PASSPORT G03 MATHS TEXTBOOK_Combine

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

Contents Class Part 1 3 3 Numbers 22 28 3.1 Count by Thousands  3.2 Compare 4-digit Numbers 41 74 Addition 56 04.2 Add 3-digit and 4-digit Numbers 69 3 1 +-5 Subtraction 73 46 x5.2 Subtract 3-digit and 4-digit Numbers 95 82 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 4 12/17/2018 4:06:35 PM

Chapter Numbers 3 I Will Learn About • writing 4-digit numbers with place value chart. • identifying and forming the greatest and the smallest number. • writing the standard and the expanded forms of the number. • comparing and ordering numbers. Concept 3.1: Count by Thousands I Think Farida went to buy one of the toy cars shown. She ` 1937.00 could not read the price on one of the cars. Can you read the price on both the cars and understand what they mean? ` 657.00 3.1 I Recall We know that 10 ones make a ten. Similarly, 10 tens make a hundred. Let us now count by tens and hundreds as: 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 When we multiply a digit by the value of its place, we get its place value. Using place values, we can write a number in its expanded form. 22 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 26 12/17/2018 4:06:36 PM

Let us answer these to revise the concept. a) The number for two hundred and thirty-four is _____________. b) In 857, there are _______ hundreds, _______ tens and _______ ones. c) The expanded form of 444 is _______________________. d) The place value of 9 in 493 is _____________. e) The number name of 255 is _______________________________________. 3.1 I Remember and Understand To know about 4-digit numbers, we count by thousands using boxes. Suppose shows 1. Ten such boxes show a 10. So, = 10 ones = 1 ten Similarly, 10 such strips show 10 tens or 1 hundred. = 10 tens = 1 hundred Numbers 23 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 27 12/17/2018 4:06:37 PM

= 1 hundred = 100 = 2 hundreds = 200 = 3 hundreds = 300 = 4 hundreds = 400 In the same way, we get 5 hundreds = 500, 6 hundreds = 600, 7 hundreds = 700, 8 hundreds = 800 and 9 hundreds = 900. 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 an orange bead on the represent 1000 next spike. This represents one thousand. We write it as 1000. 1000 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. 24 12/17/2018 4:06:37 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 28

Thousands (Th) Hundreds (H) Tens (T) Ones (O) The greatest 4-digit 4 7 32 number is 9999. We count by 1000s as 1000 (one thousand), 2000 (two thousand)... till 9000 (nine thousand). Expanded form of 4-digit numbers The form in which a number is written as the sum of the place values of its digits is called its expanded form. Let us now learn to write the expanded form of 4-digit numbers. Example 1: Expand the following numbers. a) 3746 b) 6307 Solution: Write the digits of the given numbers in the place value chart, as shown. Expanded forms: Th H TO a) 3746 = 3000 + 700 + 40 + 6 a) 3 7 46 b) 6307 = 6000 + 300 + 0 + 7 b) 6 3 0 7 Writing number names of 4-digit numbers Observe the expanded form and place value chart for a 4-digit number, 8015. Th H TO Place values 80 15 5 ones = 5 1 tens = 10 0 hundreds = 0 8 thousands = 8000 We can call 8015 as the standard form of the number. Let us look at an example. Example 2: Write the expanded forms and number names of these numbers. a) 1623 b) 3590 Solution: To expand the given numbers, write them in the correct places in the place value chart. Numbers 25 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 29 12/17/2018 4:06:37 PM

Expanded forms: Th H T O a) 1623 = 1000 + 600 + 20 + 3 a) 1 6 2 3 b) 3590 = 3000 + 500 + 90 + 0 b) 3 5 9 0 Writing in words (Number names): a) 1623 = One thousand six hundred and twenty-three b) 3590 = Three thousand five hundred and ninety 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 numbers in the place value Th H T O chart in the correct places. Write the 3 46 5 digits one beside the other, starting from the thousands place. 3000 + 400 + 60 + 5 = 3465 So, the standard form of 3000 + 400 + 60 + 5 is written as 3465. Train My Brain Write the number names of: a) 2884 b) 4563 c) 9385 26 12/17/2018 4:06:37 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 30

Concept 3.2: Compare 4-digit Numbers I Think Farida has 3506 paper clips and her brother has 3605 paper clips. Farida wants to know who has more paper clips. But the numbers appear to be the same, and she is confused. Can you tell who has more number of paper clips? 28 12/17/2018 4:06:37 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 32

3.2 I Recall In class 2, we have learnt to compare 3-digit numbers and 2-digit numbers. Let us quickly revise the concept. 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 with more number of digits is always greater than a number with lesser digits. We use the symbols >, < or = to compare two numbers. 3.2 I Remember and Understand Comparing two 4-digit numbers is similar to comparing two If two numbers have 3-digit numbers. an equal number of digits, start comparing Let us understand the steps to compare through an example. from the leftmost digit. Example 9: Compare: 5382 and 5380 Solution: Follow these steps to compare the given numbers. Steps Solved Solve this 5382 and 5380 7469 and 7478 Step 1: Compare the number of digits Both 5382 and Count the number of digits in the given numbers. 5380 have 4 The number having more number of digits is digits. greater. Step 2: Compare thousands 5=5 ____ = ____ If two numbers have the same number of digits, compare the thousands digits. The number with the greater digit in the thousands place is greater. Step 3: Compare hundreds 3=3 ____ = ____ 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. Numbers 29 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 33 12/17/2018 4:06:37 PM

Steps Solved Solve this 5382 and 5380 7469 and 7478 Step 4: Compare tens 8=8 ____ > ____ If the digits in the hundreds place are also same, So, 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 same, So, compare the digits in the ones place. The 5382 > 5380 number with the greater digit in the ones place is greater. When the ones place are the same, the numbers are equal. Note: Once we can decide a greater/smaller number, the steps that follow need not be carried out. Train My Brain Find the greater number in each of the following pairs. a) 7364, 7611 b) 8130, 8124 c) 4371, 4378 30 12/17/2018 4:06:37 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 34

Concept 4.2: Add 3-digit and 4-digit Numbers I Think Farida’s father bought her a shirt for ` 335 and a skirt for ` 806. Farida wants to find how much her father had spent in all. How do you think she can find that? 4.2 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 earlier concept and solve the following. a) 22 + 31 = _________ b) 42 + 52 = _________ c) 82 + 11 = _________ d) 101 + 111 = _________ e) 100 + 200 = _________ f) 122 + 132 = _________ Addition 41 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 45 12/17/2018 4:06:38 PM

4.2 I Remember and Understand Let us now understand the addition of two 3-digit numbers with While adding, regrouping. We will also learn to add two 4-digit numbers. regroup if the Add 3-digit numbers with regrouping sum of the digits is more than 9. Sometimes, the sum of the digits in a place is more than 9. In such cases, we need to regroup the sum. We then carry forward the digit to the next place. Example 8: Add 245 and 578. Solution: Arrange the numbers one below the other. Regroup if necessary. Step 1: Add the ones. Solved Step 3: Add the hundreds. H TO Step 2: Add the tens. H TO 1 11 245 H TO 245 11 +578 245 +578 3 +578 823 23 H TO Solve these H TO H TO 823 171 +197 390 +219 +121 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 9: Add 1352 and 3603. Solution: Arrange the numbers one below the other. 42 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 46 12/17/2018 4:06:38 PM

Solved Step 1: Add the ones. Step 2: Add the tens. Th H T O Th H T O 135 2 135 2 +3 6 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 +3 6 0 3 955 49 5 5 Th H T O Solve these Th H T O 41 9 0 11 1 1 +2 0 0 0 Th H T O +2 2 2 2 200 2 +3 0 0 3 Add 4-digit numbers with regrouping We regroup the sum when it is equal to or more than 10. Example 10: Add 1456 and 1546. Solution: Arrange the numbers one below the other. Add and regroup, if necessary. Solved Step 1: Add the ones. Step 2: Add the tens place. Th H T O Th H T O 1 11 1456 1456 +1 5 4 6 +1 5 4 6 2 02 Addition 43 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 47 12/17/2018 4:06:38 PM

Solved Step 3: Add the hundreds. Step 4: Add the thousands. Th H T O Th H T O 111 111 1456 1456 +1 5 4 6 +1 5 4 6 002 3002 Th H T O Solve these O Th H T O Th H T 175 8 459 2 +5 6 6 2 267 8 +1 4 5 6 +1 3 3 2 Train My Brain Solve: a) 321 + 579 b) 725 + 215 c) 8837 + 1040 44 12/17/2018 4:06:38 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 48

Concept 5.2: Subtract 3-digit and 4-digit Numbers I Think The given grid shows the number of men and women in Farida’s town in the years 2017 and 2018. Years 2017 2018 Men 2254 2187 How can Farida find out how may more men than women lived in her town in the two years? Women 2041 2073 5.2 I Recall Recall that we can subtract numbers by writing the smaller number below the greater number. A 2-digit number can be subtracted from a larger 2-digit number or a 3-digit number. Similarly, a 3-digit number can be subtracted from a larger 3-digit number. Let us answer these to revise the concept. a) 15 – 0 = _________ b) 37 – 36 = _________ c) 93 – 93 = _________ f) 50 – 45 = _________ d) 18 – 5 = _________ e) 47 – 1 = _________ 5.2 I Remember and Understand We have learnt how to subtract two 3-digit numbers without While subtracting, regrouping. Let us now learn how to subtract them with always start from regrouping. the ones place. Subtract 3-digit numbers with regrouping When a larger number is to be subtracted from a smaller number, we regroup the next higher place and borrow. Let us understand this with an example. Example 6: Subtract 427 from 586. Solution: To subtract, write the smaller number below the larger number. 56 12/17/2018 4:06:39 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 60

Step 1: Subtract the ones. But, 6 – 7 is Solved Step 3: Subtract the not possible as 6 < 7. So, regroup the hundreds. digits in the tens place. Step 2: Subtract the tens. H TO 7 16 8 tens = 7 tens + 1 tens. Borrow 1 ten to the ones place. Reduce the tens by 1 5 \\8 \\6 ten. Now subtract 7 ones from 16 ones. –4 2 7 H TO H TO 15 9 7 16 7 16 5 –4 8\\ 6\\ 5 \\8 \\6 27 –4 2 7 9 59 H TO Solve these H TO H TO 6 23 5 52 4 53 – 3 76 – 2 63 – 2 64 Subtract 4-digit numbers without regrouping Subtracting a 4-digit number from a larger 4-digit number is similar to subtracting a 3-digit number from a larger 3-digit number. The following examples help you understand this better. Example 7: Subtract: 5032 from 7689 Solution: To subtract, write the smaller number below the larger number. Step 1: Subtract the ones. O Solved O 9 9 Th H T 2 Step 2: Subtract the tens. 2 768 7 7 −503 Th H T 768 −503 5 Subtraction 57 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 61 12/17/2018 4:06:39 PM

Step 3: Subtract the hundreds. Solved Step 4: Subtract the thousands. Th H T O 7689 Th H T O −5032 7 68 9 − 5 03 2 657 2 65 7 Th H T O Solve these Th H T O 2879 8000 –2137 Th H T O –2000 4789 –2475 Subtract 4-digit numbers with regrouping In subtraction of 4-digit numbers, we can regroup the digits in thousands, hundreds and tens places. Let us see an example. Example 8: What is the difference 7437 and 4868? Solution: Write the smaller number below the larger number. Steps Solved O Solve these Step 1: Subtract the ones. Th H T O Th H T 17 But, 7 − 8 is not possible as 2 1654 \\7 −1 2 4 6 7 < 8. So, regroup the tens digit, 7 4 3\\ 8 3. 3 tens = 2 tens + 1 ten. Borrow −4 8 6 9 1 ten to the ones place. Step 2: Subtract the tens. But, Th H T O 2 − 6 is not possible as 2 < 6. 12 So, regroup the hundreds digit, 3 \\2 17 4. 4 hundreds = 3 hundreds + − 7 4\\ 3\\ \\7 1 hundred. Borrow 1 hundred to 4 8 6 8 the tens place. 69 58 12/17/2018 4:06:39 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 62

Steps Solved Solve these Th H T O Step 3: Subtract the hundreds. Th H T O But, 3 − 8 is not possible. So, 13 12 5674 regroup the thousands digit, −2 3 8 2 7. 7 thousands = 6 thousands + 6 \\3 \\2 17 1 thousand. Borrow 1 thousand \\7 4\\ 3\\ \\7 to the hundreds place. −4 8 6 8 569 Step 4: Subtract the thousands. Th H T O Th H T O 13 12 7468 6 \\3 \\2 17 −4 8 3 7 \\7 4\\ 3\\ \\7 −4 8 6 8 2569 Train My Brain Solve the following: a) 719 – 320 b) 813 – 621 c) 3678 – 2466 Subtraction 59 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 63 12/17/2018 4:06:39 PM

Chapter Multiplication 6 I Will Learn About • using repeated addition to construct multiplication tables. • multiplying 2-digit numbers with and without regrouping. • doubling the numbers mentally. Concept 6.1: Multiply 2-digit Numbers I Think Farida bought 2 boxes of toffees to distribute among her classmates on her birthday. Each box has 25 toffees inside it. If there are 54 students in her class, do you think she has enough toffees? 6.1 I Recall In Class 2, we have learnt that multiplication is repeated addition. The symbol ‘×’ indicates multiplication. Multiplication means having a certain number of groups of the same size. NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 73 69 12/17/2018 4:06:40 PM

Let us recall the multiplication tables of numbers from 1 to 6. 1 2 3 1×1=1 2×1=2 3×1=3 1×2=2 2×2=4 3×2=6 1×3=3 2×3=6 3×3=9 1×4=4 2×4=8 3 × 4 = 12 1×5=5 2 × 5 = 10 3 × 5 = 15 1×6=6 2 × 6 = 12 3 × 6 = 18 1×7=7 2 × 7 = 14 3 × 7 = 21 1×8=8 2 × 8 = 16 3 × 8 = 24 1×9=9 2 × 9 = 18 3 × 9 = 27 1 × 10 = 10 2 × 10 = 20 3 × 10 = 30 4 5 6 4×1=4 5×1=5 6×1=6 4×2=8 5 × 2 = 10 6 × 2 = 12 4 × 3 = 12 5 × 3 = 15 6 × 3 = 18 4 × 4 = 16 5 × 4 = 20 6 × 4 = 24 4 × 5 = 20 5 × 5 = 25 6 × 5 = 30 4 × 6 = 24 5 × 6 = 30 6 × 6 = 36 4 × 7 = 28 5 × 7 = 35 6 × 7 = 42 4 × 8 = 32 5 × 8 = 40 6 × 8 = 48 4 × 9 = 36 5 × 9 = 45 6 × 9 = 54 4 × 10 = 40 5 × 10 = 50 6 × 10 = 60 Let us now construct multiplication tables of 7, 8 and 9. We can then learn to multiply 2-digit numbers. 6.1 I Remember and Understand In multiplication of two numbers: • The number written to the left of the ‘×’ sign is called the multiplicand. • The number written to the right of the ‘×’ sign is called the multiplier. • The number written to the right of the ‘=’ sign is called the product. 70 12/17/2018 4:06:40 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 74

Multiplication Fact ↓↓ ↓ Multiplicand Multiplier Product Note: (a) R epresenting the multiplicand, multiplier and product using the symbols ‘×’ and ‘=’ is called a multiplication fact. (b) T he multiplicand and the multiplier are also Order Property: Changing called the factors of the product. the order in which the numbers are multiplied (c) The product is also called the multiple of both does not change the the multiplicand and the multiplier. product. This is called order For example, 2 × 7 = 14 = 7 × 2; property of multiplication. 4 × 5 = 20 = 5 × 4 and so on. Using multiplication facts and order property, let us now construct the multiplication tables of 7, 8 and 9. 7 8 9 7×1=7 8×1=8 9×1=9 7 × 2 = 14 8 × 2 = 16 9 × 2 = 18 7 × 3 = 21 8 × 3 = 24 9 × 3 = 27 7 × 4 = 28 8 × 4 = 32 9 × 4 = 36 7 × 5 = 35 8 × 5 = 40 9 × 5 = 45 7 × 6 = 42 8 × 6 = 48 9 × 6 = 54 7 × 7 = 49 8 × 7 = 56 9 × 7 = 63 7 × 8 = 56 8 × 8 = 64 9 × 8 = 72 7 × 9 = 63 8 × 9 = 72 9 × 9 = 81 7 × 10 = 70 8 × 10 = 80 9 × 10 = 90 Multiply 2-digit numbers by 1-digit numbers Now, let us learn to multiply a 2-digit number by a 1-digit number. Consider the following example. Example 1: Find the product: 23 × 7 Solution: Follow these steps to find the product. Multiplication 71 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 75 12/17/2018 4:06:40 PM

Steps Solved Solve these Step 1: Multiply the ones. 3 × 7 = 21 H TO Step 2: Regroup the product. 21 ones = 2 tens and 1 ones 17 Step 3: Write the ones digit of ×9 the product in the product TO and carry over the tens digit 2 H TO to the tens place. 23 15 ×7 ×4 Step 4: Multiply the tens. Step 5: Add the carry over 1 from step 3 to the product. Step 6: Write the sum in the 2 × 7 = 14 tens place. 14 + 2 = 16 H TO 2 23 ×7 161 Train My Brain Solve: a) 17 × 7 b) 28 × 9 c) 19 × 8 72 12/17/2018 4:06:40 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 76

Concept 6.2: Multiply 3-digit Numbers by 1-digit and 2-digit Numbers I Think Farida collected some shells and put them into 9 bags. If each bag has 110 shells, how many shells did she collect? 6.2 I Recall We have learnt to multiply a 2-digit number with a 1-digit number. We have also learnt to regroup the ones in multiplication. Multiplication 73 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 77 12/17/2018 4:06:40 PM

Let us answer these to revise the concept. a) 22 × 2 = _________ d) 33 × 4 = _________ b) 42 × 1 = _________ e) 50 × 2 = _________ c) 11 × 7 = _________ f) 45 × 3 = _________ 6.2 I Remember and Understand We multiply 3-digit numbers just as we multiply 2-digit numbers. Multiply 3-digit numbers by 1-digit numbers without regrouping Let us understand the step-by-step procedure through a While multiplying, few examples. always start multiplying the ones of the Example 6: Multiply: 401 × 3 multiplicand by the ones of the multiplier. Solution: Follow these steps to multiply the given numbers. Step 1: Multiply the ones Solved Step 3: Multiply the hundreds Step 2: Multiply the tens H TO Th H T O 401 H TO 401 401 ×3 ×3 3 ×3 1203 03 H TO Solve these H TO 220 232 HTO ×4 13 0 ×3 ×2 Multiply 3-digit numbers by 1-digit numbers with regrouping When a 3-digit number is multiplied by a 1-digit number, we may get a 2-digit product in any or all of the places. We regroup these products and carry over the tens digit of the product to the next place. Let us understand this better through an example. 74 12/17/2018 4:06:40 PM NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 78

Example 7: Multiply: 513 × 5 Solution: Follow these steps to multiply the given numbers. Steps Solved Solve these H TO Step 1: Multiply the ones and write the H TO product under ones. Regroup if the 444 product has two or more digits. 1 3 ×8 5 51 5 ×   Step 2: Multiply the tens. Add the carry H TO H TO over (if any) to the product. Write the sum under tens. 1 342 ×5 Regroup if the product has two or more 513 digits. ×5 65 Step 3: Multiply the hundreds. Add the Th H T O H TO carry over (if any) to the product and write the sum under hundreds. Regroup if 1 635 the product has two or more digits. ×7 513 ×5 2 565 Multiply 3-digit numbers by 2-digit numbers Multiplication of 3-digit numbers by 2-digit numbers may sometimes involve regrouping too. Let us understand this concept through step-by-step procedure. Consider the following examples. Example 8: Multiply: 243 × 34 Solution: Follow these steps to multiply the given numbers. Multiplication 75 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 79 12/17/2018 4:06:40 PM

Steps Solved Solve these Step 1: Arrange the numbers in columns, H TO as shown. H TO 141 243 ×22 Step 2: Multiply the ones of the ×34 multiplicand by the ones digit of the H TO multiplier. 3 × 4 = 12 H TO 453 1 ×13 Write 2 in the ones place of the product. Write 1 in the tens place as the carry over. 243 H TO ×34 263 Step 3: Multiply the tens by the ones digit ×23 of the multiplier. 4 × 4 = 16 2 12/17/2018 4:06:40 PM Add the carry over from the previous H TO step. So, 16 + 1 = 17. Write 7 in the tens 11 place of the product and 1 in the 243 hundreds place as the carry over. ×34 Step 4: Multiply the hundreds by the ones digit of the multiplier. 2 × 4 = 8 72 Add the carry over from the previous H TO step. So, 8 + 1 = 9. Write 9 in the hundreds 11 place of the product. 243 ×34 Step 5: Write 0 in the ones place. 972 Multiply the ones of the multiplicand by HTO the tens digit of the multiplier. Write the 11 product under the tens place. 243 ×3 4 3×3=9 972 Step 6: Multiply the tens by the tens digit 90 of the multiplier. H TO 4 × 3 = 12 1 Write 2 in the hundreds place of the 11 product and 1 in hundreds place of the 243 multiplicand as the carry over. ×34 972 290 76 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 80

Steps Solved Solve these Step 7: Multiply the hundreds by the tens digit of the multiplier. Th H T O H TO 2×3=6 1 352 ×23 Add the carry over from the previous 11 step. So, 6 + 1 = 7. Write 7 in the thousands 243 place of the multiplicand. ×34 972 7290 Step 8: Add the products and write the Th H T O sum. The sum is the required product. 1 11 243 ×34 972 7290 8262 Train My Brain Find the following products: a) 341 × 2 b) 156 × 4 c) 222 × 23 Multiplication 77 NR_BGM_9789388751032 PASSPORT G03 MATHS TEXTBOOK PART 1_Text.pdf 81 12/17/2018 4:06:40 PM

Contents Class Part 2 3 8 Division 15 21 8.1 Division as Equal Grouping 33 8.2 Divide 2-digit and 3-digit Numbers by 1-digit Numbers 79 Fractions 3945016+-x9.1 Fraction as a Part of a Whole 82 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 4 12/17/2018 4:12:36 PM

Chapter Division 8 I Will Learn About • equal grouping and sharing. • repeated subtraction and division facts. • dividing 2-digit number by 1-digit number. • checking the correctness of division. Concept 8.1: Division as Equal Grouping I Think Farida and her brother Piyush got a chocolate bar with 14 pieces for Christmas. Piyush divided it and gave Farida 6 pieces. Do you think Farida got an equal share? How can we find out? 8.1 I Recall In the previous chapter, we have learnt multiplication. Multiplication is finding the total number of objects that have been grouped equally. Let us use this to distribute objects equally in groups. Consider 12 bars of chocolate. The different ways in which they can be distributed are as follows. NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 19 15 12/17/2018 4:12:37 PM

Distributing in 1 group: 1 × 12 = 12 Distributing in 2 groups: 2 × 6 = 12 Distributing in 3 groups: 3 × 4 = 12 Distributing in 4 groups: 4 × 3 = 12 Distributing in 6 groups: 6 × 2 = 12 Distributing in 12 groups: 12 × 1 = 12 Distributing a given number of objects into equal groups is called division. We can understand division better by using equal sharing and equal grouping. 16 12/17/2018 4:12:37 PM NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 20

8.1 I Remember and Understand Equal sharing means having equal number of objects or things in a group. We use division to find the number of things in a group and the number of groups. Suppose 9 balloons are to be shared 1st round: 1 balloon is taken by each equally among 3 friends. Let us use friend. repeated subtraction to distribute the balloons. 9 – 3 = 6. So, 6 balloons remain. 2nd round: From the remaining 6 balloons, 3rd round: From the remaining 3 balloons, 1 more balloon is taken by each friend. 1 more balloon is taken by each friend. Now, each of them has 3 balloons. Now, each friend has 2 balloons. 3 – 3 = 0. So, 0 balloons remain. Each friend gets 3 balloons. 6 – 3 = 3. So, 3 balloons remain. Division 17 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 21 12/17/2018 4:12:37 PM

We can write it as 9 divided by 3 equals 3. The symbol for ‘is divided by’ is ÷. 9 divided by 3 equals 3 is written as ↓ ↓ ↓ Total Number of Number of number of objects in each groups objects group Dividend Divisor Quotient In a division, the number that is divided is called the dividend. The number that divides is called the divisor. The answer in division is called the quotient. The number (part of the dividend) that remains is called the remainder. 9 ÷ 3 = 3 is called a division fact. In this, 9 is the dividend, 3 is the divisor and 3 is the quotient. Note: Representing the dividend, divisor and quotient using the symbols ÷ and = is called a division fact. We use multiplication tables to find the quotient in a division. We find the factor which when multiplied by the divisor gives the dividend. Let us understand this through a few examples. Example 1: 18 pens are to be shared equally by 3 children. How many pens does each of them 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 18 12/17/2018 4:12:37 PM NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 22

Number of vases used = 10 ÷ 2 = 5 (since 5 × 2 = 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 table: Dividend ÷ Divisor = Quotient Multiplicand × Multiplier = Product 6 × 3 = 18 18 ÷ 6 = 3 ↓↓ ↓ ↓↓ ↓ Divisor Quotient Dividend Product Factor Factor (Multiplicand) (Multiplier) 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. Let us now understand this through an activity. We can show a multiplication fact on the number line. For example, 5 × 3 = 15 means 5 times 3 is 15. Division 19 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 23 12/17/2018 4:12:37 PM

To show 5 times 3 on the number line, we take steps of 3 for 5 times. We go forward from 0 to 15. 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 take steps of 3 for 5 times. We go backward from 15 to 0 as shown. Train My Brain Write two multiplication facts for each of the following division facts. a) 20 ÷ 5 = 4 b) 49 ÷ 7 = 7 c) 10 ÷ 2 = 5 20 12/17/2018 4:12:37 PM NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 24

Concept 8.2: Divide 2-digit and 3-digit Numbers by 1-digit Numbers I Think Farida has 732 stickers. She wants to distribute them equally among her three friends. How will she distribute? Division 21 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 25 12/17/2018 4:12:37 PM

8.2 I Recall In the previous section, we have learnt that division is related to multiplication. For every division fact, we can write two multiplication facts. For example, the two multiplication facts of 35 ÷ 7 = 5 are: a) 7 × 5 = 35 and b) 5 × 7 = 35. Let us answer these to recall the concept of division. a) The number which divides a given number is called _________________. b) The answer we get when we divide a number by another is called ______________________. c) The division facts for the multiplication fact 2 × 4 = 8 are ________________ and __________________. 8.2 I Remember and Understand We can make equal shares or groups and divide with the help A number of vertical arrangement. Let us see some examples. divided by the same number is Dividing a 2-digit number by a 1-digit number always 1. (1-digit quotient) Example 7: Solve: 45 ÷ 5 Solution: Follow these steps to divide a 2-digit number by a 1-digit number. Steps Solved Solve these Step 1: Write the dividend and 5)45 Dividend = _____ )divisor as shown: Divisor Dividend Divisor = ______ Quotient = ____ Step 2: Find the multiplication fact 45 = 5 × 9 8) 56 Remainder = _____ which has the dividend and divisor. - Step 3: Write the other factor as the 9 quotient. Write the product of the factors below the dividend. 5)45 − 45 22 12/17/2018 4:12:38 PM NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 26

Steps Solved Solve these Step 4: Subtract the product 9 4) 36 Dividend = _____ from the dividend and write the Divisor = ______ difference below the product. 5)45 - Quotient = ____ This difference is called the Remainder = _____ remainder. − 45 00 45 = Dividend 5 = Divisor 9 = Quotient 0 = Remainder Note: If the remainder is zero, the divisor is said to divide the dividend exactly. Checking for correctness of division: The multiplication fact of the division is used to check its correctness. Step 1: Compare the remainder and divisor. The remainder must always be less than the divisor. Step 2: Check if (Quotient × Divisor) + Remainder = Dividend Let us now check if our division in example 7 is correct or not. Step 1: Remainder < Divisor 0 < 5 (True) Step 2: Quotient × Divisor 9×5 Step 3: (Quotient × Divisor) + Remainder = Dividend 45 + 0 = 45 = Dividend Note: The division is incorrect if: a) Remainder > or = divisor b) (Quotient × Divisor) + Remainder ≠ Dividend 2-digit quotient In the examples we have seen so far, the quotients are 1-digit numbers. In some divisions, the quotients may be 2-digit numbers. Let us see some examples. Example 8: Solve: 57 ÷ 3 Solution: Follow these steps to divide a 2-digit number by a 1-digit number. Division 23 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 27 12/17/2018 4:12:38 PM

Steps Solved Solve these Step 1: Check if the tens digit of the 5>3 5) 60 dividend is greater than the divisor. 1 − Step 2: Divide the tens and write the quotient. 3)57 − Write the product of quotient and divisor, −3 below the tens digit of the dividend. Step 3: Subtract and write the difference. 1 Dividend = _____ Divisor = ______ Step 4: Check if difference < divisor is true. 3)57 Quotient = ____ Step 5: Bring down the ones digit of the Remainder = ___ dividend and write it beside the remainder. −3 2 2 < 3 (True) 1 3)57 − 3↓ 27 Step 6: Find the largest number in the 3 × 8 = 24 1 multiplication table of the divisor that can )3 × 9 = 27 3 57 be subtracted from the 2-digit number in )3 × 10 = 30Tra−in3↓My Brain the previous step. 24 < 27 < 30. 27 3 42 So, 27 is the − required number. Step 7: Write the factor of required number, 19 − other than the divisor, as the quotient. Write the product of the divisor and the quotient 3)57 below the 2-digit number. Subtract and write the difference. − 3↓ 27 − 27 00 24 12/17/2018 4:12:38 PM NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 28

Steps Solved Solve these Step 8: Check if remainder < divisor is true. 0 < 3 (True) Stop the division. Dividend = _____ Divisor = ______ (If this is false, the division is incorrect.) Quotient = 19 Quotient = ____ Step 9: Write the quotient and the Remainder = 0 Remainder = ___ remainder. Step 10: Check if (Divisor × Quotient) + 3 × 19 + 0 = 57 Remainder = Dividend is true. 57 + 0 = 57 57 = 57 (True) (If this is false, the division is incorrect.) Divide 3-digit numbers by 1-digit numbers (2-digit quotient) Dividing a 3-digit number by a 1-digit number is similar to dividing a 2-digit number by a 1-digit number. Let us understand this through a few examples. Example 9: Solve: a) 265 ÷ 5 Solution: Follow these steps to divide a 3-digit number by a 1-digit number. Steps Solved Solve these Step 1: Check if the hundreds digit of 4) 244 the dividend is greater than the divisor. 5)265 − If it is not, consider the tens digit too. 2 is not greater than 5. So, consider 26. Step 2: Find the largest number that 5 − can be subtracted from the 2-digit number of the dividend. Write the 5)265 Dividend = _____ quotient. Divisor = ______ Write the product of the quotient and − 25 Quotient = ____ the divisor below the dividend. Remainder = ___ 5 × 4 = 20 Step 3: Subtract and write the 5 × 5 = 25 difference. 5 × 6 = 30 25 < 26 5 5)265 − 25 1 Division 25 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 29 12/17/2018 4:12:38 PM

Steps Solved Solve these 1 < 5 (True) Step 4: Check if difference < divisor 9) 378 is true. (If it is false, the division is incorrect.) − Step 5: Bring down the ones digit 5 − of the dividend. Write it beside the remainder. 5)265 Dividend = _____ Divisor = ______ Step 6: Find the largest number in the − 25↓ Quotient = ____ multiplication table of the divisor that 15 Remainder = ___ can be subtracted from the 2-digit number in the previous step. 5 5) 245 Step 7: Write the factor of required 5)265 − number, other than the divisor, as quotient. Write the product of divisor − 25↓ − and quotient below the 2-digit 15 number. Then, subtract them. Dividend = _____ 5 × 2 = 10 Divisor = ______ Step 8: Check if remainder < divisor is 5 × 3 = 15 Quotient = ____ true. Stop the division. (If this is false, 5 × 4 = 20 Remainder = ___ the division is incorrect.) 15 is the required number. 53 5)265 − 25↓ 15 − 15 00 0 < 5 (True) Step 9: Write the quotient and Quotient = 53 remainder. Remainder = 0 Step 10: Check if (Divisor × Quotient) + 5 × 53 + 0 = 265 Remainder = Dividend is true. (If this is 265 + 0 = 265 false, the division is incorrect.) 265 = 265 (True) 26 12/17/2018 4:12:38 PM NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 30

3-digit quotient Example 10: Solve: 784 by 7 Solution: Follow these steps to divide a 3-digit number by a 1-digit number. Steps Solved Solve these Step 1: Check if the hundreds digit of the dividend is greater than or equal to the 7)784 8) 984 divisor. Step 2: Divide the hundreds and write the 7=7 − quotient in the hundreds place. 1 Write the product of the quotient and the − divisor under the hundreds place of the 7)784 dividend. − Step 3: Subtract and write the difference. −7 Dividend = _____ Step 4: Check if difference < divisor is true. 1 Divisor = ______ Step 5: Bring down the next digit of the Quotient = ____ dividend. Check if it is greater than or 7)784 Remainder = ___ equal to the divisor. −7 5) 965 Step 6: Find the largest number in the 0 multiplication table of the divisor that can − be subtracted from the 2-digit number in 0 < 7 (True) the previous step. 1 − Write the factor other than the divisor as quotient. 7)7 84 − Write the product of the quotient and the divisor below it. − 7↓ 08 8>7 11 7)784 − 7↓ 08 −7 7×1=7<8 The required number is 7. Division 27 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 31 12/17/2018 4:12:38 PM

Steps Solved Solve these Step 7: Subtract and write the difference. 11 Dividend = _____ Bring down the next digit (ones digit) of the Divisor = ______ dividend. 7)784 Quotient = ____ Remainder = ___ Check if the dividend is greater than or − 7↓ equal to the divisor. 08 2) 246 −7 − 14 − − Step 8: Find the largest number in the 14 > 7 multiplication table of the divisor that can Dividend = _____ be subtracted from the 2-digit number in 112 Divisor = ______ the previous step. Quotient = ____ 7)784 Remainder = ___ Write the factor other than the divisor as the quotient. − 7↓ 08 Write the product of the quotient and the divisor below it. −7 14 − 14 Step 9: Subtract and write the difference. 7 × 2 = 14 The required Check if it is less than the divisor. Stop the number is 14. division. 112 7)784 − 7↓ 08 −7 14 − 14 00 Step 10: Write the quotient and the Quotient = 112 remainder. Remainder = 0 Step 11: Check if (Divisor × Quotient) + Remainder = Dividend is true. (If it is false, 7 × 112 + 0 = 784 the division is incorrect.) 784 + 0 = 784 784 = 784 (True) 28 12/17/2018 4:12:38 PM NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 32

Train My Brain Solve the following: a) 12 ÷ 4 b) 648 ÷ 8 c) 744 ÷ 4 Division 29 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 33 12/17/2018 4:12:38 PM

Chapter Fractions 9 I Will Learn About • fractions as a part of a whole and their representation. • identify parts of fractions. • fractions of a collection. • applying the knowledge of fractions in real life. Concept 9.1: Fraction as a Part of a Whole I Think Farida and her three friends, Joseph, Salma and Rehan, went on a picnic. Farida had only one apple with him. He wanted to share it equally with everyone. What part of the apple does each of them get? 9.1 I Recall Look at the rectangle shown below. We can divide the whole rectangle into many equal parts. Consider the following: NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 37 33 12/17/2018 4:12:38 PM

1 part: 2 equal parts: 3 equal parts: 4 equal parts: 5 equal parts: and so on. Let us understand the concept of parts of a whole through an activity. 9.1 I Remember and Understand Suppose we want to share an apple with our friends. First, we count our friends with whom we want to share the apple. Then, we cut it into as many equal pieces as the number of persons. Thus, each person gets an equal part of the apple after division. Parts of a whole A complete or full object is called a whole. Observe the following parts of a chocolate bar: whole 2 equal parts 3 equal parts 4 equal parts We can divide a whole into equal parts as shown above. Each such division has a different name. To understand this better, let us do an activity. 34 12/17/2018 4:12:38 PM NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 38

Activity: Halves Take a square piece of paper. Fold it into two equal parts as shown. Each of the equal parts is called a ‘half’. ‘Half’ means 1 out of 2 equal parts. Putting these 2 equal parts together makes the complete piece of paper. We write ‘1 out of 2 equal parts’ as 1 . 2 In 1 , 1 is the number of parts taken and 2 is the total number of equal parts the whole 2 is divided into. Note: 1 and 1 make a whole. 2 2 Thirds In figure (a), observe that the three parts are not equal. We can also divide a whole into three equal parts. Fold a rectangular piece of paper as shown in figures (b) and (c). 11 1 33 3 three parts three equal parts Fig. (c) Fig. (a) Fig. (b) Each equal part is called a third or one-third. The shaded part in figure (c) is one out of three equal parts. So, we call it a one-third. Two out of three equal parts of figure (c) are not shaded. We call it two-thirds (short form of 2 one-thirds). We write one-third as 1 and two-thirds as 2 . 3 3 Note: 1 , 1 and 1 or 1 and 2 makes a whole. 3 3 3 3 3 Fractions 35 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 39 12/17/2018 4:12:38 PM

Fourths Similarly, fold a square piece of paper into four equal parts. Each of them is called a fourth or a quarter. In figure (d), the four parts are not equal. In figure (e), each equal part is called a fourth or a quarter and is written as 1 . 4 1 4 1 4 1 4 1 Four parts Fig. (d) 4 Four equal parts Fig. (e) Two out of four equal parts are called two-fourths and three out of four equal parts are called three-fourths, written as 2 and 3 respectively. 44 Note: Each of 1 and 3; 1 , 1 , 1 and 1 and 1 , 1 and 2 make a whole. 4 4 444 4 44 4 The total number of equal parts a whole is divided into is called the denominator. The number of such equal parts taken is called the numerator. Representing the parts of a whole as  Numerator  is called a fraction. Thus, a fraction is a part of a whole.  Denominator  For example, 1 , 1, 1, 2 and so on are fractions. 2 3 4 3 36 12/17/2018 4:12:38 PM NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 40

Let us now see a few examples. Example 1: Identify the numerator and denominator in Numbers of the form Numerator are each of the following fractions: Denominator a) 1 b) 1 c) 1 2 3 4 called fractions. Solution: S. No Fractions Numerator Denominator a) 1 1 2 2 b) 1 1 3 3 c) 1 1 4 4 Example 2: Identify the fraction for the shaded parts in the figures below. a) b) Solution: Steps Solved Solve this a) b) Step 1: Count the number of equal parts, the figure is divided into Total number of Total number of equal (Denominator). parts = _______ equal parts = 8 Number of parts shaded Step 2: Count the number of Number of parts = ______ shaded parts (Numerator). shaded = 5 Fraction = Step 3: Write the fraction Fraction = 5  Numerator  . 8  Denominator  Fractions 37 NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 41 12/17/2018 4:12:38 PM

Example 3: The circular disc shown in the figure is divided into equal parts. What fraction of the disc is painted yellow? Write the fraction of the disc that is painted white. Solution: Total number of equal parts of the disc is 16. The fraction of the disc that is painted yellow = Number of parts painted yellow = 3 Total number of equal parts 16 The fraction of the disc that is painted white = Number of parts painted white = 7 Total number of equal parts 16 Example 4: Find the fraction of parts that are not shaded in the following figures. a) b) c) Solution: We can find the fractions as: Steps Solved Solve these a) b) c) Total number of equal parts 2 Number of parts not shaded 1 Number of parts not shaded 1 2 Fraction = Total number of equal parts Train My Brain Identify the fraction of the shaded parts in the given figures. a) b) c) 38 12/17/2018 4:12:38 PM NR_BGM_9789388751070 PASSPORT G03 MATHS TEXTBOOK PART 2_Text.pdf 42