PASSPORT G04 MATHS TEXTBOOK_Combine

MATHEMATICS TEXTBOOK – Grade 4 Name: _________________________ Section: ________Roll No: _______ School: ________________________

Part 1 Class 4 Addition and Subtraction 4 4.1 Add and Subtract 5-digit Numbers 39 46 5 Multiplication 75 5.1 Multiply 3-digit and 4-digit Numbers 7 Division 7.1 Divide Large Numbers

Chapter Addition and 4 Subtraction I Will Learn About • adding and subtracting 5-digit numbers. • applying addition and subtraction operations in real-life situations. Concept 4.1: Add and Subtract 5-digit Numbers I Think In Jasleen’s town, there were 27023 adults and 1567 children. 1400 adults and 1200 children went out of the town on 23rd March 2015. What was the total population of the town on 23rd March? What was the population on the 22nd, if all of them were present in the town that day? Can you also solve it? 4.1 I Recall We know the addition and subtraction of 4-digit numbers. Let us recall the steps followed. Step 1: A rrange the numbers one below the other according to their places. For subtraction, ensure that the smaller number is placed below the larger number. 39

Step 2: Start adding or subtracting from the ones place. Step 3: At every stage, see if regrouping is required and then add or subtract. Step 4: Write the answer. Solve the following to revise the concept. a) Th H T O b) Th H T O c) Th H T O 4216 1335 5985 +1 2 5 9 +1 2 3 5 +2 4 5 3 d) Th H T O e) Th H T O f) Th H T O 7452 4322 6200 –1 3 2 3 –1 4 7 2 –4 5 0 0 4.1 I Remember and Understand Addition or subtraction of large numbers is similar to the addition or Always begin subtraction of 4-digit numbers. addition and subtraction from Let us see an example of addition involving 5-digit numbers. the ones place. Example 1: Add: 48415 + 20098 Solution: Arrange the numbers one below the other. Steps Solved Solve these T Th Th H T O Step 1: Add the tens and ones. T Th Th H T O Write the sum under the ones. Regroup if needed. 1 4 8415 5 7383 +3 1347 +2 0098 3 40

Steps Solved Solve these Step 2: Add the tens and also T Th Th H T O T Th Th H T O the carry forward (if any) from the previous step. Write the 11 2 5347 sum under the tens. Regroup if + 6 2567 needed. 4 8415 +2 0098 513 Step 3: Add the hundreds T Th Th H T O T Th Th H T O and also the carry forward (if any) from the previous 11 4 2688 step. Write the sum under + 1 2912 the hundreds. Regroup if 4 8415 needed. +2 0098 513 Step 4: Add the thousands T Th Th H T O T Th Th H T O and also the carry forward 11 (if any) from the previous 3 4765 step. Write the sum under 4 8415 + 2 1178 the thousands. Regroup if +2 0098 needed. 8513 Step 5: Add the ten thousands T Th Th H T O T Th Th H T O and also the carry forward (if any) from the previous step. 11 8 2633 Write the sum under the ten + 1 0120 thousands. 4 8415 Thus, 48415 + 20098 = 68513. +2 0098 6 8513 We will now learn subtraction of 5-digit numbers. Example 2: Subtract: 56718 – 16754 Solution: Arrange the numbers in columns. Addition and Subtraction 41

Steps Solved Solve these T Th Th H T O T Th Th H T O Step 1: Subtract the ones and write the difference under the 5 6718 9 7054 ones. −1 6754 – 2 3567 4 T Th Th H T O 7 5400 Step 2: Subtract the tens. That is, T Th Th H T O 1 − 5, which is not possible. – 3 2689 5 6⁄ 1⁄1 Regroup the hundreds to −1 T Th Th H T O tens, subtract and write the 6718 8 5464 difference under the tens. 6754 – 1 2078 64 T Th Th H T O Step 3: Subtract the hundreds. T Th Th H T O 5 4635 That is, 6 − 7, which is not possible. 1⁄6 – 1 2789 5⁄ 6⁄ 1⁄1 Regroup the thousands to T Th Th H T O hundreds, subtract and write the 5 6718 8 9576 difference under the hundreds. −1 6754 – 4 5689 964 Step 4: Subtract the thousands. T Th Th H T O That is, 5 − 6, which is not possible. 4 165⁄⁄5 167⁄⁄6 11⁄1 8 5 Regroup the ten thousands to thousands, subtract and −1 6754 write the difference under the thousands. 9964 Step 5: Subtract the ten T Th Th H T O thousands, and write the difference under the ten 54⁄ 165⁄⁄5 167⁄⁄6 11⁄1 8 thousands −1 6754 Thus, 56718 – 16754 = 39964. 3 9964 42

Train My Brain Solve the following: b) 45601 + 11419 c) 42363 – 18945 a) 34567 + 27092 Addition and Subtraction 43

Chapter Multiplication 5 I Will Learn About • multiplying 3-digit and 4-digit numbers. • properties of multiplication. • multiplying using standard and lattice algorithms. • multiplying mentally. Concept 5.1: Multiply 3-digit and 4-digit Numbers I Think Jasleen went to the stadium to watch a rugby match with her parents. She observed that the seats are arranged in many rows and columns. All the seats were occupied. She wanted to guess the total number of people who watched the match that day. How will she be able to do that? 5.1 I Recall We have learnt to multiply 2-digit and 3-digit numbers by 1-digit and 2-digit numbers. 46

Let us solve the following to revise the concept of multiplication. TO H TO H TO H TO 39 256 589 875 ×2 ×3 ×4 ×5 5.1 I Remember and Understand Let us now learn to multiply 3-digit numbers by 3-digit numbers Standard algorithm is the and 4-digit numbers by 1-digit numbers. method of multiplication in which the product is Multiply a 3-digit number by a 3-digit number regrouped as ones and tens. Multiplying a 3-digit number by a 3-digit number is similar to multiplying a 3-digit number by a 2-digit number. Let us see an example. Example 1: Multiply: 159 × 342 Solution: To multiply the given numbers, follow these steps. Steps Solved Solve these Step 1: Multiply the multiplicand by the ones of the Th H T O T Th Th H T O multiplier, 11 526 159 that is, 159 × 2. ×235 ×342 Regroup if necessary. 318 Step 2: Put a 0 below the ones Th H T O place of the product obtained 23 in the above step. Multiply the multiplicand by the tens of the 11 multiplier, that is, 159 × 4. 159 ×342 Regroup if necessary. 318 6360 Multiplication 47

Steps Solved Solve these Step 3: Put two 0s below the T Th Th H T O ones and the tens places of T Th Th H T O the product obtained in the 425 previous step. Multiply the 12 ×119 multiplicand by the hundreds of the multiplier, that is, 159 × 3. 23 T Th Th H T O Regroup if necessary. 301 11 Step 4: Add the products from 159 ×769 steps 1, 2 and 3. This sum gives ×342 the required product. 318 6360 4 7700 T Th Th H T O 12 23 11 159 ×342 1 1 3 1 8 + 6360 + 4 7 7 0 0 54 378 Multiply a 4-digit number by a 1-digit number Multiplying a 4-digit number by a 1-digit number is similar to multiplying a 3-digit number by a 1-digit number. Let us see an example. Example 2: Multiply: 3628 × 7 Solution: T Th Th H T O 4 15 3 628 ×7 2 5 396 48

Th H T O Solve these Th H T O Th H T O 2568 1259 ×8 5689 ×4 ×2 Properties of Multiplication Identity Property: For any number ‘a’, a × 1 = 1 × a = a. 1 is called the multiplicative identity. For example, 461 × 1 = 1 × 461 = 461. Zero Property: For any number ‘a’, a × 0 = 0 × a = 0. For example, 568 × 0 = 0 × 568 = 0. Commutative Property: If ‘a’ and ‘b’ are any two numbers, then a × b = b × a. For example, 12 × 3 = 36 = 3 × 12. Associative Property: If ‘a’, ‘b’ and ‘c’ are any three numbers, then a × (b × c) = (a × b) × c. For example, 3 × (4 × 5) (3 × 4) × 5 3 × 20 12 × 5 60 60 (3 × 4) × 5 = 3 × (4 × 5) Distributive Property: 1) If 'a', 'b' and 'c' are any three numbers, then: a × (b + c) = (a × b) + (a × c). For example, 2 × (3 + 5) = (2 × 3) + (2 × 5). 2 × 8 = 6 + 10 16 = 16 Multiplication distributes over addition. Multiplication 49

2) If 'a', 'b' and 'c' are any three numbers then: a × (b − c) = (a × b) − (a × c). For example, 2 × (8 − 5) = (2 × 8) − (2 × 5). 2 × 3 = 16 − 10 6 = 6 Multiplication distributes over subtraction. Train My Brain Solve the following: a) 222 × 333 b) 692 × 132 c) 5632 × 4 50

Chapter Division 7 I Will Learn About • dividing 4-digit numbers by 1-digit and 2-digit numbers. • dividing 3-digit numbers by 2-digit numbers. • properties of division. Concept 7.1: Divide Large Numbers I Think Jasleen and seven of her friends want to share 3540 papers equally among themselves. Do you think the papers can be divided, without some being left over? 7.1 I Recall Recall that we can write two multiplication facts for a division fact. For example, a multiplication fact for 45 ÷ 9 = 5 can be written as 9 × 5 = 45 or 5 × 9 = 45. 45 ÷ 9 = 5 ↓ ↓ ↓ Dividend Divisor Quotient The number that is divided is called the dividend. The number that divides is called the divisor. The number of times the divisor divides the dividend is called the quotient. 75

Factors Factors Multiplicand × Multiplier = Product Multiplicand × Multiplier = Product 5 × 9 = 45 9 × 5 = 45 ↓ ↓ ↓ ↓ ↓ ↓ Divisor Quotient Dividend Divisor Quotient Dividend The part of the dividend that remains without being divided is called the remainder. Let us solve the following to revise the concept of division. a) 72 ÷ 9 b) 42 ÷ 3 c) 120 ÷ 5 d) 80 ÷ 4 e) 24 ÷ 1 7.1 I Remember and Understand In Class 3, we have learnt that division means equal sharing and equal grouping of things. Let us now understand the division of large numbers. Division and Division of a 4-digit number by a 1-digit number multiplication are Dividing a 4-digit number by a 1-digit number is similar to that of a reverse operations. 3-digit number by a 1-digit number. Example 1: Solve: 2065 ÷ 5 Solution: Steps Solved Solve these Step 1: Check if the thousands digit of the )5 2065 )7 3748 dividend is greater than the divisor. If it is not, consider the hundreds digit also. 2 is not greater than 5. So, consider 20. Step 2: Find the largest number in the 4 multiplication table of the divisor that can be subtracted from the 2-digit number of )5 2065 the dividend. Write the quotient. Write the product of the quotient and divisor below -2 0 the dividend. 5 × 4 = 20 5 × 5 = 25 25 > 20 Step 3: Subtract and write the difference. 4 Dividend = _____ Divisor = ______ )5 2065 Quotient = ____ Remainder = ___ -20 0 76

Steps Solved Solve these Step 4: Check if difference < 0 < 5 (True) divisor is true. )3 2163 4 If it is false, the division is incorrect. Dividend = _____ Step 5: Bring down the tens digit of the )5 2065 Divisor = ______ dividend and write it near the remainder. Quotient = ____ −20↓ Remainder = ___ 06 )5 1555 Step 6: Find the largest number in the 5×1=5 multiplication table of the divisor that can 5 × 2 = 10 Dividend = _____ be subtracted from the 2-digit number in 5 < 6 < 10 Divisor = ______ the previous step. So, 5 is the required Quotient = ____ number. Remainder = ___ Step 7: Write the factor of the required 41 number, other than the divisor, as the quotient. )5 2 0 6 5 Write the product of the divisor and the − 20 ↓ quotient below the 2-digit number. 06 Then subtract them. − 05 01 Step 8: Repeat steps 6 and 7 till all the digits 1 < 5 (True) of the dividend are brought down. 4 13 Check if remainder < divisor is true. )5 2 0 6 5 Stop the division. (If this is false, the division is incorrect.) −2 0 ↓ 06 − 05 0 15 − 015 000 Step 9: Write the quotient and the Quotient = 413 remainder. Remainder = 0 Step 10: Check if (Divisor × Quotient) + 5 × 413 + 0 = 2065 Remainder = Dividend is true. If this is false, 2065 + 0 = 2065 the division is incorrect. 2065 = 2065 (True) Division 77

Division of a 3-digit number by a 2-digit number Let us understand the division of 3-digit numbers by 2-digit numbers, through some examples. Example 2: Divide: 414 ÷ 12 Solution: )Write the dividend and the divisor as Divisor Dividend Steps Solved Solve these Step 1: Guess the quotient by thinking of )12 414 dividing 41 by 12. )14 324 Find the multiplication fact which has 12 × 3 = 36 the number less than or equal to the 12 × 4 = 48 dividend and the divisor. 36 < 41 < 48 So, 36 is the number to be subtracted from 41. Step 2: Write the factor other than the Write 3 in the quotient and Dividend = _____ dividend and the divisor as the quotient. 36 below 41, and subtract. Divisor = ______ Quotient = ____ Then bring down the next Remainder = ___ number in the dividend. 3 )12 414 −36 ↓ 054 Step 3: Guess the quotient by thinking of 12 × 4 = 48 dividing 54 by 12. 12 × 5 = 60 )16 548 Find the multiplication fact which has 48 < 54 < 60 Dividend = _____ the number less than or equal to the So, 48 is the number to be Divisor = ______ dividend and divisor. Write the factor subtracted from 54. Quotient = ____ other than the dividend and the divisor Remainder = ___ as the quotient. Write 4 in the quotient and 48 below 54, and subtract. 34 )12 414 −36 ↓ 054 − 048 6 Quotient = 34 Remainder = 6 78

Checking for the correctness of division: We can check whether our division is correct or not using a multiplication fact of the division. Step 1: Compare the remainder and the divisor. [Note: 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 2 is correct. Steps Checked Step 1: Remainder < Divisor Dividend = 414 Step 2: (Quotient × Divisor) + Divisor = 12 Remainder = Dividend Quotient = 34 Remainder = 6 6 < 12 (True) 34 × 12 + 6 = 414 408 + 6 = 414 414 = 414 (True) Note: a) If remainder > divisor, the division is incorrect. b) If (Quotient × Divisor) + Remainder is not equal to Dividend, the division is incorrect. Dividing a 4-digit number by a 2-digit number Dividing a 4-digit number by a 2-digit number is similar to dividing a 3-digit number by a 2-digit number. Let us understand this through the following example. Example 3: Solve: 2340 ÷ 15 Solution: Steps Solved Solve these Step 1: Check if the thousands digit 2 is not greater than 15. So, )12 5088 of the dividend is greater than the consider 23. divisor. If it is not, consider also the hundreds digit too. )15 2340 Division 79

Steps Solved Solve these Step 2: Guess the quotient by 1 Dividend = _____ thinking of dividing 23 by 15. Divisor = ______ )15 2340 Quotient = _____ Remainder = _____ Find the multiplication fact which has −15 )14 4874 a number less than or equal to the 15 × 1 = 15 dividend and the divisor. 15 × 2 = 30 15 < 23 < 30 So, 15 is the required number. Step 3: Write the factor other than Write 1 in the quotient and 15 the dividend and the divisor as the below 23 and subtract. Then quotient. bring down the next number in the dividend. )1 15 2340 −15 ↓ 84 Step 4: Guess the quotient by 15 × 5 = 75 thinking of dividing 84 by 15. 15 × 6 = 90 Find the multiplication fact which has 75 < 84 < 90 Dividend = _____ a number less than or equal to the Divisor = ______ So, 75 is the required number Quotient = _____ dividend and the divisor. Remainder = _____ that is to be subtracted from Write the factor other than the dividend and the divisor as the 84. 156 quotient. )15 2340 − 15↓ 84 − 75 9 80

Steps Solved Solve these Step 5: Subtract and write the 15 × 5 = 75 )16 3744 difference. Repeat till all the digits of 15 × 6 = 90 the dividend are brought down. 90 = 90 So, 90 is the required number. 156 )15 2340 − 15↓ Dividend = _____ 84 Divisor = ______ Quotient = _____ − 75 90 − 90 00 Quotient = 156 Remainder = 0 Step 6: Check if (Divisor × Quotient) + 15 × 156 + 0 = 2340 Remainder = _____ Remainder = Dividend is true. If this is 2340 + 0 = 2340 false, the division is incorrect. 2340 = 2340 (True) Let us see some properties of division. Properties of division 1) D ividing a number by 1 gives the same number as the quotient. For example: 15 ÷ 1 = 15; 1257 ÷ 1 = 1257; 1 ÷ 1 = 1; 0 ÷ 1 = 0 2) D ividing a number by itself gives the quotient as 1. For example: 15 ÷ 15 = 1; 1257 ÷ 1257 = 1; 1 ÷ 1 = 1 3) D ivision by zero is not possible and is not defined. For example: 10 ÷ 0; 1257 ÷ 0; 1 ÷ 0 are not defined Train My Brain Solve the following: a) 2868 ÷ 4 b) 7890 ÷ 12 c) 723 ÷ 15 Division 81

Contents Class 4 Part 2 8 Fractions - I 8.1 Equivalent Fractions�����������������������������������������������������������������������������������������������������1 8.3 Add and Subtract Like Fractions ..............................................................................10 0 710 Decimals 39456+-x10.1 Conversion Involving Fractions ��������������������������������������������������������������������������������30 82 NR_BGM_9789388751193 PASSPORT G04 MATHS TEXTBOOK PART 2_Text.pdf 4 12/17/2018 4:34:54 PM

Chapter Fractions - I 8 I Will Learn About • equivalent fractions. • problems related to equivalent fractions. • like and unlike fractions. • adding and subtracting like fractions. Concept 8.1: Equivalent Fractions I Think Jasleen cuts 3 apples into 18 equal pieces. Ravi cuts an apple into 6 equal pieces. Did both of them cut the apples into equal pieces? 8.1 I Recall In Class 3, we have learnt that a fraction is a part of a whole. A whole can be a region or a collection. When a whole is divided into two equal parts, each part is called ‘a half’. 11 22 ‘Half’ means 1 out of 2 equal parts. We write ‘half’ as 1 . 2 NR_BGM_9789388751193 PASSPORT G04 MATHS TEXTBOOK PART 2_Text.pdf 5 1 12/17/2018 4:34:54 PM

Two halves make a whole. Numerator Numbers of the form Denominator are called fractions. The total number of equal parts into which a whole is divided is called the denominator. The number of such equal parts taken is called the numerator. Similarly, each of the three equal parts of a whole is called a third. We write one-third as 1 and, two-thirds as 2 . 33 Three-thirds or 3 make a whole. 3 Each of four equal parts of a whole is called a fourth or a quarter written as 1 . 4 Two such equal parts are called two-fourths, and three equal parts are called three-fourths, written as 2 and 3 respectively. Four quarters make a whole. 44 2 halves, 3 thirds, 4 fourths, 5 fifths, …, 10 tenths make a whole. So, we write a whole as 2 , 3 , 4 , 5 ,...,10 and so on. 2 3 4 5 10 8.1 Fractions that denote I Remember and Understand the same part of a whole are called Let us now understand what equivalent fractions are. equivalent fractions. Suppose there is 1 bar of chocolate with Ram and Raj each as shown. chocolate with Ram chocolate with Raj Ram eats 1 of the chocolate. 5 Then the piece of chocolate he gets is Raj eats 2 of the chocolate. 10 Then the piece of chocolate he gets is We see that both the pieces of chocolates are of the same size. So, we say that the fractions 1 5 and 2 are equivalent. We write them as 1 = 2 . 10 5 10 2 12/17/2018 4:34:55 PM NR_BGM_9789388751193 PASSPORT G04 MATHS TEXTBOOK PART 2_Text.pdf 6

Example 1: Shade the regions to show equivalent fractions. [ 1 and 2 ] a) 36 b) [ 1 and 2 ] 48 Solution: a) 1 3 2 6 b) 1 4 2 8 Example 2: Find the figures that represent equivalent fractions. Also, mention the fractions. a) b) c) d) Solution: The fraction represented by the shaded part of figure a) is 1 . 2 The shaded part of figure b) represents 2 . The shaded part of figure d) 4 represents 1 . 2 So, the shaded parts of figures a), b) and d) represent equivalent fractions. Fractions - I 3 NR_BGM_9789388751193 PASSPORT G04 MATHS TEXTBOOK PART 2_Text.pdf 7 12/17/2018 4:34:55 PM

Train My Brain Answer the following: a) How many thirds make a whole? b) Are 1 and 3 equivalent? 55 c) What is the value of 8 eighths? 4 12/17/2018 4:34:55 PM NR_BGM_9789388751193 PASSPORT G04 MATHS TEXTBOOK PART 2_Text.pdf 8

Concept 8.3: Add and Subtract Like Fractions I Think Jasleen has a cardboard piece, equal parts of which are coloured in different colours. Some of the equal parts are not coloured. She wants to find the part of the cardboard that has been coloured and left uncoloured. How do you think Jasleen can find that? Train My Brain 8.3 I Recall Recall that like fractions have the same denominators. To compare them, we compare their numerators. Let us answer the following to recall the concept of like fractions. Compare the following using >, < and =. a) 2 ____ 1 b) 4 ____ 8 c) 3 ____ 5 d) 7 ____ 3 e) 1 ____ 4 33 10 10 77 88 55 10 12/17/2018 4:34:55 PM NR_BGM_9789388751193 PASSPORT G04 MATHS TEXTBOOK PART 2_Text.pdf 14

8.3 I Remember and Understand Let us understand addition and subtraction of like fractions through some examples. Example 13: In the given figures, find the fractions While adding or subtracting represented by the shaded parts like fractions, add or subtract using addition. Then find the fractions only their numerators. Write represented by the unshaded parts using the sum or difference on the subtraction. same denominator. a) b) c) Solution: Solved Solve these Steps Step 1: Count the total Total number of equal Total number of Total number of number of equal parts. equal parts = ____ parts = 6 equal parts = ___ Step 2: Count the a) N umber of parts a) N umber of parts a) N umber of parts number of parts of each coloured pink = 1 coloured yellow coloured violet = colour. = ______ _______ b) N umber of parts coloured blue = 2 b) N umber of parts b) N umber of parts coloured violet = coloured brown _______ = ______ Step 3: Write the fraction Pink: 1 , Blue: 2 Yellow: ________ Violet: ________ representing the number 66 Violet: ________ Brown: ________ of parts of each colour. Fractions - I 11 NR_BGM_9789388751193 PASSPORT G04 MATHS TEXTBOOK PART 2_Text.pdf 15 12/17/2018 4:34:55 PM

Solved Solve these Steps Step 4: To add the like The fraction that The fraction that The fraction that fractions in step 3, add represents the their numerators and represents the shaded represents the shaded part of the write the sum on the given figure is same denominator. part of the given shaded part of the ____ + ____=____. figure is given figure is 1 + 2 = 1+ 2 = 3 . ____ + ____=____. 66 6 6 Step 5: Write the whole Like fraction Like fraction Like fraction representing the representing the as a like fraction of the representing the whole = 6 . whole = _______. whole = _______. sum in step 4. Then, to 6 So, the fraction So, the subtract the like fractions, that represents the subtract their numerators. So, the fraction unshaded part of fraction that Write the difference on that represents the the given figure is represents the the same denominator. unshaded part of the unshaded part of given figure is ____ − ____=____. the given figure is 6−3 =6−3 = 3. ____ − ____=_____. 66 6 6 Example 14: Add: a) 3 + 1 45 23 57 Solution: 88 b) + c) + a) 3 + 1 = 3 + 1 = 4 13 13 100 100 Example 15: 88 8 8 c) 48 – 26 Solution: b) 4 + 5 = 4 + 5 = 9 125 125 13 13 13 13 c) 23 + 57 = 23 + 57 = 80 100 100 100 100 Subtract: a) 8 – 4 b) 33 – 25 99 37 37 a) 8 – 4 = 4 99 9 33 25 = 33 − 25 = 8 b) – 37 37 37 37 48 26 48 − 26 22 c) – = = 125 125 125 125 12 NR_BGM_9789388751193 PASSPORT G04 MATHS TEXTBOOK PART 2_Text.pdf 16 12/17/2018 4:34:55 PM

Train My Brain Solve: b) 3 + 1 c) 11 − 3 a) 1 + 2 34 34 15 15 99 Fractions - I 13 NR_BGM_9789388751193 PASSPORT G04 MATHS TEXTBOOK PART 2_Text.pdf 17 12/17/2018 4:34:55 PM

Chapter Decimals 10 I Will Learn About • the term ‘decimal’ and its parts. • understanding decimal system. • expanding decimal numbers with place value charts. • converting fractions to decimals and vice versa. Concept 10.1: Conversion Involving Fractions I Think Jasleen and her friends participated in the long jump event in their Jasleen – 4.1m Ravi – 2.85m games period. Her sports teacher noted the distance they jumped on Rajiv – 3.05 m a piece of paper as shown here. Amit – 2.50m Jasleen wondered why the numbers had a point between them as in the case of writing money. Do you know what the point means? 10.1 I Recall Recall that in Class 3 we have learnt to measure the lengths, weights and volumes of objects. 30 12/17/2018 4:34:56 PM NR_BGM_9789388751193 PASSPORT G04 MATHS TEXTBOOK PART 2_Text.pdf 34

For example, a pencil is 12.5 cm long. 12. 5 cm A crayon is 5.4 cm long. 5.4 cm The weight of your mathematics textbook is 0.905 kg. A milk packet has 0.250 of milk, and so on. In all these values, we see numbers with a point between them. Have you read price tags on some items when you go shopping? ` 300.75 ` 439.08 They also have numbers with a point between them. Let us learn why a point is used in such numbers. 10.1 I Remember and Understand We know how to write fractions. In this figure, 3 portion is coloured and 7 portion is not coloured. 10 10 3 or 0.3 and the We can write the coloured portion of the figure as 10 portion that is not coloured as 7 or 0.7. 10 Numbers such as 0.3, 0.7, 3.0, 3.1, 4.7, 58.2 and so on are called decimal numbers or simply decimals. Tenths: The figure below is divided into ten equal parts. 1 111 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 Each column is of the same size. Then, each of the ten equal parts is 1 . It is read as one-tenth. Fractional form of each equal part is 1 . 10 10 Decimals 31 NR_BGM_9789388751193 PASSPORT G04 MATHS TEXTBOOK PART 2_Text.pdf 35 12/17/2018 4:34:57 PM

Decimal form of each equal part is 0.1. A decimal number has two parts. We read numbers like 0.1, 0.2, 0.3 … as ‘zero point one’, ‘zero point two’, ‘zero point three’ and so on. Zero is written to 48 . 35 indicate the place of the whole number. Note: T he numbers in the decimal part are read as separate Whole or Decimal digits. integral part part (< 1) (= or > 0) Recall the place value chart of numbers. Decimal Point 100 × 10 10 × 10 1 × 10 1 Thousands Hundreds Tens Ones 6 2 5 5 3 2 2 6 5 2 We know that in this chart, as we move from right to left, the value of the digit increases 10 1 times. Also, as we move from left to right, the value of a digit becomes times. The place 10 value of the digit becomes one-tenth, read as a tenth. Its value is 0.1 read as ‘zero point one’. 2 is read as ‘two-tenths’, 7 is read as ‘seven–tenths’ and so on. 10 10 We can extend the place value chart to the right as follows: 1 × 1000 1 × 100 1 × 10 1 . 1 Thousands Hundreds Tens 10 Ones Decimal Tenths 2 7 . 2 14 4 . 3 3 01 3 . 6 5 . 7 The number 3015.7 is read as three thousand and fifteen point seven. Similarly, the other numbers are read as follows: Seven point two; twenty-four point three and one hundred and forty-three point six. The point placed in between the number is called the decimal point. The system of writing numbers using a decimal point is called the decimal system. 32 NR_BGM_9789388751193 PASSPORT G04 MATHS TEXTBOOK PART 2_Text.pdf 36 12/17/2018 4:34:57 PM

[Note: ‘Deci’ means 10.] Tens Ones Decimal Tenths Hundredths Hundredths: 1 point Study this place value chart. 2 1 1 . 10 100 Thousands Hundreds 3 . 9 1 × 1000 1 × 100 1 × 10 2 8 6 When the number moves right from the tenths place, we get a new place, which is 1 of the tenths place. It is called the ‘hundredths’ place written as 1 and read 10 100 as one-hundredths. Its value is 0.01, read as ‘zero point zero one’. 2 is read as two-hundredths, 5 is read as five-hundredths and so on. 100 100 So, the number in the place value chart is read as ‘two thousand eight hundred and sixty-two point three nine’. Expansion of decimal numbers Using the place value chart, we can expand decimal numbers. Let us see a few examples. Example 1: Expand these decimals. a) 1430.8 b) 359.65 c) 90045.75 d) 654.08 Solution: To expand the given decimal numbers, first write them in the place value chart as shown. S. no Ten Thousands Hundreds Tens Ones Decimal Tenths Hundredths thousands 1 point 4 3 0 . 8 a) 0 3 5 9 65 0 4 5 . 75 b) 6 5 4 08 . c) 9 . d) Expansions: 1 a) 1430.8 = 1 × 1000 + 4 × 100 + 3 × 10 + 0 × 1 + 8 × 10 b) 359.65 = 3 × 100 + 5 × 10 + 9 × 1 + 6 × 1 + 5 × 1 10 100 Decimals 33 NR_BGM_9789388751193 PASSPORT G04 MATHS TEXTBOOK PART 2_Text.pdf 37 12/17/2018 4:34:57 PM

c) 90045.75 = 9 × 10000 + 0 × 1000 + 0 × 100 + 4 × 10 + 5 × 1 + 7 × 1 + 5 × 1 10 100 Example 2: 1 1 d) 654.08 = 6 × 100 + 5 × 10 + 4 × 1 + 0 × + 8 × 10 100 Write these as decimals. Solution: a) 7 × 1000 + 2 × 100 + 6 × 10 + 3 × 1 + 9 × 1 + 3 × 1 10 100 b) 3 × 10000 + 0 × 1000 + 1 × 100 + 9 × 10 + 6 × 1 + 4 × 1 + 5 × 1 10 100 c) 2 × 1000 + 2 × 100 + 2 × 10 + 2 × 1 + 2 × 1 + 2 × 1 10 100 d) 5 × 100 + 0 × 10 + 0 × 1 + 0 × 1 + 5 × 1 10 100 First write the numbers in the place value chart as shown. S. no Ten Thousands Hundreds Tens Ones Decimal Tenths Hundredths thousands point a) 7 2 63 . 93 b) 3 0 1 96 . 45 c) 2 2 22 . 22 d) 5 00 . 05 Standard forms of the given decimals are: a) 7263.93 b) 30196.45 c) 2222.22 d) 500.05 Conversion of fractions to decimals Fractions can be written as decimals. Consider an example. Example 3: Express these fractions as decimals. Solution: a) 18 2 b) 43 5 c) 26 1 d) 4 9 10 10 10 10 To write the given fractions as decimals, follow these steps. Step 1: Write the integral part as it is. Step 2: Place a point to its right. Step 3: Write the numerator of the proper fraction part. a) 18 2 = 18.2 b) 43 5 = 43.5 10 10 c) 26 1 = 26.1 d) 4 9 = 4.9 10 10 34 12/17/2018 4:34:57 PM NR_BGM_9789388751193 PASSPORT G04 MATHS TEXTBOOK PART 2_Text.pdf 38

Example 4: Express these fractions as decimals. Solution: a) 25 b) 17 2 c) 43 d) 5 92 100 100 100 100 a) 25 = 25 hundredths = 0.25 100 b) 17 2 = 17 and 2 hundredths = 17.02 100 c) 43 = 43 hundredths = 0.43 100 d) 5 92 = 5 and 92 hundredths = 5.92 100 Shortcut method: Fractions having 10 or 100 as their denominators, can be expressed in their decimal form by following the steps given below. Step 1: Write the numerator. Step 2: Then count the number of zeros in the denominator. Step 3: Place the decimal point after the same number of digits from the right as the number of zeros. For example, the decimal form of 232 = 2.32 100 Note: F or the decimal equivalent of a proper fraction, place a 0 as the integral part of the decimal number. Conversion of decimals to fractions To convert a decimal into a fraction, follow these steps. Step 1: Write the number without the decimal. Step 2: Count the number of decimal places (that is, the number of places to the right of the decimal number). Step 3: Write the denominator with 1 followed by as many zeros as the decimal point. Example 5: Write these decimals as fractions. a) 2.3 b) 13.07 c) 105.43 d) 0.52 Solution: a) 2.3 = 23 b) 13.07 = 1307 10 100 c) 105.43 = 10543 d) 0.52 = 52 100 100 Decimals 35 NR_BGM_9789388751193 PASSPORT G04 MATHS TEXTBOOK PART 2_Text.pdf 39 12/17/2018 4:34:57 PM

Alternate method: A decimal having an integral part can be written as a mixed fraction. So, 2.3 = 2 and 3 tenths = 2 3 10 13.07 = 13 and 7 hundredths = 13 7 100 105.43 = 105 and 43 hundredths = 105 43 100 Train My Brain Solve the following: a) Expand 35.098. b) Write 4.78 as a fraction. c) Express 37 as a decimal. 100 36 12/17/2018 4:34:57 PM NR_BGM_9789388751193 PASSPORT G04 MATHS TEXTBOOK PART 2_Text.pdf 40