MATHEMATICS TEXTBOOK – Grade 3 Name: _________________________ Section: ________Roll No: _______ School: ________________________

Contents Part 1 3 Numbers 3.1 Count by Thousands�������������������������������������������������������������������������������������� 24 3.2 Compare 4-digit Numbers����������������������������������������������������������������������������� 30 4 Addition 4.1 Add 3-digit and 4-digit Numbers .................................................................. 38 5 Subtraction 5.1 Subtract 3-digit and 4-digit Numbers����������������������������������������������������������� 50

Numbers3Chapter I Will Learn About • reading and writing 4-digit numbers with place value chart. • identifying greater and smaller number, ascending and descending orders. • forming numbers. 3.1 Count by Thousands I Think Neena went to buy one of the toy cars shown. She could ` 1937.00 not read the price on one of them. Can you read the ` 657.00 price on both the cars? I Recall We know that 10 ones make a ten. Similarly, 10 tens make a hundred. We can count by tens and hundreds. Counting by 10s: 10, 20, 30, 40, 50, 60, 70, 80 and 90 Counting by 100s: 100, 200, 300, 400, 500, 600, 700, 800 and 900 A digit multiplied by the value of its place gives its place value. Using place values, we can write the numbers in the expanded form. 24

Let us answer these to revise the concept. a) The number for two hundred and thirty-four is _____________. b) The expanded form of 444 is _______________________. c) The place value of 9 in 493 is _____________. d) The number name of 255 is _______________________________________. I Remember and Understand To know about 4-digit numbers, we count by thousands using boxes. 10 hundreds = 1 thousand Using a spike abacus and beads of different colours, we represent 999 as shown. 9 blue, 9 green and 9 pink beads on the abacus represent 999. H TO Remove all the beads and Th H T O Represent 999 put a orange bead on the Represent 1000 next spike. This represents a thousand. It is written as 1000. It is the smallest 4-digit number. Now, we know four places – ones, tens, hundreds and thousands. Let us represent 4732 in the place value chart. The greatest Thousands (Th) Hundreds (H) Tens (T) Ones (O) 4-digit 4 7 32 number is 9999. Numbers 25

We count by 1000s as 1000 (one thousand), 2000 (two thousand), ... till 9000 (nine thousand). Expanded form of 4-digit numbers We can write a number as the sum of the place values of its digits. This form of the number is called its expanded form. Let us now learn to write the expanded forms of 4-digit numbers. Example 1: Expand the given numbers: a) 3746 b) 6307 Solution: Write the digits of the given numbers in the place value chart, as shown. ExpTahndeHd formT s: O a) 3 7 4 6 a) 3746 = 3000 + 700 + 40 + 6 b) 6 3 0 7 b) 6307 = 6000 + 300 + 0 + 7 Writing number names of 4-digit numbers We can write the number name of a number by writing its expanded form. Observe the place value chart and the place values of a 4-digit number, 8015. Th H TO Place values 80 15 5 ones = 5 1 tens = 10 0 hundreds = 0 8 thousands = 8000 So, the expanded form of 8015 is 8000 + 0 + 10 + 5. The number name of 8015 is Eight thousand fifteen. Note: 8015 is called the standard form of the number. Example 2: Write the number, its expanded form and the number name from the following figure: 26

Solution: There are 1 thousand, 6 hundreds, 9 tens and 3 Th H T O ones in the given figure. 1 693 So, the number it represents is 1693. To expand the given number, write its digits in the correct places of the place value chart as shown: Expanded form: 1693 = 1000 + 600 + 90 + 3 Writing in words:1693 = One thousand six hundred ninety-three We can write the standard form of a number from its expanded form. Let us see an example. Example 3: Write the standard form of 3000 + 400 + 60 + 5. Solution: Write the digits in the correct places in the place value chart as shown. F rom the thousands place to ones Th H T O place, write the digits one beside the 3 46 5 other. Therefore, the standard form of 3000 + 400 + 60 + 5 is 3465. ? Train My Brain Say the number names of the following numbers: a) 2884 b) 4563 c) 9385 Numbers 27

3.2 Compare 4-digit Numbers I Think Neena has 3506 paper clips and her brother has 3605 paper clips. Neena wants to know who has more paper clips. But she is confused as the numbers look the same. Can you tell who has more paper clips? I Recall In class 2, we learnt to compare 3-digit numbers and 2-digit numbers. Let us now revise the same. A 2-digit number is always greater than a 1-digit number. A 3-digit number is always greater than a 2-digit number and a 1-digit number. So, a number having more digits is always greater than the other. We use the symbols >, < or = to compare two numbers. I Remember and Understand Comparing two 4-digit numbers is similar to If two numbers comparing two 3-digit numbers. have equal number of digits, start Let us understand the steps through an example. comparing from their leftmost digit. Example 9: Compare: 5382 and 5380 Solution: To compare the given numbers, follow these steps. Steps Solved Solve this Step 1: Compare the number of digits 5382 and 5380 7469 and 7478 Count the number of digits in the given numbers. The number having more digits is Both 5382 and greater. 5380 have 4 digits. 30

Steps Solved Solve this 5382 and 5380 7469 and 7478 Step 2: Compare thousands 5=5 ____ = ____ If two numbers have the same number of digits, compare the thousands digits. 3=3 ____ = ____ The number with the greater digit in the thousands place is greater. Step 3: Compare hundreds If the digits in the thousands place are the same, compare the digits in the hundreds place. The number with the greater digit in the hundreds place is greater. Step 4: Compare tens 8=8 ____ > ____ If the digits in the hundreds place are also So, same, compare the digits in the tens place. The number with the greater digit in the tens ____ > ____ place is greater. Step 5: Compare ones 2>0 - If the digits in the tens place are also the So, same, compare the digits in the ones place. 5382 > 5380 The number with the greater digit in the ones place is greater. Note: Once we find the greater/smaller number, we need not carry out the next steps. Train My Brain ? Train My Brain Find the greater number from each of the following pairs: a) 7364, 7611 b) 8130, 8124 c) 4371, 4378 Numbers 31

Addition4Chapter I Will Learn About • using addition of 3-digit numbers in real-life. • adding numbers with and without regrouping. 4.1 Add 3-digit and 4-digit Numbers I Think Neena’s father bought her a shirt ` 335 ` 806 for ` 335 and a skirt for ` 806. Neena wants to find how much her father had spent in all. How do you think she can find that? I Recall We can add 2-digit or 3-digit numbers by writing them one below the other. This method of addition is called vertical addition. Let us revise the concept by solving the following. a) 22 + 31 = _________ b) 42 + 52 = _________ 38

c) 82 + 11 = _________ d) 101 + 111 = _________ e) 101 + 201 = _________ f) 122 + 132 = _________ I Remember and Understand Let us now understand the addition of two 3-digit numbers with regrouping. We will also learn to add two 4-digit numbers. Add two 3-digit numbers with regrouping Sometimes, the sum of the digits in a place is more than While adding, 9. In such cases, we carry the tens digit of the sum to the regroup if the next place. sum of the digits is more than 9. Example 1: Add 245 and 578. Solution: Arrange the numbers one below the other. Add the digits under a place. Regroup if needed and write the sum. Step 1: Add the ones. Step 2: Add the tens. Step 3: Add the hundreds. H TO H TO H TO 1 11 11 245 245 245 +578 +578 +578 823 23 3 H TO Solve these H TO HTO 823 39 0 171 +197 +12 1 +219 Addition 39

Add two 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. Add the digits under a place. Write the sum. Step 1: Add the ones. Step 2: Add the tens. Th H T O Th H T O 13 5 2 135 2 + 36 0 3 +3 6 0 3 5 55 Step 3: Add the hundreds. Step 4: Add the thousands. Th H T O Th H T O 135 2 13 5 2 +3 6 0 3 + 36 0 3 49 5 5 955 Th H T O Solve these Th H T O 419 0 111 1 +2 0 0 0 Th H T O +2 2 2 2 200 2 +3 0 0 3 ? Train My Brain c) 8837 + 1040 Solve the following: a) 321 + 579 b) 725 + 215 40

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

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, start from the ones regrouping. Let us now learn to subtract them with place. regrouping. 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 5 \\8 \\6 \\8 6\\ –4 27 –4 2 7 27 1 9 59 59 Subtraction 51

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

Th H T O Solve these Th H T O 8000 4789 – 2000 Th H T O –2475 2879 –2137 ? Train My Brain Solve the following: a) 719 – 320 b) 813 – 621 c) 3678 – 2466 Subtraction 53

Contents Part 2 6 Multiplication 6.1 Multiply 2-digit Numbers���������������������������������������������������������������������������������� 1 8 Division 8.1 Division as Equal Grouping���������������������������������������������������������������������������� 27

6Chapter Multiplication I Will Learn About • using repeated addition to construct multiplication tables from 2 to 10. • estimation of two products. • mental multiplication of two numbers. 6.1 Multiply 2-digit Numbers I Think Neena bought 2 boxes of toffees for her birthday. Each box has 25 toffees inside it. If there are 54 students in her class, do you think she has enough toffees? I Recall In Class 2, we have learnt that multiplication is repeated addition. In Fig. (a), the number ‘3‘ is repeated 4 times. So, using repeated addition we can write, 3 + 3 + 3 + 3 = 12. Fig. (a) Fig. (b) 1

Similarly, in Fig. (b), the number ‘2‘ is repeated twice. Hence, using repeated addition we can write 2 + 2 = 4. Thus, we can say that repeated addition is adding the same number repeatedly (again and again). Let us answer a few questions on repeated addition. a) 5 + 5 + 5 + 5 + 5 = __________ b) 3 + 3 + 3 = __________ c) 10 + 10 + 10 + 10 = __________ d) 6 + 6 = __________ I Remember and Understand The symbol ‘×’ indicates multiplication. Multiplication means having a certain number of groups of the same size. In the 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. Multiplication Fact ↓ ↓ ↓ Multiplicand Multiplier Product Note: (a) Representation of the multiplicand, multiplier and the product using the symbols ‘×’ and ‘=’ is called a multiplication fact. (b) The multiplicand and the multiplier are also called the factors of the product. For example, in the multiplication fact 2 × 7 = 14 = 7 × 2, 2 and 7 are the factors of 14. Similarly, in the multiplication fact 4 × 5 = 20 = 5 × 4, 5 and 4 are the factors of 20. 2

(c) A ny number multiplied by 0 gives a Order Property: Changing product 0. For example, 6 × 0 = 0. the order in which numbers are multiplied does not (d) A ny number multiplied by 1 gives the change the product. This is number as the product. called the order property of multiplication. For example, 6 × 1 = 6. Using multiplication facts and order property, let us now construct the multiplication tables from numbers 2 to 10. 2 Multiplication Tables 4 2×1=2 4×1=4 2×2=4 3 4×2=8 2×3=6 3×1=3 4 × 3 = 12 2×4=8 3×2=6 4 × 4 = 16 2 × 5 = 10 3×3=9 4 × 5 = 20 2 × 6 = 12 3 × 4 = 12 4 × 6 = 24 2 × 7 = 14 3 × 5 = 15 4 × 7 = 28 2 × 8 = 16 3 × 6 = 18 4 × 8 = 32 2 × 9 = 18 3 × 7 = 21 4 × 9 = 36 2 × 10 = 20 3 × 8 = 24 4 × 10 = 40 3 × 9 = 27 3 × 10 = 30 5 6 7 5×1=5 6×1=6 7×1=7 5 × 2 = 10 6 × 2 = 12 7 × 2 = 14 5 × 3 = 15 6 × 3 = 18 7 × 3 = 21 5 × 4 = 20 6 × 4 = 24 7 × 4 = 28 5 × 5 = 25 6 × 5 = 30 7 × 5 = 35 5 × 6 = 30 6 × 6 = 36 7 × 6 = 42 5 × 7 = 35 6 × 7 = 42 7 × 7 = 49 5 × 8 = 40 6 × 8 = 48 7 × 8 = 56 5 × 9 = 45 6 × 9 = 54 7 × 9 = 63 5 × 10 = 50 6 × 10 = 60 7 × 10 = 70 Multiplication 3

8 9 10 10 × 1 = 10 8×1=8 9×1=9 10 × 2 = 20 8 × 2 = 16 9 × 2 = 18 10 × 3 = 30 8 × 3 = 24 9 × 3 = 27 10 × 4 = 40 8 × 4 = 32 9 × 4 = 36 10 × 5 = 50 8 × 5 = 40 9 × 5 = 45 10 × 6 = 60 8 × 6 = 48 9 × 6 = 54 10 × 7 = 70 8 × 7 = 56 9 × 7 = 63 10 × 8 = 80 8 × 8 = 64 9 × 8 = 72 10 × 9 = 90 8 × 9 = 72 9 × 9 = 81 10 × 10 = 100 8 × 10 = 80 9 × 10 = 90 Solve these Multiplying 2-digit numbers by 1-digit numbers H TO There are two ways to multiply numbers: 1) Standard algorithm 2) Lattice algorithm 17 Let us now learn both these methods. ×9 Standard Algorithm H TO Example 1: Find the product: 23 × 7 Solution: Follow these steps to find the product. 15 ×4 Steps Solved Step 1: Multiply the ones. 3 × 7 = 21 Step 2: Regroup the product. 21 ones = 2 tens and 1 ones Step 3: Write down the ones TO digit of the product from step 2. Carry forward its tens digit 2 to the tens place. 23 ×7 1 4

Steps Solved Solve these Step 4: Multiply the tens. Step 5: Add the carry over 2 × 7 = 14 H TO from step 3 to the product. 23 14 + 2 = 16 ×8 Step 6: Write the sum in the tens place. H TO 2 23 ×7 161 Lattice Algorithm Important features of the lattice algorithm: • Setting up the lattice before we begin multiplying • Doing all the multiplications first, followed by additions • There is no carry over in the multiplication phase of the algorithm Example 2: Multiply: 29 × 3 Solution: Follow these steps to find the product. Steps Solved Solve these Step 1: Construct a lattice as shown 3 2× such that: 5 (a) Number of rows = Number of digits in the multiplier. (b) N umber of columns = Number of digits in the multiplicand. Step 2: Write the multiplicand 2 9× 5 2× along the top of the lattice and 3 4 the multiplier along the right, one digit for each row or column. Draw diagonals to divide each box into parts as shown. Multiplication 5

Steps Solved Solve these 6 1× Step 3: Multiply each digit of the 2 9× 3 multiplicand by each digit of the multiplier. Write the products in the 2 3 5 7× cells where the corresponding rows 7 3 and columns meet. 2 9× 6 3× Step 4: If the product is a single digit 0627 3 3 number, put 0 in the tens place. (2 × 3 = 6) = 06 Step 5: Add the numbers along the 2 9× diagonals from the right to find the 02 product. Regroup if needed. Write 0 6 73 the sum from left to right. 87 Therefore, 29 × 3 = 087 = 87. ? Train My Brain Find the product: a) 17 × 7 b) 28 × 9 c) 19 × 8 6

8Chapter Division I Will Learn About • equal grouping and sharing. • repeated subtraction and division facts. 8.1 Division as Equal Grouping I Think Neena and her brother Piyush got a chocolate bar with 14 pieces for Christmas. Piyush divided it and gave Neena 6 pieces. Do you think Neena got an equal share? How can we find out? I Recall Suppose, we have to divide a group of 12 chocolate bars among 3 students. We can subtract 3 from 12 repeatedly to find how many chocolate bars each student will get. 27

12 chocolate bars in 1 group can be represented as: By repeated subtraction, we can have 12 – 3 = 9; 9 – 3 = 6; 6 – 3 = 3; 3 – 3 = 0 (1) (2) (3) (4) Thus, each student will receive 4 chocolate bars. Repeated subtraction is subtracting the same number over and over again. Fill in these blanks to revise the concept repeated subtraction. a) 16 – 4 = 12 ; 12 – 4 = ______ ; ______ – 4 = 4 ; ______ – ______ = ______ b) 21 – 7 = 14; ; 14 – 7 = ______ ; ______ – 7 = ______ c) ______ – 6 = 18 ; 18 – 6 = ______ ; 12 – ______ = 6 ; 6 – ______ = 0 I Remember and Understand In Grade 2, we have learnt about equal grouping and equal sharing. If 9 balloons are to be shared equally among 3 girls, each one of them gets 3 balloons. We can write it as 9 divided by 3 equals 3. It is represented as: Division Fact ↓ ↓ ↓ Dividend Divisor Quotient Note: Representation of the dividend, The symbol for ‘is divided by’ is ÷. divisor and quotient using the symbols ‘÷’ and ‘=’ is called a division fact. We can represent division as: In a division, the number that is divided [Total number] ÷ [Number in is called the dividend. The number that each group] = [Number of divides is called the divisor. The answer in groups] division is called the quotient. The number 28

(part of the dividend) that remains is called the remainder. We use multiplication tables to find the quotient in a division. We find the factor which when multiplied by the divisor gives the dividend. Example 1: 18 pens are to be shared equally by 3 children. How many pens does each child get? Solution: Total number of pens = 18 Number of children = 3 Number of pens each child gets = 18 ÷ 3 = 6 (since 6 × 3 = 18) Therefore, each child gets 6 pens. Example 2: 10 flowers are put in some vases. If each vase has 2 flowers, how many vases are used? Solution: Number of flowers = 10 Number of flowers in each vase = 2 Number of vases used = 10 ÷ 2 = 5 (since 2 × 5 = 10) Therefore, 5 vases are used to put 10 flowers. We get two division facts from a multiplication fact. The divisor and the quotient are the factors of the dividend. Observe the following: Dividend ÷ Divisor = Quotient Multiplicand × Multiplier = Product 18 ÷ 6 = 3 ↓↓ ↓ 6 × 3 = 18 Product Factor Factor ↓ ↓↓ (Multiplicand) (Multiplier) Divisor Quotient Dividend From the multiplication fact 6 × 3 = 18, we can write two division facts: a) 18 ÷ 3 = 6 and b) 18 ÷ 6 = 3 Multiplication and division are reverse operations. We can show a multiplication fact on the number line. For example, 3 × 5 = 15 means 5 times 3 is 15. Division 29

To show 5 times 3 on the number line, we go forward from 0 to 15. While doing so, we jump forward 5 times, covering 3 steps in every jump. Similarly, we can show the division fact 15 ÷ 3 = 5 on the number line. To show 15 divided by 3 on the number line, we go backward from 15 to 0. While doing so, we go back 5 times, covering 3 steps each time. ? Train My Brain Write two multiplication facts for each of the following: a) 20 ÷ 5 = 4 b) 48 ÷ 6 = 8 c) 36 ÷ 4 = 9 30