to subtract two 1-digit numbers mentally? If yes, first try to describe the steps in your own words. When we subtract two 1-digit numbers, we keep the larger of the two numbers in mind and then subtract the smaller one from it. We can apply the same principle when mentally subtracting 2-digit numbers as well. How do we subtract 2-digit numbers mentally? Let’s learn this concept with the help of an example. Suppose you have to subtract 35 from 69, here are the steps: 1) Mentally subtract the digits in the ones place of the two numbers: 9 – 5 = 4. 2) Then, mentally subtract the digits in the tens place of the two numbers: 6 – 3 = 3. 3) Now write the differences obtained in steps 1) and 2) as the difference between the two numbers; so, 69 – 35 = 34. Do you know how to mentally subtract numbers when the digit in the ones place of the smaller number is more than the digit in the ones place of the larger number like in the case of 83 – 46? Try and remember the concept of regrouping and discuss with your partner how you would use it to mentally subtract 46 from 83? How do we subtract 2-digit numbers mentally by regrouping? Suppose you want to mentally subtract 29 from 56. Follow the steps below. 1) Regroup the numbers as tens and ones. So 29 = 20 + 9 and 56 = 50 + 6. 2) Notice that we cannot subtract the digits in the ones place; 6 – 9 is not possible because 6 < 9. So, regroup the digit in the tens place: 5 tens = 4 tens + 1 ten. 3) Borrow the 1 ten to the 6 in the ones place: 10 + 6 = 16. Subtraction 55 Ascend_G3_Maths_Book_TB_Part1.indb 55 8/3/2023 11:37:39 AM
4) Now, subtract the digits in the ones place of the two numbers mentally. Use regrouping again if needed: 16 – 9 = 7. 5) Then, subtract the digits in the tens place of the two numbers mentally: 4 tens – 2 tens = 2 tens. 6) Write down the answers from the steps 4) & 5) together as the final difference: 2 tens + 7 ones = 20 + 7 = 27. 7) So, 56 – 29 = 27 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 Term II than in Term I? Solve mentally. C an you think of a few similar problems using 3-digit or 4-digit numbers and subtract them mentally? Work on it with your partner and share it with the class. Reflection Time! 1) Imagine that your father gave you `1000 to buy your favourite comic books. When you are visiting the comic exhibition, subtract mentally the cost of each comic book that you would like to buy from the `1000 your father gave you. How many comic books would you be able to buy in all? 2) If you can’t visit a comic exhibition, find out the approximate cost of comic books from your parents and do the calculation mentally. 3) Why is regrouping important ? Draw the place value chart up to 4 places and explain regrouping to your friends. 56 Subtraction Ascend_G3_Maths_Book_TB_Part1.indb 56 8/3/2023 11:37:41 AM
Drill Time Concept 5.3: Subtract 2-digit Numbers Mentally 1) 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 f) 46 from 98 2) 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 f) 35 from 73 3) Word problems a) R ehmat has 48 pencils. He has used 29 pencils. How many pencils are left with him? b) S am 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? c) T here are 36 monkeys in a forest, of which 18 are male. How many female monkeys are there in a forest? d) J ay has 69 oranges. He gives 42 oranges to Raj. How many oranges are left with Jay? Maths Munchies 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 57 Ascend_G3_Maths_Book_TB_Part1.indb 57 8/3/2023 11:37:41 AM
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 every day or even taking their help in making basic calculations during shopping or calculating monthly expenses. 58 Subtraction Ascend_G3_Maths_Book_TB_Part1.indb 58 8/3/2023 11:37:41 AM
6 Multiplication I Will Learn using multiplication facts and order property to construct About multiplication tables multiplying 2-digit numbers with and without regrouping doubling the numbers mentally 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 adding a certain number of groups of the same size. 59 Ascend_G3_Maths_Book_TB_Part1.indb 59 8/3/2023 11:37:43 AM
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. 60 Multiplication Ascend_G3_Maths_Book_TB_Part1.indb 60 8/3/2023 11:37:43 AM
Multiplication Fact ↓↓ ↓ Multiplicand Multiplier Product Note: (a) R epresenting the multiplicand, multiplier and product using the symbols ‘×’ and ‘=’ is called a multiplication fact. (b) The multiplicand and the multiplier are also Order Property: Changing called the factors of the product. the order in which the numbers are multiplied (c) T he product is also called the multiple of both does not change the the multiplicand and the multiplier. product. This is called order For example, 2 × 7 = 14 = 7 × 2; property of multiplication. 4 × 5 = 20 = 5 × 4 and so on. Using multiplication facts and order property, let us now construct the multiplication tables of 7, 8 and 9. 7 8 9 7×1=7 8×1=8 9×1=9 7 × 2 = 14 8 × 2 = 16 9 × 2 = 18 7 × 3 = 21 8 × 3 = 24 9 × 3 = 27 7 × 4 = 28 8 × 4 = 32 9 × 4 = 36 7 × 5 = 35 8 × 5 = 40 9 × 5 = 45 7 × 6 = 42 8 × 6 = 48 9 × 6 = 54 7 × 7 = 49 8 × 7 = 56 9 × 7 = 63 7 × 8 = 56 8 × 8 = 64 9 × 8 = 72 7 × 9 = 63 8 × 9 = 72 9 × 9 = 81 7 × 10 = 70 8 × 10 = 80 9 × 10 = 90 Multiply 2-digit numbers by 1-digit numbers Now, let us learn to multiply a 2-digit number by a 1-digit number. Consider the following example. Example 1: Find the product: 23 × 7 Solution: Follow these steps to find the product. Multiplication 61 Ascend_G3_Maths_Book_TB_Part1.indb 61 8/3/2023 11:37:45 AM
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 one 17 Step 3: Write the ones digit of T O ×9 the product in the product 2 and carry over the tens digit 2 3 H TO to the tens place. × 7 15 1 ×4 Step 4: Multiply the tens. 2 × 7 = 14 Step 5: Add the carry over 14 + 2 = 16 from step 3 to the product. Step 6: Write the sum in the H TO tens place. 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 62 Multiplication Ascend_G3_Maths_Book_TB_Part1.indb 62 8/3/2023 11:37:45 AM
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. So, the distance 25 he travels in 25 days = 25 × 7. ×7 Therefore, Manoj travels 175 km in 25 days. 175 6.1 I Explore 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? Drill Time 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) T here were 23 students in one group. The school had 4 such groups. How many students were there in all the groups? b) V iraj travelled for 30 km in one day. He travelled the same distance every day for 7 days. How many kilometres did he travel in 7 days? Multiplication 63 Ascend_G3_Maths_Book_TB_Part1.indb 63 8/3/2023 11:37:45 AM
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. 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 64 Multiplication Ascend_G3_Maths_Book_TB_Part1.indb 64 8/3/2023 11:37:46 AM
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. Example 7: Multiply: 513 × 5 Solution: Follow these steps to multiply the given numbers. Steps Solved Solve these H TO Step 1: Multiply the ones and write the H TO product under ones. Regroup if the 1 444 product has two or more digits. ×8 513 ×5 5 Step 2: Multiply the tens. Add the carry H TO H TO over (if any) to the product. Write the sum under tens. 1 342 ×5 Regroup if the product has two or more 513 digits. ×5 65 Step 3: Multiply the hundreds. Add the Th H T O H TO carry over (if any) to the product and write the sum under hundreds. Regroup if 1 635 the product has two or more digits. ×7 513 ×5 2 565 Multiply 3-digit numbers by 2-digit numbers Multiplication of 3-digit numbers by 2-digit numbers may sometimes involve regrouping too. Let us understand this concept through step-by-step procedure. Consider the following examples. Multiplication 65 Ascend_G3_Maths_Book_TB_Part1.indb 65 8/3/2023 11:37:46 AM
Example 8: Multiply: 243 × 34 Solution: Follow these steps to multiply the given numbers. 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 Multiplication Add the carry over from the previous H TO step. So, 16 + 1 = 17. Write 7 in the tens 11 8/3/2023 11:37:46 AM 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 ×34 972 Step 5: Write 0 in the ones place. HTO 11 Multiply the ones of the multiplicand by 243 the tens digit of the multiplier. Write the ×3 4 product under the tens place. 972 3×3=9 90 Step 6: Multiply the tens by the tens digit H TO of the multiplier. 4 × 3 = 12 1 Write 2 in the hundreds place of the product and 1 in hundreds place of the 11 multiplicand as the carry over. 243 ×34 66 972 290 Ascend_G3_Maths_Book_TB_Part1.indb 66
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 11 972 +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 13 Distance Rohan ran in a day = 315 m Distance he ran in a week = 315 m × 7 = 2205 m 315 So, Rohan covered a total distance of 2205 m in one × 7 week. 2205 Multiplication 67 Ascend_G3_Maths_Book_TB_Part1.indb 67 8/3/2023 11:37:47 AM
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 Number of months in a year = 12 11 175 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 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 × 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. 68 Multiplication Ascend_G3_Maths_Book_TB_Part1.indb 68 8/3/2023 11:37:47 AM
Drill Time 6.2: Multiply 3-digit Numbers by 1-digit and 2-digit Numbers 1) 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 f) 430 × 2 2) 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 f) 546 × 3 3) Multiply 3-digit numbers by 2-digit numbers. a) 769 × 21 b) 759 × 10 c) 578 × 42 d) 619 × 66 e) 290 × 30 f) 825 × 12 4) Word problems a) S usan drove 462 km every day for a week. What distance did she drive in that week? b) If Maya bakes 162 loaves of bread every day, how many loaves of bread will she bake in 8 days? c) S ohail spends `616 for a set of books. How much will he spend on 24 such sets? d) A n elephant eats 225 bananas every day. How many bananas will it eat in 15 days? e) A box of cashews cost `964. What is the cost of 27 such boxes? Multiplication 69 Ascend_G3_Maths_Book_TB_Part1.indb 69 8/3/2023 11:37:47 AM
6.3: Double 2-digit and 3-digit Numbers Mentally We have learnt mental addition and subtraction in the previous lessons. Now let us look at how to double a given number mentally. How do we double a 2-digit number? Doubling a number means multiplying the number by 2. To double a number, we must be thorough with the multiplication table of 2 first. For example, 3 × 2 = 6, 5 × 2 = 10, 10 × 2 = 20 and so on. Let us now understand how to double a 2-digit number mentally using an example. Suppose we want to double the number 53. To do so, you can use the following steps. Steps Doubling 53 Double 41 The tens digit is 5. The tens digit is ____. Step 1: Multiply the tens digit by 2. So, 5 × 2 = 10. So, ___ × 2 = ___. The ones digit is 3. The ones digit is ___ Step 2: If the ones digit is less than or 3 < 4 (True) ___ < ___ (True/ False) equal to 4, write the product in step 1 as it is. If not, add 1 to it and write. 3×2=6 ___ × 2 = ___ Step 3: Multiply the ones digit by 2. 53 × 2 = 106 ___ × 2 = ___ Step 4: Write the products in steps 1 and 3 together. This gives us the double of the given number. 1) Double the given numbers mentally. a) 22 b) 43 c) 51 2) Sony is 36 years old. Her aunt is double her age. How old is Sony’s aunt? Calculate mentally. 3) Rohan bought 42 books in Year 1 and double the number in Year 2. How many books did he buy in Year 2? Calculate mentally. 70 Multiplication Ascend_G3_Maths_Book_TB_Part1.indb 70 8/3/2023 11:37:48 AM
Now, how do we double a 3-digit number? Think of a 3-digit number. Can the same method shown earlier be used? Work on it with your partner and share it with the class. Double the given numbers mentally. 1) 172 2) 530 Reflection Time! 1) Help your friend calculate the total number of chocolates he has to bring to school on his birthday, if he wants to give two chocolates each to all the teachers in the school and all his classmates. 2) Your mother wants to buy exactly the same number of toys, books, clothes and sweets for both you and your sibling. How can you help her get to that number quickly for each of them? Drill Time 6.3: Double 2-digit and 3-digit Numbers Mentally 1) Double the given numbers mentally. a) 23 b) 52 c) 61 d) 120 e) 131 2) Solve word problems mentally. a) Sonal earned `28 on Monday. She earned double the amount on Tuesday. How much did she earn on Tuesday? b) A fruitseller sells 38 apples on day 1 and double the apples on day 2. How many apples did he sell on day 2? Multiplication 71 Ascend_G3_Maths_Book_TB_Part1.indb 71 8/3/2023 11:37:48 AM
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. 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 Connect the Dots Social Studies Fun All the arrangements of Charbagh Garden of Taj Mahal are based on four or its multiples. The entire garden is divided into four parts. There are 16 flowerbeds. It is said that each of the flowerbeds is planted with 400 plants. English Fun Compose a poem on multiplication as: Six times six. Magic tricks. Abracadabra. Thirty-six. 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. 72 Multiplication Ascend_G3_Maths_Book_TB_Part1.indb 72 8/3/2023 11:37:53 AM
MATHS LAB Aim: To find the smallest difference Requirement: Number cards from 0 to 9 (1 set per group) Steps : 1) Make groups of four with your friends. 2) Make four sets of cards numbered from 0 to 9, using blank sheets of paper as shown in these figures. 3) Shuffle the cards. Each group draws four cards. 4) Each group then makes the greatest and the smallest 4-digit numbers with the numbers on the cards they have drawn. 5) Find the difference between the greatest and the smallest numbers you’ve made and fill in the record table as shown below. Record Table Greater number Smaller number Difference 9652 2569 9652 – 2569 = 7083 6) The group with the smallest difference wins the round. Repeat steps 3 to 5, five times. 7) The group that wins the most rounds wins the game. Ascend_G3_Maths_Book_TB_Part1.indb 73 73 8/3/2023 11:37:54 AM
Student Reflection Come to this page after you complete a chapter. Choose the smiley that shows how well you have understood the chapter. Shapes Patterns Very clear Clear Somewhat clear Not clear at all Very clear Clear Somewhat clear Not clear at all I need help with ..........………………...............……… I need help with ..........………………...............……… ...................................................................................... ...................................................................................... What I liked about this chapter ............................... What I liked about this chapter ............................... …………………………………………............................ …………………………………………............................ Numbers Addition Very clear Clear Somewhat clear Not clear at all Very clear Clear Somewhat clear Not clear at all I need help with ..........………………...............……… I need help with ..........………………...............……… ...................................................................................... ...................................................................................... What I liked about this chapter ............................... What I liked about this chapter ............................... …………………………………………............................ …………………………………………............................ Subtraction Multiplication Very clear Clear Somewhat clear Not clear at all Very clear Clear Somewhat clear Not clear at all I need help with ..........………………...............……… I need help with ..........………………...............……… ...................................................................................... ...................................................................................... What I liked about this chapter ............................... What I liked about this chapter ............................... …………………………………………............................ …………………………………………............................ 74 8/3/2023 11:37:54 AM Ascend_G3_Maths_Book_TB_Part1.indb 74
Search
