Hazelwood G3 Maths TB P1_Nameslip.pdf 1 8/4/2023 1:17:33 PM Name: _________________________________________ Section: ________________ Roll No.: ______________ School: ________________________________________ MATHEMATICS TEXTBOOK Part - 1
PREFACE The latest National Curriculum Framework (NCF), furthering 1 the vision of the National Education Policy (NEP) 2020, provides a comprehensive framework for the holistic 5 2 development of students. It places a strong emphasis on 4 foundational literacy and numeracy and a competency-based and learner-centred approach to ensure a well-rounded education that prepares students for the challenges of the 21st century. ClassKlap by Eupheus partners with schools and supports them through the steps of planning, teaching, learning, 3 personal revision and assessment to equip students with the desired knowledge and skills relevant to the 21st century. The present series has been carefully crafted to provide a solid foundation for students keeping in mind the principles outlined in the NCF. The books promote active learning and skill development and strive to ensure inclusiveness in terms of gender and diversity in representation, catering to the heterogeneous Indian classroom. The books have been split into two parts for lighter bag weight. The larger aim of Mathematics teaching is to develop the abilities of a student to think and reason mathematically, pursue assumptions to their logical conclusions and handle abstraction. To this end, the Mathematics textbooks and workbooks offer the following features: Skill-based lessons are structured as per Bloom’s Revised Taxonomy (Remember-Understand-Apply-Analyse-Evaluate-Create) Inquiry-based lessons are structured based on a Socratic approach using a question-answer format, aiming at discovery-based learning as per NCF guidelines Student engagement through simple, age-appropriate language Increasing rigour in sub-questions for every question in order to scaffold learning for students Word problems based on real-life scenarios help students relate Mathematics to their everyday experiences Mental Maths practice to inculcate level-appropriate mental calculation skills Stepwise breakdown of solutions to provide an easier premise for learning problem-solving skills Fostering interdisciplinary learning by connecting themes and concepts across subjects The Mathematics textbooks, workbooks and teacher companion books aim to enhance logical reasoning, problem-solving and critical thinking skills that are at the heart of Mathematics teaching and learning. It is our sincere hope that this series will enable students to deepen their understanding and appreciation of Mathematics. Hazelwood_Maths_G03_TB_Part 1.indb 2 05-08-2023 21:35:30
ENGLISH COURSEBOOK FEATURESTEXTBOOK FEATURES Art-Integrated Learning Let Us Learn About Lesson plans provided for Indicates the learning outcomes to be covered in the lesson art-integrated learning Recall SKILL-BASED LESSONS Revises the pre-requisite knowledge needed for the concept covered Think previously Introduces the concept and arouses Remembering and curiosity about it among students Understanding Application Explains the fundamental aspects of the concept in detail, in an age-appropriate Connects the concept to real-life situations and engaging manner by enabling students to apply what has been learned through practice questions Drill Time Higher Order Thinking Additional practice questions at the Skills (H.O.T.S.) end of every concept Encourages students to extend the Connect the Dots concept to advanced scenarios using higher-order thinking skills A multidisciplinary section to connect the lesson theme with other subjects INQUIRY-BASED LESSONS Reflection Time! Concepts organised using a Thought-provoking questions to question-answer approach to foster encourage reflection on the concept and a mindset of inquiry and reasoning on how it is related to the student's life, experiences and the world around Hazelwood_Maths_G03_TB_Part 1.indb 3 05-08-2023 21:35:32
Contents 3Class 1 Shapes 1 1.1 Vertices and Diagonals of Two-dimensional Shapes 9 Art-Integrated Learning Skill-Based 15 2 Patterns 22 2.1 Patterns in Shapes and Numbers Inquiry-Based 29 32 3 Numbers 37 3.1 Count by Thousands Skill-Based 40 3.2 Compare 4-digit Numbers Skill-Based 42 49 4 Addition 52 4.1 Estimate the Sum of Two Numbers Inquiry-Based 56 4.2 Add 3-digit and 4-digit Numbers 62 Art-Integrated Learning Skill-Based 4.3 Add 2-digit Numbers Mentally Inquiry-Based 5 Subtraction 5.1 Estimate the Difference between Two Numbers Inquiry-Based 5.2 Subtract 3-digit and 4-digit Numbers Skill-Based 5.3 Subtract 2-digit Numbers Mentally Inquiry-Based 6 Multiplication 6.1 Multiply 2-digit Numbers Art-Integrated Learning Skill-Based 6.2 Multiply 3-digit Numbers by 1-digit and 2-digit Numbers Skill-Based 6.3 Double 2-digit and 3-digit Numbers Mentally Inquiry-Based Hazelwood_Maths_G03_TB_Part 1.indb 4 05-08-2023 21:35:38
Chapter Shapes 1 Let Us Learn About • identifying 2D shapes with straight and curved lines. • identifying sides, corners and diagonals. • making a tangram. • recognising 3D shapes and their faces and edges. Concept 1.1: Vertices and Diagonals of Two-dimensional Shapes Think There is a paper folding activity in Farida’s class. Her teacher asked the students to fold the paper across the vertices or the diagonals. How will Farida fold the paper? Recall We have learnt various shapes formed by straight lines or curved lines. Let us recall them. AB A BA B line line segment ray Hazelwood_Maths_G03_TB_Part 1.indb 1 1 05-08-2023 21:35:40
horizontal lines vertical lines slant lines curved lines The straight and curved lines help us make closed and open figures. Figures which end at the point from where they start are called closed figures. Figures which do not end at the point from where they start are called open figures. closed figures open figures Try this! Write ‘open figure’ or ‘closed figure’ in the given blanks. ____________ ____________ ____________ ____________ Shapes such as rectangle, triangle, square and circle that can be drawn flat on a piece of paper are called two-dimensional shapes. Their outlines are called two-dimensional figures. In short, they are called 2D figures. Identify the following shapes and separate them as 1D or 2D shapes. One has been done for you. Object Shape Triangle 2D Name of the shape 1D or 2D 2 05-08-2023 21:35:41 Hazelwood_Maths_G03_TB_Part 1.indb 2
& Remembering and Understanding As we have already learnt various shapes, let us now name their parts. Consider a rectangle ABCD as shown. DC In the given rectangle, AB, BC, CD and DA are called A B its sides. There are lines joining A to C and B to D. These lines named AC and BD are called the diagonals of the rectangle. Points A, B, C and D where two sides of the rectangle meet are called the vertices. Vertex: The point where at least two sides of a figure meet is called a vertex. The plural of vertex is vertices. Diagonal: A straight line inside a shape that joins the opposite vertices is called a diagonal. A square also has sides, diagonals and vertices. Note: A triangle and a circle do not have any diagonals. Try this! Complete the table with vertices, sides and diagonals of the given different shapes. One has been done for you. CS R Y D Shape ZX W A B Q P Vertices A, B, C, D Sides AB, BC, CD, DA Diagonals AC, BD Application A We know that a 2D shape has length and breadth. Let us now learn to find the number of sides of a 2D shape. Consider a triangle as shown. B C Shapes 3 Hazelwood_Maths_G03_TB_Part 1.indb 3 05-08-2023 21:35:41
The given triangle has 3 sides named as AB, BC and CA. We can also name them as BA, CB and AC. The different number of markings on the sides of the triangle show that the lengths of all the 3 sides are different. If all the sides have the same number of markings, we can say that the lengths of all the 3 sides are the same. Let us now find the number of sides of a few 2D shapes and name them. Shape S RD C A P QA B BC Name of the shape Square Rectangle Triangle Number of sides 4 4 3 (All sides are equal.) (Opposite sides are (All sides are equal equal.) in this case.) Names of sides PQ, QR, RS, SP AB, BC, CD, DA AB, BC, CA We find objects of various shapes around us. Complete the following table by writing the basic shapes, number of the vertices and diagonals of the given objects. Object Basic shape 36 Number of vertices 4 1 Number of diagonals 7 5 Tangram 2 A tangram is a Chinese geometrical puzzle. It consists of a square that is cut into pieces as shown in the given figure. To create different shapes, we arrange these tangram pieces with their sides or vertices touching one another. 4 Hazelwood_Maths_G03_TB_Part 1.indb 4 05-08-2023 21:35:41
Let us make our own tangram. Materials needed: a square sheet of paper a pair of scissors a ruler (optional) Procedure: Figure Steps Step 1: Fold the square sheet of paper as shown. Step 2: Cut the square into two triangles, A across the fold. B Step 3: Cut one of the triangles obtained A1 in step 2, into two equal parts. We get two 2 smaller triangles as shown. Step 4: Fold the bigger triangle as shown. B Step 5: Unfold this piece and cut it across the fold. We get one more triangle. 3 Shapes 5 Hazelwood_Maths_G03_TB_Part 1.indb 5 05-08-2023 21:35:42
Steps Figure Step 6: Fold the boat-shaped piece from one 4 end as shown. We get a triangle again on cutting at the fold. Step 7: Fold the remaining part of the paper 5 as shown. We get a square on cutting at the fold. Step 8: Fold the remaining paper again as 6 shown. We now get one more triangle on 7 cutting at the fold. We, thus, get the seven pieces of the tangram. Step 9: Colour these shapes using different colours. You can use these tangram pieces to make different shapes. Higher Order Thinking Skills (H.O.T.S.) Observe the given figure. It looks like a box. Each side of the box is a square. In the figure, AB is the length and BF is the breadth of the box. AD is E F B called the height of the box. So, this shape has three dimensions - A length, breadth and height. Such shapes are called three-dimensional shapes or 3D shapes or HG solid shapes. DC In the figure, cube • The points A, B, C, D, E, F, G and H are called vertices. • The lines AB, BC, CD, DA, BF, FE, EA, CG, GH, HD, HE and GF are called edges. • The squares ABCD, ABFE, BFGC, GCDH, EFGH and AEHD are called faces. Solid shapes with all flat square faces are called cubes. 6 Hazelwood_Maths_G03_TB_Part 1.indb 6 05-08-2023 21:35:42
Let us learn how to draw a cube in a few simple steps. Step 1: Draw a square Step 2: Draw another Step 3: Join DH, AE, BF Steps ABCD. square EFGH cutting and CG. square ABCD as shown. Figure D C H G A B HG D C DC E F EF A B AB A few other such three-dimensional shapes are cuboids and cones. Solid shapes with six flat rectangular faces are called cuboids. A solid shape with a circular base, a vertex and a curved surface is called a cone. Cuboid Cone Try this! Draw a cuboid and a cone showing the formation of the figure in steps. Shape Step 1 Step 2 Step 3 Cuboid Cone Shapes 7 Hazelwood_Maths_G03_TB_Part 1.indb 7 05-08-2023 21:35:42
Drill Time Concept 1.1: Vertices and Diagonals of Two-dimensional Shapes 1) Find the number of vertices and diagonals of the following shapes: a) b) c) d) e) Connect the Dots 05-08-2023 21:35:43 English Fun Try drawing a square while reciting the rhyme. From the bottom to the top, straight across right and then you stop. Straight down to the bottom again, across left and stop where you began. If the lines are the same size, then a square is formed for you a surprise. 8 Hazelwood_Maths_G03_TB_Part 1.indb 8
Chapter Patterns 2 Let Us Learn About • identifying and creating patterns in shapes and numbers • identifying and creating growing patterns in shapes and numbers 2.1: Patterns in Shapes and Numbers Things around us display different patterns. Window grill Rangoli Cloth pattern Do you know what a pattern is? A pattern consists of a series of shapes or numbers that are arranged in a specific order and they repeat themselves based on some rule. Hazelwood_Maths_G03_TB_Part 1.indb 9 9 05-08-2023 21:35:45
Look at the following patterns. These are made up of lines and shapes. a) b) c) d) Now complete the patterns below. Do we have patterns in numbers too? We have seen that patterns are formed by repeating shapes in a particular way. Similarly, we can also create patterns using numbers. Few of the common patterns in numbers are that of even numbers and odd numbers. An even number always ends with 2, 4, 6, 8 or 0. You can make a pattern with even numbers by adding 2 to the previous even number. For example, 2 + 2 = 4; 4 + 2 = 6; 6 + 2 = 8 and so on. 10 05-08-2023 21:35:47 Hazelwood_Maths_G03_TB_Part 1.indb 10
An odd number always ends with 1, 3, 5, 7 or 9. You can make a pattern with odd numbers by adding 2 to the previous odd number. For example, 1 + 2 = 3; 3 + 2 = 5; 5 + 2 = 7 and so on. Colour the even numbers in green and the odd numbers in yellow. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 Look at this set of numbers. Do you think there is a pattern in this set? 2, 5, 7, 10, 14 …. What are growing patterns? A growing pattern is a pattern where a unit (a number or shape) is added every time the sequence repeats. Look at the following growing patterns in shapes and complete them. Patterns 11 Hazelwood_Maths_G03_TB_Part 1.indb 11 05-08-2023 21:35:49
Do we have growing patterns in numbers too? Growing patterns in numbers are formed by units (or terms) that increase by a certain number. We can find this number by subtracting the 2nd unit from the 1st, the 3rd from the 2nd, and so on. Let us look at an example first and try completing the next two growing patterns. Solved: Pattern 1 Solve: Pattern 2 Solve: Pattern 3 20, 30, 40, 50… 100, 200, 300… 11, 21, 31, 41 … What comes next? What comes next? What comes next? The unit by which the growing pattern is increasing can be found by subtraction: 30 – 20 = 10 So, the rule is: the pattern increases by 10. Therefore, the next unit is: 50 + 10 = 60 Now, complete each pattern by writing the next three terms. a) 9, 29, 49, 69, _____, _____, _____ b) 13, 23, 33, 43, _____, _____, _____ c) 5, 10, 15, 20, _____, _____, _____ F ind the rule followed in the given patterns. Then, write the next three terms for each of them. a) 12, 24, 36, _____, _____, _____ b) 1 + 2 = 3, 2 + 3 = 5, 3 + 4 = 7, ____________, ____________, ____________ 12 05-08-2023 21:35:49 Hazelwood_Maths_G03_TB_Part 1.indb 12
Reflection Time! 1) Take a look around the room you are in right now. Identify a few patterns that you see in the objects or things in the room. 2) Can you look at this growing pattern and draw what comes next? Drill Time 2.1: Patterns in Shapes and Numbers 1) Complete the following patterns. a) _________ _________ __________ ☺☺☻☺☺☻ b) _______ ________ c) _________ __________ d) ____________ ____________ e) ________________ ______________ Patterns 13 Hazelwood_Maths_G03_TB_Part 1.indb 13 05-08-2023 21:36:00
Drill Time f) ________________ ______________ 2) Fill the blanks with the next two terms of the given patterns. a) 122, 133, 144, ______, ______ b) 303, 304, 305, ______, ______ c) 40, 42, 44, ______, ______ d) 8, 24, 40, ______, ______ e) 35, 30, 25, ______, ______ f) 82, 72, 62, ______, ______ Connect the Dots Science Fun We see patterns all around us. Flowers, leaves, stripes on animals and so on have patterns. Here are a few pictures in which we can observe patterns that are found in nature. 14 05-08-2023 21:36:01 Hazelwood_Maths_G03_TB_Part 1.indb 14
Chapter Numbers 3 Let Us Learn About • writing 4-digit numbers with place value chart. • writing the standard and the expanded forms of the number. • comparing and ordering numbers. • identifying and forming the greatest and the smallest number. Concept 3.1: Count by Thousands Think Farida went to buy one of the toy cars shown. She could not read not read the price on one of the cars. Can you read the `1937.00 price on both the cars and understand what they mean? `657.00 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 Hazelwood_Maths_G03_TB_Part 1.indb 15 15 05-08-2023 21:36:03
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. 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 _______________________________________. & Remembering and Understanding 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 16 05-08-2023 21:36:08 Hazelwood_Maths_G03_TB_Part 1.indb 16
= 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. Numbers 17 Hazelwood_Maths_G03_TB_Part 1.indb 17 05-08-2023 21:36:11
Thousands (Th) Hundreds (H) Tens (T) Ones (O) 4 7 32 We count by 1000s as 1000 (one thousand), 2000 (two thousand)... till 9000 (nine thousand). The greatest 4-digit number is 9999. 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 18 05-08-2023 21:36:11 Hazelwood_Maths_G03_TB_Part 1.indb 18
Solution: To expand the given numbers, write them in the correct places in the place value chart. 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. Application We can solve a few real-life examples using the knowledge of 4-digit numbers. Example 4: Ram has some money with him as shown. Calculate the amount that Ram has and write it in figures and words. Numbers 19 Hazelwood_Maths_G03_TB_Part 1.indb 19 05-08-2023 21:36:13
Solution: 2 notes of `500 = `1000 1 note of `100 = `100 3 notes of `10 = `30 1 coin of `5 = `5 So, the amount that Ram has = `1000 + `100 + `30 + `5 = `1135 In words, `1135 is one thousand one hundred and thirty-five rupees. Example 5: The number of students in different schools is given in the table. Read the table and answer the questions that follow. Name of schools Number of students Juniper High School 2352 Peony High School 4782 Plumeria High School 7245 Amaryllis High School 9423 Hiptage High School 1281 a) What is the number of students in Plumeria High School? Write the number in words. b) H ow many students are there in Hiptage High School? Write the number in words. Solution: a) T he number of students in Plumeria High School is 7245. In words, it is seven thousand two hundred and forty-five. b) The number of students in Hiptage High School is 1281. In words, it is one thousand two hundred and eighty-one. A place value chart helps us to form numbers using given digits. Here is an example. Example 6: A number has 6 in the thousands place and 5 in the hundreds place. It has 1 in the tens place and 4 in the ones place. What is the number? Solution: Write the digits in the place value chart according to Th H T O their places as shown. So, the required number is 6514. 6 5 1 4 Higher Order Thinking Skills (H.O.T.S.) We have learnt the concepts of expanded form and place value chart. Now, we will solve a few examples to identify numbers from the abacus. 20 Hazelwood_Maths_G03_TB_Part 1.indb 20 05-08-2023 21:36:13
Example 7: Write the numbers represented by these abacuses. a) b) c) Th H T O Th H T O Th H T O Solution: Follow these steps to write the numbers. Step 1: Write the number of beads in each Th H T O Number Step 2: place in the place value chart. a) 1 3 3 2 1332 Put a 0 in the places where there are b) 5 0 3 0 5030 no beads. c) 4 0 3 4 4034 Example 8: Draw beads on the abacus to show the given numbers. a) 3178 b) 6005 c) 4130 Th H T O Solution: Step 1: Follow these steps to show the given numbers. a) 3 1 7 8 Write the digits of the given numbers in the place b) 6 0 0 5 value chart. c) 4 1 3 0 Step 2: Draw the number of beads on each spike of the abacus to show the digit in each place of the number. Th H T O Th H T O Th H T O a) 3178 b) 6005 c) 4130 Drill Time Concept 3.1: Count by Thousands 1) Write the numbers in the place value chart. a) 1451 b) 8311 c) 9810 d) 1000 e) 7613 e) 9819 2) Write the numbers in their expanded forms. a) 8712 b) 6867 c) 1905 d) 4000 Numbers 21 Hazelwood_Maths_G03_TB_Part 1.indb 21 05-08-2023 21:36:13
3) Write the number names of the following numbers: a) 9125 b) 5321 c) 3100 d) 1900 e) 7619 4) Form 4-digit numbers from the following: a) 4 in the thousands place, 3 in the hundreds place, 0 in the tens place and 2 in the ones place b) 9 in the thousands place, 1 in the hundreds place, 4 in the tens place and 0 in the ones place c) 5 in the thousands place, 4 in the hundreds place, 9 in the tens place and 7 in the ones place d) 8 in the thousands place, 2 in the hundreds place, 6 in the tens place and 5 in the ones place e) 1 in the thousands place, 2 in the hundreds place, 3 in the tens place and 4 in the ones place 5) Word problems a) The number of people in different rows in a football stadium is as given: Row 1: 2345 Row 2: 6298 Row 3: 7918 Row 4: 8917 Row 5: 1118 (A) What is the number of people in Row 1? Write the number in words. (B) How many people are there in Row 4? Write the number in words. b) R am has 4 notes of `500, a note of `200, a note of `20 and a coin of `2. How much money does he have? Write the amount in figures and words. Concept 3.2: Compare 4-digit Numbers 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? Recall In class 2, we have learnt to compare 3-digit numbers and 2-digit numbers. Let us quickly revise the concept. 22 Hazelwood_Maths_G03_TB_Part 1.indb 22 05-08-2023 21:36:14
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. & Remembering and Understanding Comparing two 4-digit numbers is similar to comparing two 3-digit numbers. Let us understand the steps to compare through an example. 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. 5=5 ____ = ____ Step 2: Compare thousands ____ If two numbers have the same number of digits, Train My Brain compare the thousands digits. (If two numbers have an equal number of digits, start comparing 3=3 ____ = from the leftmost digit.) 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 same, So, compare the digits in the tens place. The number with the greater digit in the tens place is greater. ____ > ____ Numbers 23 Hazelwood_Maths_G03_TB_Part 1.indb 23 05-08-2023 21:36:14
Steps Solved Solve this 5382 and 5380 7469 and 7478 Step 5: Compare ones If the digits in the tens place are also the same, 2>0 compare the digits in the ones place. The So, - number with the greater digit in the ones place is greater. When the ones place are the same, the 5382 > 5380 numbers are equal. Note: Once we can decide a greater/smaller number, the steps that follow need not be carried out. Application We can apply the knowledge of comparing numbers and place value to: 1) arrange numbers in the ascending and descending orders. 2) form the greatest and the smallest numbers using the given digits. Ascending and descending orders Ascending Order: The arrangement of numbers from the smallest to the greatest Descending Order: The arrangement of numbers from the greatest to the smallest Example 10: Arrange 4305, 4906, 4005 and 4126 in the ascending and descending orders. Solution: Follow these steps to arrange the given numbers in the ascending and descending orders. Ascending Order Step 1: Compare the digits in the thousands place: All the numbers have 4 in their thousands place. Step 2: Compare the digits in the hundreds place: 4005 – 0 hundreds, 4126 –1 hundred, 4305 – 3 hundreds and 4906 – 9 hundreds. So, 4005 < 4126 < 4305 < 4906. Step 3: Arranging the numbers in ascending order: 4005, 4126, 4305, 4906 24 05-08-2023 21:36:14 Hazelwood_Maths_G03_TB_Part 1.indb 24
Descending Order Step 1: Compare the digits in the thousands place: All the numbers have 4 in their thousands place. Step 2: Compare the digits in the hundreds place: 4005 – 0 hundreds, 4126 – 1 hundred, 4305 – 3 hundreds and 4906 – 9 hundreds. So, 4906 > 4305 > 4126 > 4005. Step 3: Arranging the numbers in descending order: 4906, 4305, 4126, 4005 Simpler way! The descending order of numbers is just the reverse of their ascending order. Forming the greatest and the smallest 4-digits numbers Let us learn to form the greatest and the smallest 4-digit numbers. Look at the following examples. Example 11: Form the greatest and the smallest 4-digit number using 4, 3, 7 and 5 (without repeating the digits). Solution: The given digits are 4, 3, 7 and 5. The steps to find the greatest 4-digit number are given below. Step 1: Arrange the digits in descending order as 7 > 5 > 4 > 3. Step 2: Place the digits in the place value chart from left to right. So, the greatest 4-digit number formed is 7543. Th H T O T he steps to find the smallest 4-digit number are given 7543 below. Step 1: Arrange the digits in ascending order as Th H T O 3 < 4 < 5 < 7. 34 5 7 Step 2: Place the digits in the place value chart from left to right. So, the smallest 4-digit number formed is 3457. Example 12: Form the smallest 4-digit number using 4, 1, 0 and 6 (without repeating the digits). Numbers 25 Hazelwood_Maths_G03_TB_Part 1.indb 25 05-08-2023 21:36:14
Solution: The given digits are 4, 1, 0 and 6. Th H T O Step 1: Arrange the digits in ascending order as 0 < 1 < 4 < 0 1 4 6 6. Step 2: Place the digits in the place value chart from left to right. But the number formed is 0146 or 146. It is a 3-digit number. In such cases, we interchange the first two digits in Th H T O the place value chart. 10 4 6 So, the smallest 4-digit number formed is 1046. Example 13: Form the smallest and the largest 4-digit numbers using 4, 0, 8 and 6 (with repeating the digits). Solution: The given digits are 4, 0, 8 and 6. Follow the steps to form the smallest 4-digit number. Step 1: Find the smallest digit. 0 is the smallest of the given digits. (But a number cannot begin with 0.) Step 2: If the smallest digit is ‘0’, find the next smallest digit, which is 4. Write ‘4’ in the thousands place. Write ‘0’ in the rest of the places. Therefore, the smallest 4-digit number is 4000. Note: If the smallest of the given digits is not ‘0’, repeat the smallest digit four times to form the smallest number. Now, let us form the largest 4-digit number from the given digits. Step 1: The largest of the given digits is 8. Step 2: Repeat the digit four times to form the largest 4-digit number. Therefore, the largest 4-digit number that can be formed is 8888. Higher Order Thinking Skills (H.O.T.S.) Let us see a few real-life examples where we use the comparison of 4-digit numbers. Example 14: 4538 people visited an exhibition on Saturday and 3980 people visited it on Sunday. On which day did fewer people visit the exhibition? Solution: Number of people who visited the exhibition on Saturday = 4538 Number of people who visited the exhibition on Sunday = 3980 Comparing both the numbers using the place value chart, 26 05-08-2023 21:36:14 Hazelwood_Maths_G03_TB_Part 1.indb 26
Th H T O Th H T O 4 53 8 3 98 0 4 > 3 or in other words, 3 < 4 So, 3980 < 4538. Therefore, fewer people visited the exhibition on Sunday. Example 15: Razia arranged the numbers 7123, 2789, 2876 and 4200 in the ascending order as 2876, 2789, 4200, 7123. Reena arranged them as 2789, 2876, 4200, 7123. Who arranged them correctly? Why? Solution: Reena’s arrangement is correct. Reason: Comparing the hundreds place of the smaller of the given numbers (that is, 2876 and 2789): 7 hundreds < 8 hundreds. As 2789 < 2876, Reena’s arrangement is correct. Drill Time Concept 3.2: Compare 4-digit Numbers 1) Compare the following numbers using <, > or =. a) 8710, 9821 b) 1689, 1000 c) 4100, 4100 d) 2221, 2222 e) 6137, 6237 f) 7091, 7019 2) Arrange the numbers in ascending and descending orders. a) 4109, 5103, 1205, 5420 b) 7611, 7610, 7609, 7605 c) 9996, 8996, 1996, 4996 d) 5234, 6213, 1344, 5161 e) 4234, 6135, 4243, 6524 f) 6512, 1814, 3797, 3893 3) Form the greatest and the smallest 4-digit numbers without repeating the digits: a) 3, 5, 9, 2 b) 1, 5, 9, 4 c) 7, 4, 1, 8 d) 9, 1, 3, 5 e) 8, 2, 3, 4 f) 4, 7, 0, 2 4) Word problems a) 5 426 people visited a museum on a Friday and 3825 people visited it on the following Sunday. On which day did fewer people visit the museum? b) A shopkeeper sold 1105 milk chocolate bars and 2671 white chocolate bars. Which type of chocolate bars did he sell more? Numbers 27 Hazelwood_Maths_G03_TB_Part 1.indb 27 05-08-2023 21:36:14
c) Manish trekked a distance of 1851 m on Day 1 and 1815 m on Day 2. On which day did he trek more distance? Connect the Dots Social Studies Fun Without the concept of thousands, we would have never been able to estimate the heights of the tallest mountain peaks in the world! Take a look at the tallest peaks across each continent. 28 05-08-2023 21:36:15 Hazelwood_Maths_G03_TB_Part 1.indb 28
Chapter Addition 4 Let Us Learn About • estimating the sum of two numbers • rounding off numbers to the nearest tens • adding numbers with and without regrouping • adding two numbers mentally 4.1: Estimate the Sum of Two Numbers You have learnt how to add 2-digit and 3-digit numbers. However, we don’t always need to know the exact sum of numbers. We can try to simply estimate the sum at times. What is estimation? When we ‘estimate’ something, we use words such as ‘around’ or ‘about’. For example, when we say there are about 50 students in a class, we mean that the number is close to 50. The actual number could be 49 or 51 or 54 or even 45! When we estimate numbers, we usually round them off. Rounding off numbers makes them easier to use. People estimate numbers by rounding them off in their day-to-day lives. What is rounding off? Rounding off is nothing but estimation. Estimating the actual number to its nearby number is called rounding off. We usually round off numbers to their nearest tens. Look at these examples. 86 is rounded off to 90. 23 is rounded off to 20. 64 is rounded off to 60. 29 Hazelwood_Maths_G03_TB_Part 1.indb 29 05-08-2023 21:36:18
Can you say why? Discuss with a partner. If the digit in the ones place is 4 or less, you round off the number down to the previous tens. And, if the digit is 5 or more, you round it off to the next tens. Do you want to see how we round off numbers on a number line? Suppose Rita has 61 boxes. Now, she wants to round it off to the nearest tens. How will she do it? 61 lies between 60 anEds7ti0m(mautlitiopnlesooff 1S0u).m 61 is closer to 60 than 70. To round off to the nearest tens, observe So, we can mWakeecaann eessttiimmaattee athnedssuamy thoaf tthReitagihvaesnanbuomutb6e0rsbboyxes. the digit in the ones rounding them off to the nearest tens, hundreds and place. Howtdhoouwseanedstsimpalatecethaes sruemquoirfetdw.o numbers? • If the digit in the Now that youTkonothwe wnheaart erostutnedninsg off is, you can use the same method to ones place is 0, 1, the sum of twEoxnaummpbleer1s as well. estim2a, t3eor 4, the digit is changed to ‘0’, keeping the other digits the same. • If the digit in the TO TO ones place is 5, 6, 60 7, 8 or 9, add 1 to 1 the tens digit and 63 +3 0 +2 8 change the ones digit to 0. 90 91 Note how theTehsetimesatitmedatseudmsius mveriys cclloossee ttoo tthhee aaccttuuaall ssuumm.of the two numbeTros.round off to the nearest hundreds, Imagine thaTt yootuhehanveear2e2spt ehnusntdordeidstsribute among your friends. observe the digit in the tens place. What will youExroaumnpdleof2f 22 to? • If the digit in the Now imagineEsthtiamt aytoeutrhteeascuhmerogfiv3e4s3yaonud2567m5otoretpheennse. aWrehsatthwuilnl ydorueds. tens place is 0, 1, 2, 3 or 4, change both round off 26 to? the tens and the Find out what theroeustnimdaedteodffsum of 22 aEnsdtim26awteildl bseu.m Actual sum ones digits to 0, HTO HTO keeping the other 343 to the 300 300 digits the same. nearest 100s 1 • If the digit in the tens place is 5, 6, 30 343 7, 8 or 9, add 1 to rounded up + 6 0 0 +5 7 5 09-08-2023 12:29:23 575 neatroestth1e00sHazelwood_Maths_G03_TB_Part 1.indb 30 600 900 918
C an you think of a similar sum using two 3-digit numbers? Try estimating the sum with a partner. Work on it and share it with the class. Hint: 3-digit numbers have to be rounded off to the nearest 100. Round off 256 to the nearest 100s. If the digit in the tens place is greater than 100 150 200 250 300 350 400 or equal to 5, round up the number to the 256 next hundreds. Far Near 256 is nearer to 300 than 200. So, it is rounded up to 300. Reflection Time! 1) How does rounding off make calculations easier? 2) Why is estimating useful? 3) Can you think of any real-life situation in which you can round off and estimate the sum of 2-digit and 3-digit numbers? Drill Time 4.1: Estimate the Sum of Two Numbers c) 85 and 90 1) Estimate the sum of the following: Ro undao)ff2413a58ndto 1th5e nearest b10)0409s.and 12 d) 222 and 524 e) 672 and 189 f) 325 and 416 3000 4000 5000 6000 If the digit in the 2) Word pro4b35l8ems hundreds place is less than 5, round Near Far and Estimate the 4358 Mukeoshffsathhmaeesnt2uhm2oubyseearlnltodowst.heroses. isan)etSaouretsaraltnnohu4am0s0b04e6trhroaenfdr5or0os0es0es..s So, it is rounded off to 4000. b) R akesh has 67 pencils and Mona has 43 pencils. Estimate the number of Example 7pencils both of them have in all. Round off 7620 to the nearest 1000s. If the digit in the Addition 31 hundreds 6000 7000 7620 8000 9000 05-08-2023 21:36:20 place is greater than 5, Far NearHazelwood_Maths_G03_TB_Part 1.indb 31 round up the number to the next thousands.
Concept 4.2: Add 3-digit and 4-digit Numbers 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? 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 = _________ & Remembering and Understanding Let us now understand the addition of two 3-digit numbers with regrouping. We will also learn to add two 4-digit numbers. Add 3-digit numbers with regrouping 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 1: Add 245 and 578. Solution: Arrange the numbers one below the other. Regroup if the sum of the digits is more than 9. 32 05-08-2023 21:36:21 Hazelwood_Maths_G03_TB_Part 1.indb 32
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 Th H T O 23 823 Solve these O Th H T O + 197 Th H T 171 390 + 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 2: Add 1352 and 3603. Solution: Arrange the numbers one below the other. Solved Step 1: Add the ones. Step 2: Add the tens. Th H T O Th H T O 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 49 5 5 955 Addition 33 Hazelwood_Maths_G03_TB_Part 1.indb 33 05-08-2023 21:36:21
Solve these Th H T O Th H T O Th H T O 41 9 0 20 0 2 111 1 +2 0 0 0 +3 0 0 3 +2 2 2 2 Add 4-digit numbers with regrouping We regroup the sum when it is equal to or more than 10. Example 3: Add 1456 and 1546. Solution: Arrange the numbers one below the other. Add and regroup, if necessary. Solved Step 1: Add the ones. Step 2: Add the tens. Th H T O Th H T O 1 11 1456 1456 +1 5 4 6 +1 5 4 6 2 02 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 34 05-08-2023 21:36:21 Hazelwood_Maths_G03_TB_Part 1.indb 34
Application Look at a few examples where we use addition of 3-digit and 4-digit numbers. Example 4: Vinod had some stamps out of which he gave 278 stamps to his brother. Vinod now has 536 stamps left with him. How many stamps did he have in the beginning? H TO Solution: Number of stamps Vinod has now = 536 11 Number of stamps he gave his brother = 278 5 36 Number of stamps Vinod had in the +2 78 beginning = 536 + 278 = 814 8 14 Therefore, Vinod had 814 stamps in the beginning. Th H TO Example 5: Ajit collected `2683 and Radhika collected 1 1 2 6 83 `3790 for donating to a nursing home. What is 3 7 90 73 the total money collected? 6 4 Solution: Amount collected by Ajit = `2683 + Amount collected by Radhika = `3790 Total amount collected for the donation = `2683 + `3790 = `6473 Example 6: The number of Class 3 students in Heena’s school is 236. The number of Class 3 students in Veena’s school is 289. How many total number of students are present in Class 3 of both the schools? Solution: Number of students in Heena’s school = 236 Number of students present in Veena’s school = 289 Total number of students present in Class 3 of both the schools = 236 + 289 = 525 Higher Order Thinking Skills (H.O.T.S.) Let us see a few more examples on the addition of 4-digit numbers. Addition 35 Hazelwood_Maths_G03_TB_Part 1.indb 35 05-08-2023 21:36:22
Example 7: Three pieces of ribbon of lengths 2134 cm, 1185 cm and 3207 cm were cut from a long piece of ribbon. What was the total length of the ribbon before the pieces were cut? Solution: The pieces of ribbon are 2134 cm, 1185 cm Th H T O and 3207 cm long. 11 Length of the ribbon before the pieces were 2134 cut = 2134 cm + 1185 cm + 3207 cm +1 1 8 5 Therefore, the ribbon was 6526 cm long before + 3 2 0 7 6526 the pieces were cut. Example 8: Payal, Eesha and Suma have 1284, 7523 and 5215 stamps respectively. Frame an addition problem. Solution: An addition problem contains words such as - in all, total, altogether and so on. So, the question can be ‘‘Payal, Eesha and Suma have 1284, 7523 and 5215 stamps respectively. How many stamps do they have altogether?” Drill Time Concept 4.2: Add 3-digit and 4-digit Numbers 1) Add 3-digit numbers with regrouping. a) 481 + 129 b) 119 + 291 c) 288 + 288 d) 346 + 260 e) 690 + 110 f) 584 + 329 2) Add 4-digit numbers without regrouping. a) 1234 + 1234 b) 1000 + 2000 c) 4110 + 1332 d) 5281 + 1110 e) 7100 +1190 f) 1403 + 2563 3) Add 4-digit numbers with regrouping. a) 5671 + 1430 b) 3478 + 2811 c) 4356 + 1753 d) 2765 + 1342 e) 4901 + 2222 f) 7625 + 1648 4) Word problems a) There are 142 people riding in Train A and 469 people in Train B. How many people rode in both the trains altogether? b) Ali scores 272 points in one level of a computer game. His friend, Jenny, scores 538 points in the next level. What is their total score in both the levels? 36 Hazelwood_Maths_G03_TB_Part 1.indb 36 05-08-2023 21:36:22
4.3: Add 2-digit Numbers Mentally We have already learnt to add two 1-digit numbers mentally. Let us now learn to add two 2-digit numbers mentally through these examples. How do we add 2-digit numbers mentally? Whenever we add two 2-digit numbers mentally, we first add the digits of the numbers separately. You can follow the steps given below to mentally add 2-digit numbers. Look at the solved example of mentally adding 29 and 56 as well. Steps Adding 29 and 56 Add 83 and 47 29 = 20 + 9 83 = ___ + ____ Step 1: Regroup the two given 56 = 50 + 6 47 = ___ + ____ numbers as tens and ones 9 + 6 = 15 ____ + ____ = ____ mentally. 20 + 50 = 70 ____ + ____ = ____ Step 2: Add the digits in the ones place of the two 70 + 15 ____ + ___ = ____ numbers mentally. = 70 + 10 + 5 = 85 So, 83 + 47 = ___. Step 3: Add the digits in the So, 29 + 56 = 85. tens place of the two numbers mentally. Step 4: Add the sums from steps 2 and 3 mentally (regroup if needed). Step 5: Write the sum of the given numbers. Solve the following mentally. a) 21 + 30 b) 42 + 57 c) 42 + 98 Suraj has 34 sheets of paper, while Kamal has 27. How many sheets of paper do they have in all? Solve mentally. Vivek has 49 bags and Shyam has 29 bags. How many bags do they have in total? Solve mentally. Addition 37 Hazelwood_Maths_G03_TB_Part 1.indb 37 05-08-2023 21:36:23
Reflection Time! 1) Name some games where you add numbers mentally. 2) Imagine you have accompanied your mother to the local fruit shop. Your mother bought apples for `40 and oranges for `33. She gave the shopkeeper a `100 note. The shopkeeper gave her back `23. Estimate mentally if she got back the correct change. Drill Time Train My Brain 4.3: Add 2-digit Numbers Mentally 1) Add 2-digit numbers mentally with regrouping. a) 45 and 47 b) 25 and 56 c) 12 and 19 d) 27 and 35 e) 17 and 37 f) 49 and 26 2) Add 2-digit numbers mentally without regrouping. a) 31 and 22 b) 22 and 42 c) 45 and 51 d) 11 and 34 e) 32 and 61 f) 54 and 13 38 05-08-2023 21:36:23 Hazelwood_Maths_G03_TB_Part 1.indb 38
Drill Time 3) Solve the word problems mentally. a) S uraj has 51 red marbles and 64 blue marbles. How many marbles does he have in all? b) Ram has `35 and his friend has `72. How much money do they have in total? c) Hari has 77 candies and his sister has 33 candies. How many candies do they have in total? d) Parul has 53 stamps and Sonu has 65 stamps. How many stamps do they have in all? Connect the Dots English Fun To remember the rules for rounding off numbers, let us read a poem in English. We will, we will round you. Find the place, look next door Five or more, you raise the score Four or less, you let it rest Look to right, put zeroes in sight We will, we will round you. Addition 39 Hazelwood_Maths_G03_TB_Part 1.indb 39 05-08-2023 21:36:23
Chapter Subtraction 5 Let Us Learn About • estimating the difference between two numbers • rounding off numbers • subtracting 3-digit numbers with regrouping • subtracting 4-digit numbers with and without regrouping • subtracting two numbers mentally 5.1: Estimate the Difference between Two Numbers Now that you’ve learned how to round off numbers and estimate the sum of two numbers, you can apply the same rules to estimate the difference between two numbers. But first, can you quickly explain to your partner what estimating and rounding off are? (If you want to revise, look at Concept 4.1.) How do we estimate the difference between two numbers? Just like estimating the sum of two 2-digit numbers, you first round off both numbers to the nearest tens and then subtract the smaller number from the bigger one. Let’s say you need to estimate the difference between 86 and 12, these are the steps: 1) You round off 86 to the nearest tens which gives you 90 and round off 12 to the nearest tens which gives you 10. 2) Then you subtract them to get the estimated difference: 90 – 10 = 80. 40 Hazelwood_Maths_G03_TB_Part 1.indb 40 05-08-2023 21:36:26
Imagine that your mother gave you 94 sweets on your birthday. What will you round off 94 to? Now imagine that you have to distribute 46 sweets among your friends. What will you round off 46 to? After distributing the sweets, how many are remaining with you? What is the estimated difference of 94 and 46? Can you think of a similar problem using 3-digit or 4-digit numbers and estimate the difference between the numbers with your partner? Work on it and share it with the class. Hints: To estimate the difference between two 3-digit numbers, we round off the numbers to the nearest 100. To estimate the difference between two 4-digit numbers, we round off the numbers to the nearest 1000. Represent the numbers on a number line to round off correctly. Round off 256 to the nearest 100s. 100 150 200 250 300 350 400 256 Far Near 256 is nearer to 300 than 200. So, it is rounded up to 300. Reflection Time! 1) Why do you think a number line helps in understanding the rounding off concept easily? 2) When you are travelling long distances by road or on a train, estimate the distance and the time taken to reach different milestones and note them in your book. 3) Think of any two situations where you can use your estimation skills. Round off 4358 to the nearest 1000s. 3000 4000 5000 6000 If the digit in the hundreds 4358 place is less thaSnu5b, rtorauncdtion Near Far 41 off the number to the 4358 is nearer to 4000 than 5000. same thousands. 05-08-2023 21:36:26 So, it is rounded off to 4000. Hazelwood_Maths_G03_TB_Part 1.indb 41
Drill Time 5.1: Estimate the Difference between Two Numbers 1) Estimate these differences: a) 65 – 15 b) 48 – 16 c) 67 – 32 d) 896 – 432 e) 679 – 387 f) 795 – 564 2) Word problems a) In a class, there are 562 students. Of them, 118 are from the red group, 321 are from the green group, and the rest are from the blue group. About how many students are in the blue group? b) S neha has 77 balloons. She gives 42 balloons to her sister. About how many balloons remain with Sneha? c) Ajit bought 38 new books from a book fair. Now he has 74 books. About how many books did he have before he bought the new books? Concept 5.2: Subtract 3-digit and 4-digit Numbers Think The given grid shows the number of men and women in Farida’s town in the years 2023 and 2024. Years 2023 2024 How can Farida find out how may more Men 2254 2187 men than women lived in her town in the Women 2041 2073 two years? 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. 42 05-08-2023 21:36:27 Hazelwood_Maths_G03_TB_Part 1.indb 42
a) 15 – 0 = _________ b) 37 – 36 = _________ c) 93 – 93 = _________ d) 18 – 5 = _________ e) 47 – 1 = _________ f) 50 – 45 = _________ & Remembering and Understanding We have learnt how to subtract two 3-digit numbers without regrouping. Let us now learn how to subtract them with regrouping. 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. And, we always start subtracting from the ones place. Let us understand this with an example. Example 1: Subtract 427 from 586. Solution: To subtract, write the smaller number below the larger number. Step 1: Subtract the ones. But, 6 – 7 is Solved Step 3: Subtract the not possible as 6 < 7. So, regroup the hundreds. digits in the tens place. Step 2: Subtract the tens. 8 tens = 7 tens + 1 tens. Borrow 1 ten to the ones place. Reduce the tens by 1 ten. Now subtract 7 ones from 16 ones. H TO H TO H TO 7 16 7 16 5 7 16 –4 8\\ 6\\ 5 \\8 \\6 5 \\8 \\6 27 –4 2 7 9 59 –4 2 7 15 9 H TO Solve these H TO H TO 6 23 5 52 4 53 – 3 76 – 2 63 – 2 64 Subtraction 43 Hazelwood_Maths_G03_TB_Part 1.indb 43 05-08-2023 21:36:27
Subtract 4-digit numbers without regrouping Subtracting a 4-digit number from a larger 4-digit number is similar to subtracting a 3-digit number from a larger 3-digit number. The following examples help you understand this better. Example 2: Subtract: 5032 from 7689 Solution: To subtract, write the smaller number below the larger number. Solved Step 1: Subtract the ones. Step 2: Subtract the tens. Th H T O Th H T O 768 9 76 8 9 −503 2 −50 3 2 7 5 7 Step 3: Subtract the hundreds. Step 4: Subtract the thousands. Th H T O Th H T O 7 68 9 7689 −5032 − 5 03 2 2 65 7 657 Solve these Th H T O Th H T O Th H T O 2879 4789 8000 –2137 –2475 –2000 Subtract 4-digit numbers with regrouping In subtraction of 4-digit numbers, we can regroup the digits in thousands, hundreds and tens places. Let us see an example. Example 3: What is the difference between 7437 and 4868? Solution: Write the smaller number below the larger number. 44 05-08-2023 21:36:27 Hazelwood_Maths_G03_TB_Part 1.indb 44
Steps Solved Solve these Step 1: Subtract the ones. Th H T O Th H T O 1654 But, 7 − 8 is not possible as −1 2 4 6 74 2 17 7 < 8. So, regroup the tens digit, −4 8 Th H T O 3. 3 tens = 2 tens + 1 ten. Borrow 3\\ \\7 5674 1 ten to the ones place. 6 8 −2 3 8 2 9 Step 2: Subtract the tens. But, Th H TO 12 2 − 6 is not possible as 2 < 6. 7 So, regroup the hundreds digit, −4 3 \\2 17 4. 4 hundreds = 3 hundreds + 4\\ 3\\ \\7 1 hundred. Borrow 1 hundred to 868 the tens place. 69 Step 3: Subtract the hundreds. Th H T O But, 3 − 8 is not possible. So, 13 12 regroup the thousands digit, 7. 7 thousands = 6 thousands + 6 \\3 \\2 17 1 thousand. Borrow 1 thousand to the hundreds place. \\7 4\\ 3\\ \\7 −4 8 6 8 569 Step 4: Subtract the thousands. Th H T O Th H T O 13 12 7468 6 \\3 \\2 17 −4 8 3 7 \\7 4\\ 3\\ \\7 −4 8 6 8 2569 Application Subtraction of 3-digit numbers is very often used in real life. Here are a few examples. Example 4: Sonu bought 375 marbles. He gave 135 marbles to his brother. Subtraction 45 Hazelwood_Maths_G03_TB_Part 1.indb 45 05-08-2023 21:36:28
Solution: How many marbles are left with him? H TO Total number of marbles Sonu bought = 375 375 −1 3 5 Number of marbles given to Sonu’s brother = 135 Number of marbles left with him = 375 – 135 = 240 2 4 0 Therefore, 240 marbles are left with Sonu. Example 5: Vinod had 536 stamps. He gave some stamps to his brother and then Vinod was left with 278 stamps. How many stamps did Vinod give his Solution: brother? H TO Total number of stamps Vinod had = 536 12 Number of stamps Vinod had after giving some to his brother = 278 4 2\\ 16 \\5 \\3 \\6 Number of stamps he gave his brother = −278 536 – 278 = 258 258 Therefore, Vinod gave 258 stamps to his brother. We can use subtraction of 4-digit numbers in real-life situations. Let us see some examples. Example 6: Mohan’s uncle stays 8630 m away from Mohan’s house. Mohan travels 6212 m of the distance. What is the distance yet to Th H T O Solution: be covered by Mohan to reach his uncle’s house? 2⁄ 1⁄0 Distance between Mohan’s house and his uncle’s 8 630 house = 8630 m − 6 212 Distance Mohan travels = 6212 m 2 418 Remaining distance Mohan has to travel = 8630 m – 6212 m = 2418 m Therefore, Mohan has to travel 2418 m more to reach his uncle’s house. Example 7: A rope is 6436 cm long. A 3235 cm long piece is cut from it. How much of the rope is left? Solution: Length of the rope = 6436 cm Th H T O 6436 Length of the piece cut = 3235 cm −3 2 3 5 The length of the remaining piece of rope 3201 = 6436 cm – 3235 cm = 3201 cm Therefore, 3201 cm of the rope is left. 46 05-08-2023 21:36:28 Hazelwood_Maths_G03_TB_Part 1.indb 46
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