Oasis School Mathematics Book-5 1 Author Shyam Datta Adhikari 5 Class Approved by the Government of Nepal, Ministry of Education, Curriculum Development Centre, Sanothimi, Bhaktapur as an additional material. Anamnagar, Kathmandu, Nepal Phone: 01-4313205
Oasis School Mathematics Book-5 2 Name : .................................................... Class : ................... Roll No. : .......... Section : ................................................... School : ................................................... Publisher Oasis Publication Pvt. Ltd. Copyright The Publisher Edition First : 2071 (B.S.) Second : 2072 (B.S.) Third : 2073 (B.S.) Fourth : 2075 (B.S.) Fifth : 2077 (B.S.) Sixth : 2080 (New Curriculum) Price : Rs. 359/- Quantity : (5000 pcs.) Contributor Rajendra Sapkota Layout Oasis Desktop Anamnagar, Kathmandu Printed in Nepal
Oasis School Mathematics Book-5 3 Oasis School Mathematics has been designed in compliance with the latest curriculum of the Curriculum Development Center (CDC), the Government of Nepal with a focus on child psychology of acquiring mathematical knowledge and skill. The major thrust is on creating an enjoyable experience in learning mathematics through the inclusion of a variety of problems which are closely related to our daily life. This book is expected to foster a positive attitude among children and encourage them to enjoy mathematics. A conscious attempt has been made to present mathematical concepts with ample illustrations, assignments, activities, exercises and project work to the students in a friendly manner to encourage them to participate actively in the process of learning. I have endeavored to present this book in a very simple and interesting form. Exercises have been carefully planned. Enough exercises have been presented to provide adequate practice. I have tried to include the methods and ideas as suggested by the teachers and subject experts who participated in the seminars, and workshops conducted at different venues. I express my sincere gratitude to my friends and well wishers for their valuable suggestions. I am extremely grateful to Man Bahadur Tamang, Laxmi Gautam, Sunil Kumar Chaudhary, Ram Prasad Sapkota, Saroj Neupane and Yadav Siwakoti for their invaluable suggestions and contributions. Sincere gratitude to Managing Director Oasis Publication for his invaluable support and cooperation in getting this series published in this shape. In the end, constructive and practical suggestions of all kinds for further improvement of the book will be appreciated and incorporated in the course of revision. Shyam Datta Adhikari Author March 2023 Preface
Oasis School Mathematics Book-5 4 Contents Unit 1 GeOMetry 5 1. Line and Angle................................................................... 6 2. Solid Objects....................................................................... 33 Unit 2 Arithmetic 39 3. Number System.................................................................. 40 4. Fundamental Operations in Mathematics....................... 81 5. Fractions............................................................................... 103 6. Decimal................................................................................ 126 7. Percentage............................................................................ 143 Unit 3 meASurement 151 8. Time...................................................................................... 152 9. Distance............................................................................... 166 10. Capacity................................................................................ 172 11. Weight................................................................................... 175 12. Perimeter, Area and Volume............................................. 180 Unit 4 StAtiSticS 197 13. Bill and Budget................................................................... 198 14. Chart and Bar graph.......................................................... 208 Unit 5 AlgebrA 219 15. Algebraic Expressions........................................................ 220 16. Algebraic Equation ............................................................ 230 Model Test Paper ........................................................................ 241
Oasis School Mathematics Book-5 5 Ruler, Protractor, Set square, Square grid paper, A4 size paper, Scissors, etc. materials required : • To draw the angles from 00 to 1800 with the help of protractor • To draw angles like 600 , 1200 , 900 with the help of compass • To measure the angles with the help of protractor • To measure the angles of a triangle and quadrilateral with the help of protractor • To identify acute angle, obtuse angle, right angle, straight angle and reflex angle • To draw the parallel lines and perpendicular line in square grid paper • Lines and angles Contents • Solid objects Expected Learning Outcomes Upon completion of the unit, students will be able to develop the following competencies: 12 3 6 9 25 Geometry 1
Oasis School Mathematics Book-5 6 • The arms of first angle are OP and OQ, where as the arms of second angle are XY and YZ. • The vertices of first angle is 'O' and the vertice of second angle is Y. • Name of first angle is angle POQ or angle QOP and the name of second angle is angle XYZ or angleZYX. Remember ! Observe the given figure, see the notations given here and discuss the answer of these questions in your classroom. • What are the arms of both angles? • What are the vertices of given angles? • Name both angles. P Q R Read : Angle PQR Write : ∠PQR Z P O Q Figure. (i) Arm Vertex Angle X Y Figure. (ii) Arm Vertex Angle Review Lines and Angles UNIT 1
Oasis School Mathematics Book-5 7 1. Show the angle, vertex and arms in the given figures. a. b. class Assignment 3. name the following angles in both ways. A B O D F E O M P Q O ∠AOB ∠BOA or or or or N 2. Write the vertex and arms of the given angles. a. b. A B O Vertex : Arms : and Vertex : Arms : and P Q O a. c. d. b.
Oasis School Mathematics Book-5 8 how to measure an angle? We use a protractor to measure an angle. To measure the angle ABC, follow the following steps. Protractor Observe the given figure and answer the questions given below. • What is the name of given figure? • For what purpose this instrument is used? • How many scales are there? Steps • Place the protractor in such a way that its centre point is exactly on the vertex B. • Adjust it so that line BC is along 0° - 180° line. • Start counting from 0°, which is above BC. Note the number of degrees at the point where the other arm AB passes. • 0° of inner scale lies on line BC, so take the inner scale. In the above figure, arm AB passes through 50° mark. So ∠ABC = 50°. A B C B C 50° A • The given figure is a protractor. • This instrument is used to measure the angle. • There are two scales in it. Measurement of an Angle
Oasis School Mathematics Book-5 9 Write the measurement of the given angles: b. ∠AOB = ∠EOF = a. O C B A O D F E class Assignment Exercise 1.1 2. Write the measurement of the given angles: 1. Answer the following questions. O C A E F O a. b. O A 130° B Use inner scale, 0° of inner scale lies on OA. O C 50° D Use outer scale, 0° of outer scale lies on OC. a. Which instrument is used to measure an angle? b. What two scales are there in the protractor? c. If an arm is coincide with 1800 of inner scale, which scale should we use to measure the angle?
Oasis School Mathematics Book-5 10 4. a. Take any three points X, Y and Z in your copy and draw ∠XYZ and measure the angle XYZ. b. Take any three points A, B and C in your copy and draw ∠ABC and measure the angle ABC. c. Draw angle PQR and measure the angle with the help of protractor. Answers Consult your teacher. e. f. O B A P Q O B C F E F G 3. measure the size of the given angles with the help of a protractor. a. A b. D c. E c. Q d. X Y O O P Project Work In a chart paper, draw 5 different angles. Measure each angle by protractor.
Oasis School Mathematics Book-5 11 C B C B A B C construction of angle with the help of protractor With the help of a protractor, we can construct an angle of given measurement. Look at these examples properly and get an idea about the construction of an angle. example 1 Construct ∠ABC = 70° Steps: • Draw a ray or line segment BC. • Place the protractor in such a way that its centre is exactly on the point B and line BC along its 0° - 180° line as in the figure. • Use the scale whose 0° lies on BC. • Start to count from 0° and mark A on 70°. • Remove the protractor and join AB. ∠ABC is a required angle with measurement of 70°. A B C A Construction of Angles construction of angles with the help of compass Draw an angle of 60°, using a compass. A C B D Steps: • Draw a ray AB • Take a suitable arc and taking A as the centre draw an arc above AB. Mark C where the arc meets AB. • With the same arc, taking C as the centre cut at D. • Join AD. ∠DAB = 60° is the required angle.
Oasis School Mathematics Book-5 12 bisection of given angle Bisection means division of an angle into two equal halves. Observe the given figure and get the idea of bisection. ∠AOB = 500 , ∠AOC = 250 and ∠BOC = 250 OC divides ∠AOB into two equal parts. So, OC is the bisector of ∠AOB. O A C B Steps: • Draw a line AB of suitable length. • Take a suitable arc and taking A as the centre draw an arc which meets AB at C. • Taking C as the centre and using the same arc, cut the first arc at D. • Taking D as the centre and using same arc, cut the first arc again at E. • Join AE and produce it to F. Steps: • Draw a line AB of suitable length. • Take a suitable arc and taking A as the centre draw an arc which meets AB at C. • Taking C as the centre and using the same arc, cut the first arc at D. • Taking D as the centre and using same arc, cut the first arc again at E. • Taking D and E as the centre cut at the point F. • Join AF. example 2 Draw an angle of 120° using a compass. example 3 Draw an angle of 90° using a compass. C E D F A C E D A B B ∠FAB is the required angle where∠FAB = 90° ∠FAB is the required angle where∠FAB = 120° F
Oasis School Mathematics Book-5 13 1. construct the following angles using a protractor: a. 15° b. 22° c. 60° d. 65° e. 86° f. 92° g. 105° h. 112° i. 124° j. 145° k. 160° l. 175° m. 170° n. 126° 3. construct the following angles with the help of a protractor and bisect them: a. 80° b. 60° c. 40° d. 110° e. 130° 2. construct the following angles using compass. a. 60° b. 90° c. 120° Exercise 1.2 Answers Consult your teacher. Steps: • With O as centre, draw an arc of suitable measure which cuts OA and OB at C and D respectively. • Taking C and D as centre draw arcs of equal radii to intersect at E. • Join OE. example 4 Bisect the given ∠AOB. A E C D O B OE bisects ∠AOB, i.e. ∠AOE = ∠BOE Project Work I. In chart paper draw three angles of different measurement. Bisect the given angle. Measure the angles after bisection. II. Using local material prepare a protractor and ruler.
Oasis School Mathematics Book-5 14 Observe the given figures and answer the questions given below: types of angle • What do the above figures represent? • Are they of same size? • Measure each angles and write their size. • Guess, how to categorise the angles? Acute angle In the given figure, ∠AOB = 50° which is less than 90°.An angle whose measurement is less than 90° is called an acute angle. \ ∠AOB is an acute angle. A O B 50° Obtuse angle In the given figure, ∠AOB = 110°, which is more than 90° and less than 180°. An angle whose measurement is more than 90° and less than 180° is called an obtuse angle. \ ∠AOB is an obtuse angle. O B A 110° Types of Angles
Oasis School Mathematics Book-5 15 right angle In the given figure, ∠AOB = 90°. An angle whose measurement is exactly 90° is called right angle. \ ∠AOB is a right angle. O B A 90° Straight angle In the given figure, ∠AOB = 180°. An angle whose measurement is 180° is called straight angle. So, ∠AOB is a straight angle. A O B 180° reflex angle An angle whose measurement is more than 180° and less than 360° is called a reflex angle. ∠AOB shown in the figure is a reflex angle. O A B 230° Angles Figure Size examples Acute angle Acute angle less than 90° 30°, 40°, 50°, etc. Obtuse angle Obtuse angle more than 90° and less than 180° 110°, 125°, 145°, etc.
Oasis School Mathematics Book-5 16 Right angle Right angle 90° 90° Reflex angle More than 180° less than 360° 190°, 200°, 230°, 300°, etc. Straight angle Straight angle 180° 180° 1. classify the angles given below into acute, right, obtuse, straight and reflex angle: a. 54° b. 67° c. 118° d. 127° e. 90° f. 180° g. 164° h. 15° i. 252° j. 192° 2. name the type of given angles without measurement. A B C a. D F E b. G H I c. M O N P Q R X Z Y d. e. f. Exercise 1.3
Oasis School Mathematics Book-5 17 3. take the measurement of given angles and categories them into acute angle, right angle and reflex angle. a. b. c. Z Y X M N O R O O S P Q d. 4. a. An angle is given in the figure. (i) Name the vertex and arms. (ii) Guess which type of angle is this? (iii) Measure this angle. (iv) Which type of angle is this? (v) Is your guess on the type of angle correct? P Q R 4. Answer the following questions: a. What is a point called where two arms of an angle meet? b. What is an angle called whose measurement is exactly 90°? c. What is an angle called whose measurement is more than 180° and less than 360°? d. Which type of angle measures 180°? e. Is 160° an obtuse angle? Give reason.
Oasis School Mathematics Book-5 18 5. in the given figure, a. name the angles which are acute b. name the angle which is obtuse c. name the angle which is right angle d. which type of angle is ∠BOC? Answers Consult your teacher. b. take any three points on your copy and draw ∠DeF. then answer the following questions. (i) Name the vertex and arms of this angle. (ii) Guess which type of angle is this? (iii) Measure ∠DEF with the help of a protractor. (iv) Which type of angle is this? (v) Is your guess correct? D E F Project Work I. On the chart paper paste tooth peaks to show acute angle, obtuse angle, right angle and reflex angle. II. Name 2 objects on the surrounding where there is (i) acute angle, (ii) obtuse angle, (iii) right angle A O D C B
Oasis School Mathematics Book-5 19 Observe the given letters and find the number of different types of angles in it. Letters Number of acute angle Number of obtuse angle Number of right angle Number of straight angle Activity
Oasis School Mathematics Book-5 20 construction of parallel lines in square grid paper Observe the given pair of lines and find their features. Let's observe following pair of lines. All three pair of lines are parallel lines. Arrow on the lines means that given lines are parallel. Fig.(i) Fig.(ii) Fig.(iii) • Which pair of lines are not meeting at a point? • Which pair of line do not meet however far they are extended? • What is the last pair of lines called? • What are the first two pair of lines called? • Are the two edges of book parallel? • Are the two blades of scissors parallel? • Are the lines of your copy parallel? • Last pair of lines are not meeting at a point. • Last pair of lines do not meet however far they are extended. • First two pair of lines are called intersecting lines • The last pair of lines are called parallel lines. • Yes, two edges of books are parallel. • No, two blades of scissors are not parallel. • Yes, the lines of copy parallel. Parallel Lines
Oasis School Mathematics Book-5 21 A A' M N M' N' B P Y X X' Y' P' Q Q' B' Take two points A and B in a square grid paper as shown in the figure. Since, we have to draw a line parallel to AB, take point A which is 2 units below A and point B', 2 units below B. Join A' and B', then A'B' is parallel to AB. Similarly, to draw a line parallel to PQ, take a point P' one unit below P and Q' one unit below Q. Join P'Q'. Then, PQ is parallel to P'Q'. Similarly, to draw the line parallel to XY, take any two points X' and Y' , 2 units below from any two points of the line. Join X' and Y' to get the line X'Y'. Hence, the line X'Y' is parallel to XY. note: Parallel lines are not necessary to be equal.
Oasis School Mathematics Book-5 22 1. identify whether the following pair of lines are parallel or not. Exercise 1.4 2. Draw the parallel lines to the lines given in the figure. E F G H L K J I P Q M N A B D C a. a. c. e. g. f. h. b. d. b. c.
Oasis School Mathematics Book-5 23 Let's observe the following pair of lines. Second pair of lines are called perpendicular lines. If the angle between two line is right angle, such lines are perpendicular lines. construction of perpendicular lines in a square grid paper Draw a line AB which is a vertical line. Take any point C on the line AB. From C draw a horizontal line CD. Hence, AB and CD are perpendicular lines. D A C B Answer the following questions. • What is the value of angle between first pair? • What is the value of angle between second pair of lines? • What is the value of angle between third pair of line? • What is type of indicated angle given in the figure (iv)? • Angle between first pair is acute angle. • Angle between second pair is 900 . • There is no angle between the third pair. • The indicated angle in figure (iv) is obtuse. Fig.(i) Fig.(ii) Fig.(iii) Fig.(iv) Perpendicular Lines
Oasis School Mathematics Book-5 24 Let's draw two perpendicular lines on the line PQ. Take any two points S and U. From two points draw two vertical lines RS and TU. In the second figure, EF and HG are two perpendicular lines on CD. Similarly, draw a horizontal line MN. Take any point 'O" on line MN. From 'O" draw a vertical line OP. Hence, OP and MN are perpendicular lines. Try to draw a perpendicular line on Z of the line XY. Remember ! Horizontal and vertical lines are perpendicular lines. C E H G D F Q U T S P R Y M O P N X Z
Oasis School Mathematics Book-5 25 1. identify whether the following pair of lines are perpendicular or not. (a) (b) (c) Exercise 1.5 2. Draw the perpendicular lines on the given lines. A B Y X P Q a. d. b. e. c. f.
Oasis School Mathematics Book-5 26 3. identify whether the following are parallel, perpendicular or neither. Remember ! Take some graph sheet and draw 3 pairs of parallel lines and 3 pairs of perpendicular lines. a. Two edges of the book. b. Length and breadth of your copy. c. Two blades of scissors. d. Length and breadth of whiteboard. The given figure is a triangle. Three line segments AB, BC and AC form a triangle ABC. The line segments are called the sides of the triangle. The meeting points of the sides are called the vertices of the triangle. \ AB, BC and AC are the sides of triangle ABC. A, B and C are the vertices of triangle ABC. ∠A, ∠B and ∠C are the angles of triangle ABC. • What is the name of given figure? • How many sides does the given figure have? Triangle Observe the given figures and answer the questions given below: A B C Triangle ABC is denoted by DABC.
Oasis School Mathematics Book-5 27 A triangle is a closed figure bounded by three line segments. ‘D’ is a symbol to denote a triangle. P Q R Figure : DPQR Sides : PQ, QR and PR Vertices : P, Q and R Angles : ∠P, ∠Q and ∠R Say : Triangle PQR Write : DPQR What is the name of the given figure? ........................ . • What are its sides? ..............., ................and.................. . • What are its angles?.............., ................and.................. . • What are its vertices?................., ................and................. Observe the given figure and answer the questions given below. P Q R class Assignment What is the name of given figure? ............................ . • What are its sides? ................., ..................and................... . • What are its angles? ................., ................and.................... . • What are its vertices?................, .................and.................. . X Y Z Take a protractor, measure three angles ∠BAC, ∠ABC and ∠ACB. measurement of angle of triangle ∠BAC ................ 0 ................ 0 ................ 0 ∠ABC ∠ACB B C A
Oasis School Mathematics Book-5 28 Observe the given figure and answer the questions given below. • What is the name of given figure? • How many line segment does it have? Four line segments AB, BC, CD and AD form a quadrilateral ABCD. It is a quadrilateral. C A B D Given figure is a quadrilateral. Let's measure all four angles of quadrilateral. ∠QPS ∠PQR ∠QRS ∠PSR ................ 0 ................ 0 ................ 0 ................ 0 P Q R S The line segments are called the sides of quadrilateral. The meeting points of the sides of the quadrilateral are called the vertices of quadrilateral. AB, BC, CD and AD are the sides of quadrilateral ABCD. A, B, C and D are the vertices of quadrilateral ABCD. ∠A, ∠B, ∠C and∠D are the angles of quadrilateral ABCD. A quadrilateral is a closed figure bounded by four line segments. Quadrilateral measurement of angle of quadrilateral
Oasis School Mathematics Book-5 29 1. measure the angle of given triangles. Find the sum of the angles. Q R B A P Exercise 1.6 Z T Y X S U a. a. c. b. b. d. 2. measure the angles of given quadrilateral. Find the sum of the angles. Q P S R C B A D
Oasis School Mathematics Book-5 30 Answers Consult your teacher. Project Work • On the chart paper draw three triangles of different measurement. Measure each angle. Find the sum of the angles and draw out the conclusion. • Take a graph sheet and draw a. Two pairs of parallel lines b. Two pairs of perpendicular lines. Identify their properties and present it in your classroom. W X Z C D F E Y c. d.
Oasis School Mathematics Book-5 31 Choose the correct alternatives. 1. The instrument which is used to measure the angle is called (i) ruler (ii) set square (iii) protractor 2. The angle which is less than 90° is called (i) an acute angle (ii) an obtuse angle (iii) a reflex angle 3. The given angle AOB is (i) an acute angle (ii) an obtuse angle (iii) a reflex angle 4. Given pair of lines are (i) intersecting lines (ii) perpendicular lines (iii) parallel lines. 5. Angle between two parallel lines is (i) 0° (ii) 90° (iii) 45° 6. Which one of the following statement is not true? (i) A reflex angle is always greater than 180°. (ii) Angle between two perpendicular lines is 90°. (iii) Length of two parallel lines must be equal. 7. Which of the following statement is not true? (i) AB and CD are parallel lines. (ii) AB and EF are perpendicular lines. (iii) AB and CD are perpendicular liens. 8. The magnitude of given angle is (i) more than 90° (ii) exactly 90° (iii) less than 90° A O B B D F A C E
Oasis School Mathematics Book-5 32 Unit test Full Marks – 22 Attempt all the questions. 1. a. Write the names of vertex and arms of given angle. 1 b. Write the name of angle in both ways. 1 2. Construct the following angles with the help of protractor. 4 a. 54° b. 112° c. 95° d. 16° 3. a. Measure the following angles with the help of protractor. 4. Construct the angle 900 with the help of compass. 2 5. Classify the following angles into acute, obtuse, reflex and right angle. 6 a. 46° b. 95° c. 90° d. 112° e. 195° f. 60° 6. Identify whether the following pair of liens are parallel or perpendicular. 2 O P Q (a) (b) b. Identify the type of above angles? 2 4 (iii) (iv) (ii) (i)
Oasis School Mathematics Book-5 33 Observe the given figure and identify the name of the given solid objects. The meeting line of two square faces of a cube is its edge. In the above cube AB, AD, CD, BC, BG, GH, AH, DE, HE, EF, GF, and CF are its edges. Hence, a cube has 12 edges. Face Edge Vertex A D E C G F B H Faces, edges and vertices of a cube Given figure is a cube. It contains 6 square faces. It's square faces are ABCD, ABGH, GHEF, CDEF, BCFG and ADEH. Review Solid Objects UNIT 2
Oasis School Mathematics Book-5 34 The meeting line of two square faces of a cube is its edge. In the above cube AB, AD, CD, BC, BG, GH, AH, DE, HE, EF, GF, and CF are its edges. Hence, a cube has 12 edges. The meeting point of the edges of a cube is called its vertex. In the above cube A, B, C, D, E, F, G and H are its vertices. A cube has 6 faces, 12 edges and 8 vertices. Activity Collect a cubical in your surrounding and show its edges, corners and faces. F D E H B C G A edges, vertices and faces of a cuboid Given figure is a cuboid. It contains 6 rectangular faces. Its rectangular faces are ABCD, BCHG, EHCD, ADEF, EFGH and AFGB. As we know that meeting line of two planes are its edges. So its edges are AB, BC, GH, GF, FE, ED, BG, AF, CD, AD and EH. Each edges of a cuboid are parallel to each other. Hence, cuboid has 12 edges. A cuboid has 8 corners. Its corners are A, B, C, H, G, E, F and D. Corners of a cuboid are its edges. A cuboid has 6 faces, 8 vertices and 12 edges. Activity Collect some cuboid available in the surrounding and show their edges, faces and vertices. Project Work I. Take 6 square pieces of paper having the same size. Paste them to form a cube and present that in your class. Also count its number of vertices edges and faces. II. Take 6 rectangular pieces of paper. Paste them to form a cuboid and present that in your classroom. Also count its number of vertices, edges and faces.
Oasis School Mathematics Book-5 35 construction of skeleton of solids We can construct the skeleton of solids by using match stick or juice pipe or pieces of straws. • Cut some pieces of straws or juice pipes. • Join these pipes with help of needle and thread. • Fold this to form a structure of rectangle. This is the skeleton of a rectangle. Similarly, we can make the skeleton of a triangle. We can use these to make a face of solid figures. Join such structure to form the skeleton of solid figure. Activity • Using match stick or juice pipe or pieces of straws make the structure of a triangle and a rectangle. • Use these structures to form a skeleton of cuboid and cube. Exercise 2.1 1. Answer the following questions. (a) What is the shape of each faces of a cube? (b) What is the shape of each face of cuboid? (c) What is the meeting line of two faces called? (d) What is the corner of a solid figure called?
Oasis School Mathematics Book-5 36 4. Observe the given figure of solid object and write whether these area vertex, an edge or a face. a. AB b. EF c. ABCD d. BCGF e. A f. B g. H h. G 5. Observe the given figure and answer the questions given below. a. What is the name of given object? b. What are its vertices? c. What are its edges? d. What are its faces? e. How many edges, faces and vertices does it have? 6. construct a cube and cuboid in your copy. 7. Write one difference between a cube and a cuboid. Project Work Take 6 square shaped paper (Hard) of equal size. Join their edges with the help of glue. Prepare a cube and show it faces, edges and vertices. Demonstrate this object in your classroom. A D E C G F B H P R Q X Z Y W S 2. identify the name of given solid objects. 3. copy the given figure in your copy and write the name of the part shown by the arrow. a. b.
Oasis School Mathematics Book-5 37 choose the correct alternatives. 1. the name of given object is (i) cylinder (ii) cylinder (iii) sphere 2. how many vertices and edges does a cube have? (i) 8 vertices and 12 edges (ii) 6 vertices 8 edges (iii) 6 vertices and 8 edges. 3. i have 6 rectangular faces, 8 vertices and 12 edges. i am a (i) cube (ii) cuboid (iii) cylinder 4. meeting line of the two faces of a cube is (i) a vertex (ii) a face (iii) an edges 5. meeting point of two or more than two edges is (i) side (ii) face (iii) vertex 6. A cube has (i) 6 square faces. (ii) 6 rectangular faces. (iii) 6 triangular faces. 7. A solid object has 6 rectangular faces, 8 vertices and 12 edges, then the solid object is (i) cube (ii) cuboid (iii) cone 8. A cuboid has (i) 6 square faces (ii) 6 rectangular faces (iii) 6 triangular faces 9. Which of the following statement is not true? (i) a cuboid has 6 rectangular faces. (ii) a cube has 6 square faces. (iii) a cube has 6 vertices. 10. A solid object has 6 vertices of 12 edges, then the object is (i) cone (ii) cube (iii) cuboid
Oasis School Mathematics Book-5 38 Unit test Full Marks – 15 Attempt all the questions. 1. Identify the name of given solid objects. (3) 2. Observe the given figure and identify whether the given parts are a vertex, an edge or a face. (6) a. AP b. CD c. ABCD d. RSBC e. A f. P 3. construct a cube and show its one edge, and one vertex and one face. (3) 4. Answer the following questions. (3) a. How many edges does a cube have? b. How many vertices does a cuboid have? c. How many square faces does a cube have? P R S B D C A Q a. b. c.
Oasis School Mathematics Book-5 39 Expected Learning Outcomes Upon completion of the unit, students will be able to develop the following competencies: materials required : Place value chart, flash card of numbers, square, grid paper, etc. • To place the numbers upto 9 digits in Local place value chart and to write their name. • To place numbers upto 9 digits in International place value chart and to write their name. • To use the comma and to write the number name using both system of numeration. • To read, write and to place the Devagari numbers in place value chart. • To identify odd or even numbers. • To separate the prime number of composite numbers from 1 to 100. • To find the factors of given number. • To find the multiples of given number. • To round off the numbers upto 5 digits to its nearest thousands and its nearest hundreds • To simplify the expression containing at most three operations among division, multiplication, addition and subtraction. • To identify proper and improper fractions. • To convert improper fraction into mixed number and mixed number into improper fraction. • To add or subtract like fractions having at most three terms. • To convert fraction into percentage and percentage into fraction. • To convert decimal into percentage and percentage into decimal. • Number system • Fundamental Operation on Mathematics • Fraction • Decimal • Percentage Contents 12 3 6 9 60 Arithmetic 2
Oasis School Mathematics Book-5 40 • Read the following numbers 15, 197, 2568, 9069, 41726, 40801, 516234, 920342, 8014672 • Use comma in these numbers. • How many thousands is equal to one lakh? • Read the following number in Devanagari, !%, !#$, !^(, %&^, *(^= Place value of the digits of a number In the previous class, we have already learnt about the place value of the numbers up to 7 digits. A place value chart is used for writing the numbers which have more than two digits. The given table shows the place value chart for larger numbers. Crores Lakhs Thousands Ones Ten Crores (100000000) Crores (10000000) Ten Lakhs (1000000) Lakhs (100000) Ten Thousands (10000) Thousands (1000) Hundreds (100) Tens (10) Ones (1) Do You Know! In about 100 A.D., the Hindus invented the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. The Arabs learnt it from the Hindus and spread the system all over the world. So the system is called Hindu Arabic number system. With these ten digits we can write any large number. Number System UNIT 3 Review
Oasis School Mathematics Book-5 41 Arabs, crores, lakhs, thousands and ones are the periods. Ones, tens, thousands, ten thousands, lakhs, ten lakhs, crores, ten crores, arabs, ten arabs are the places of the digits in a number. Place value of a digit = digit × its place Let's take a number 281794613 and discuss the place value of its digits. Crores Lakhs Thousands Ones Ten Crores Crores Ten Lakhs Lakhs Ten Thousands Thousands Hundred Tens Ones 2 8 1 7 9 4 6 1 3 2 8 1 7 9 4 6 1 3 Ones 3 × 1 3 Tens 1 × 10 10 Hundreds 6 × 100 600 Thousands 4 × 1000 4000 Ten thousands 9 × 10000 90000 Lakhs 7 × 100000 700000 Ten lakhs 1 × 1000000 1000000 Crores 8 × 10000000 80000000 Ten crores 2 × 100000000 200000000 Showing this number in place value chart Number Places Digit × its place Place value Twenty eight crore seventeen lakh ninety four thousand six hundred thirteen
Oasis School Mathematics Book-5 42 The number name is: Twenty eight crore seventeen lakh ninety four thousand six hundred thirteen. While reading the number, we have to read the number, along with their periods. types of place value system There are two types of place value system in which the numbers are arranged. They are : a. Local place value system b. International place value system local place value system Ones, tens, hundreds, thousands, ten thousands, etc. are the places of Local place value system and ones, thousands, lakhs, crores etc. are the periods. Let's write a number in place value chart according to Local system of numeration. Take a number 543216159. Period Place Place values Ones Ones Tens Hundreds 1 10 100 Thousands Thousands Ten thousands 1000 10000 Lakhs Lakhs Ten lakhs 100000 1000000 Crores Crores Ten crores 10000000 100000000 Crores Lakhs Thousands Ones Ten crores Crores Ten lakhs Lakhs Ten thousands thousands Hundreds Tens Ones 5 4 3 2 1 6 1 5 9 Period Place The name of this number is: Fifty four crore thirty two lakh sixteen thousand one hundred fifty nine.
Oasis School Mathematics Book-5 43 use of comma in local place value system Comma separates the periods of the number, so there are different methods of using comma in Local and international place value system. 74,26,83,91,214 1. Show the number 274821093 in the place value chart and write its number name. 2. Separate the periods using comma according to nepali place value system and write their number names. 56041292 Number name: .................................................................................................. .............................................................................................................................. Number name: .................................................................................................. 508264316 Number name: ................................................................................................. ............................................................................................................................. 432045932 Number name: ................................................................................................. ............................................................................................................................. 3. Write the place value of each of the digits of the given number. Starting from the right, put the first comma after three digits then put commas in the gap of two digits. Separate the periods ones, thousands, lakhs, crores and arabs by using comma. 74,26,83,91,214 class Assignment 4 6 2 1 5 3 2 8
Oasis School Mathematics Book-5 44 Let's take a number 384176427 and write it in a place value chart according to international system of numeration. The name of this number is, Three hundred eighty four millions one hundred seventy six thousand four hundred and twenty seven. Millions thousands Ones Hundred millions Ten millions Millions Hundred thousands Ten thousands Thousands Hundreds Tens Ones 3 8 4 1 7 6 4 2 7 Period Place Place values Ones Ones Tens Hundreds 1 10 100 Thousands Thousands Ten thousands Hundred thousands 1000 10000 100000 Millions Millions Ten millions Hundred millions 1000000 10000000 100000000 international Place Value System Ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions etc. are the places of international place value system of numeration. Ones, thousands, millions, billions, etc. are its periods.
Oasis School Mathematics Book-5 45 Ten crores Crores Ten lakhs Lakhs Ten thousands Thousands Hundreds Tens Ones Hundred millions Ten millions Millions Hundred thousands Ten thousands Thousands Hundreds Tens Ones 7 2 9 4 3 7 2 1 4 According to Nepali place value system, the number name is: Seventy two crore ninety four lakh thirty seven thousand two hundred fourteen. According to international system, the number name is: Seven hundred twenty nine million four hundred thirty seven thousand two hundred and fourteen. 1 lakh = 100 thousand 10 lakhs = 1 million 1 crore = 10 million 10 crores = 100 million In case of international place value system 270,146,945. use of comma in international place value system Starting from the right put the comma in the gap of three digits. Separate the periods ones, thousands, millions, billions by using comma. 270,146,945. Let's write a number in Nepali as well as International place value chart and obtain the relation of their place value. Take a number 34729437214. comparison of nepali and international place value system
Oasis School Mathematics Book-5 46 450321482 Number name: .................................................................................................... ...................................................................................................... 824316096 Number name: ................................................................................................... ...................................................................................................... 3. Separate the period using comma and write the number name using international place value system. 2. Show the number 238204152 in the place value chart and write its number name using international place value system. Number name: .................................................................................................. Remember ! • While writing number name write the number along with its periods. • Ones, thousands, millions, Billions, etc. are the periods of International place value system. • Ones, thousands, lakhs, crore, etc. are the periods of local place value system. 1. What are the periods in international place value system? ............................................................................................................................ ............................................................................................................................ class Assignment
Oasis School Mathematics Book-5 47 5. Show the following numbers in the place value chart according to international system of numeration and write their number name. a. 2384096342 b. 5639842014 c. 500215026 d. 1932645357 e. 2670807365 3. Put the commas in each number according to nepali as well as international place value system and write their number names: a. 437893216 b. 5021037418 c. 637401894 d. 201050112 4. Write the numerals for the given number name, using comma. a. Forty two crore sixty three lakh seventy eight thousand five hundred twenty seven b. Sixty crore eighty four lakh eighty seven thousand seven hundred forty three c. Twenty one arab seventy nine crore sixty two thousand eight hundred twenty one d. Thirty two crore eight lakh forty nine thousand two hundred twenty seven e. Thirty two crore seven lakh seventeen thousand six hundred twenty eight 2. Write the following numbers in place value chart according to local as well as international system of numeration and also write their number names: a. 132706432 b. 261479025 c. 573264135 d. 503261451 1. Answer the following questions: a. What are the first 9 places in local place value system? b. What are the first 4 periods in local place value system? c. What are the first 9 places in local place value system? d. What are the first 3 periods in local place value system? Exercise 3.1
Oasis School Mathematics Book-5 48 6. Put comma (,) in the following numbers using international place value system of numeration and write their name. a. 459304321 b. 703841932 c. 5670863214 d. 234316142 e. 502100214 7. Write the numerals for the given number name, using comma: a. Thirty seven million, two hundred forty six thousand eight hundred thirty nine b. Two hundred twenty six million, five hundred sixty nine thousand eight hundred sixty five c. Five hundred twenty one million sixty three thousand seven hundred eighty one d. Two hundred eighty eight million three hundred forty six thousand nine hundred eighty one e. Three hundred twenty five million eight hundred thirty one thousand nine hundred sixty four 9. Answer the following questions: a. How many lakh are there in 1 million? b. How many thousand are there in 1 lakh? c. How many million are there in 1 crore? d. How many crore are there in 100 million? 7. Write the place value of underlined digits: a. 368509263 b. 926582019 c. 872314091 d. 572439012 e. 579216374 f. 123742813 8. Write the place value of each of the digits of the number 250132506:
Oasis School Mathematics Book-5 49 Place value of any digit of a number is the product of the digit and its place. So the expanded form of a number is the sum of all the place values of the digits. Let's write the number 2463210897 in expanded form. Place value = digit × its place. Expanded form of a number = sum of the place value of all digits. Ten Crores (100000000) Crores (10000000) Ten Lakhs (1000000) Lakhs (100000) Ten Thousands (10000) Thousands (1000) Hundred (100) Tens (10) Ones (1) 4 6 3 2 1 0 8 9 7 \ 463210897 = 4 × 100000000 + 6 × 10000000 + 3 × 1000000 + 2 × 100000 + 1 × 10000 + 0 × 1000 + 8 × 100 + 9 × 10 + 7 × 1 Standard form Expanded form 2. Write in standard form: a. 4 × 100000000 + 3 × 10000000 + 6 × 1000000 + 4 × 100000 + 5 × 10000 + 8 × 100 + 7 × 10 + 6 = ........................................... a. 6 × 100000000 + 4 × 1000000 + 2 × 100000 + 3 × 10000 + 0 × 1000 + 2 × 100 + 1 × 10 + 8 = ........................................................................................ 1. Write the given numbers in expanded form. a. 75640218 = .................. + .................. + .................. + .................. + .................. + .................. + .................. + .................. b. 462839702 = .................. + .................. + .................. + .................. + .................. + .................. + .................. + .................. + .................. class Assignment Expanded and Standard form of a Number
Oasis School Mathematics Book-5 50 the greatest and the Smallest number of Different Digits The Hindu Arabic system consists of 10 digits which are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Study the given table properly and get the idea about the greatest and the smallest number of different digits. Digit Smallest number Greatest number 1 2 3 4 5 6 7 8 9 10 1 10 100 1000 10000 100000 1000000 10000000 100000000 1000000000 9 99 999 9999 99999 999999 9999999 99999999 999999999 9999999999 Greatest number of one digit = 9 9 + 1 = 10 = smallest number of two digits. Greatest number of two digits = 99 99 + 1 = 100 = smallest number of three digits. I got an idea! 9 is the greatest number of one digit. The greatest number of other digits can be obtained by repeating 9 in all places. I understand, greatest number of proceeding digit + 1 = smallest number of one more digit. Forming the smallest and the greatest number with given digits: Let's select three digits 0, 1, 8. The possible 3 digit numbers from the given digits are 108, 801, 810, 180, Among these numbers, The greatest number = 810 The smallest number = 108