Math5

Multiplication of Two Decimals 312 Example 1: Find the product of 2.9 and 3.j.2. x 28 Step 1: lgnore the decimal points and take the numbers as 2g +6240 and 372. . 6 / 3b Step 2: Find their product. Step 3: The number of digits after the decimal point in 2.8 is 1 and the number of digits after the decimal point in 3.12 is 2. Total number of digits after the decimal point = 1 + 2 = 3 Step4: putthedecimal pointafterthree digits starting from the rightto get the answer, that is, 8.736. Thus, the product of 2.8 and 3.12 is 8.736. 152L Example 2: Find the product of 18.7 and 1.521. x 187 L87 x 152L = 284427 r0647 Number of digits after the decimal point in 18.7 is 1. 1.2t680 Number of digits after the decimal point in j..52 j. is 3. +152100 Total number of decimal places is 3 + 1 = 4 Place the decimal point in the product after 4 digits 2a4427 from the right. Therefore, the answet is 28.4427. Example 3: lf 1 litre of petrol costs { 68.50, then how much should Jeniffer pay for 23 litres of petrol? Cost of i. litre of petrol = t 68.50 6850 Cost of 23 litres of petrol = < 68.50 x 23 x 23 Thus, Jeniffer should pay ? 1575.50 t..the total number of decimal 20550 +137000 places is 2 in the product.) r5/)5U Remember The product of a decimal number and 1 is the decimal number itselt and the product of a decimal number and 0 is zero,

1. Find the product of the following: c. 731.1 x 1OO d. 48.92 x 100 a. 1.81 x 10 h. 2372x7O g. 35.3 x 1OO h. 92.92 x Io e. 52.9 x 1OO0 f. LZI'237 x7O0O .i 7 .lgL x 12 j. 42'72 x 16 k. 881.213 x l. 218.3 x 9 m. 98.5 x 13 n. 138 23 x 7 o. 48.48x4 P. 80005x15 q. 3 51 x 7.9 r' 5'3 x 6'2 s. :.2.28 x !4.7 t. 15.21 x 1'37 u. 8.12 x 4.8 v' 13.23 x 5'27 w. 6.25 x 5.5 x. 53.6 x 2L'4 2.MrPate|canrun3'3Tkminonehour.Howmanyki|ometrescanherunin12hours? 3. Pinky can fill 7.82 litres of water in 1 minute' How much water can she fill in 15 minutes? 4. A car can cover a distance of 68 52 km in one hour' How much distance will it cover in 15 5 hours? 5. The price of 1 kg of rice is I 50 75' Find the price of 2 5 kg of rice' Il<Aas'ht'\"n\"aiiautetaa.baocwalloorifefrsufiotsrhbarevainkfgals5t'oH.3e5r cbaro|othreiersAarnundhaated3agsl|icaesssooffmpizi|zka and a a cup of lup oirt'rlti,\"na ior breakfast Each slice of pizza has 75'5 calories and shrikhand has 120 calories' Who consumed more calories and by how much? Who is having a healthier breakfast? Justify' List at least 5 breakfast meals which are healthy and tasty' 1. Given that 5.001 x 4.5 = 22.5045. Find the following, without actually multiPlYing a. 500.1 x 45 = b. 5.001 x 0.45 = c. 50.01 x 4.5 = 2. Anush can fill 22.75 litres of water into a tank in 10 minutes. How much water can he fill in 11; hours?

Division of Decimals \" Division by a Whole Number The process of division of a decimal number by a whole number is the same as the division of a whole number by another whole number except the extra care that needs to be taken in placing the decimal point in the quotient. Example 1: Solve: 38.25 + 9 4.25 Step 1: Since 3 < 9, therefore divide 38 by 9. ThisgivesQ=4andR=2. Step 2: Now, place a decimal point in the quotient corresponding to the decimal point in the dividend. Bring down 2 and divide 22 by 9. Bring down the next digit, and divioe. Thus, the quotient is 4.25 and the remainder is O. 4/ol.;2;0ltl6t Example 2: Divide 0.824 bv 4. -0.8 + + 024 step 1i Here, there is no whole part in the dividend. -24 Therefore, write zero in the quotient and place a decimal point in the quotient corresponding to the 0.307 decimal point in the dividend. Divide the first disit after the decimal point by 4. .-lrn- o-T, 'i' Step 2: Bring down 2. Since 2 cannot be divided by 4 as 2 is -0.e + I less than 4. Therefore, write zero in the quotient and o27 bring down the next digit, and divide. -2L Thus, the quotient is 0.205 and the remainder is O. Example 3: Divide 0.921 by 3. Step 1: Again, there is no whole part in the dividend. Therefore, write zero in the quotient and olace a decimal point in the quotient corresponding to the decimal point in the dividend. Divide the first disit after the decimal point by 3. Step 2: Bring down 2. NoW 2 cannot be divided bv 3 as 2 is less than 3. Therefore, write zero ln the ouotient and bring down the next digit, and divide. Thus, the quotient is 0.307 and the remainder is 0.

4:Example Divide 45.87 bY 4. While dividing decimols by o whole tL. 467 5 number, divide unfil there is no remoinder. 45.87 i-44++ | n-_si I I 18 6 27 1A 30 (Remainder is not zero, so write zero next to 3 and continue -24 to divide.) 02 (Again, the remainder is not zero, so write one more zero 9-? sn6 continue to divide till the remainder is zero.) 0 Therefore, 45.87 + 4 = 71.467 5 Division by 10, 100 or 1000 Let us check if the division of a decimal number by 10, 100 or 1000 is different from normal division method. 2a.25 5.723 L.47 2L 10 100 )s7 2.1ol0 1000 -s00 I I 7r 3l 25 -70,nol -20 -2 0 0 5U 300 0 - 300 Therefore, we have 282.5O=70=28.25 1000 - 1000 572.300+100=s.723 747 2.LOOO + l0OO = 1.47 21' What do vou observe from the above results? When a decimal number is divided by 10, 1oo or 1ooo, the decimal point gets shifted to Fthe left by as many digits as the number of zeros in the divisor' I e4 lf -\\g,Ttr

so, shift the decimal point while dividing by 10, 1\"00 or 1000. There rs no need to go through the whole process of diviston. What if 32.41 is divided bv IOOO? Put a zero to the left of 32 and then shift the decimal point by three digits to the left. 32.4t-1OO0=O.O324L Remember Shifting of the decimal point can be done only while dividing the decimal number bv 10, 100 or L000. Division of a Decimal by Another Decimal To divide a decimal number by another decimal number, Step 1: Move the decimal point in the divisor to the right until it is a whote number and count the number of places moved. step2: Movethedecimar point in the dividend to the right by the same number of praces. Step 3: Then divide the new dividend by the new divisor. Example 1: Calculate: 8.4 + 0.7 8.4 8.4 + 0.7 = A7 (Moving the decimal point by 1 place to the right) - 84 -\" 7 Thus, 8.4 + 0.7 = i.2 Example 2: Divide 4.62 by 0.21. Iq.AZ + O.2f = (Moving the decimal point by 2 places to the right) Thus, 4.62 + O.21, = 22 462 A@Bq zz 021- 2tz r 22 Example 3: Calculate: 4.2625 + 0.05 -:=A lCar 4.2625 + O.O5 = 0.05 (Moving the decimal point by 2 places to the right) +zo. z5

85.25 The number of decimol 426.25 points moved should be the some: both in the numeroton -t_9- ond denominotor. lo -25 I2 25 - 25 0 Thus, 4.2625 + 0.05 = 85.25 Example 4: Two friends, Meera and Jessica contributed ( 7.75 and { 8.45, respectively to buy 36 cookies. Find the price of each cookie' Meerapaid=(7.75 0.45 L6.20 Jessica Paid = t845 .'. Total amount paid=<7.75 + { 8.45 = { 16.20 L 80 .'. Price of one cookie = { 16.20 + 36 = t 0.45 -_1__Cg 0 Therefore, the price of each cookie is { 0.45 or 45 paise. 1. Divide the following: a. 6469.2 + b. 48 O24 + t2 c. 36.93 + 3 d. t 394.08 + 16 h. 787.7 + 0.24 e.30.25+25 j. 213.8 + 8 C. 49O.32 + 3.2 i. 0.4127 + 3.3 18.41 + 1.1 m. 82.9 + 10 n I2L.7 + 7OO k. 540.5 + 0.25 o. 328.71+ LOO 2. lf 110.25 kg of rice is to be distributed equally among 100 children, then how much would each child get? 3. lf 112 litres of oil is to be filled equally in bottles whose capacity is 3'5 litres, then find how manv such bottles will be needed?

4. Aakash bought 64.75 litres of milk and made 18.5 kg of dessert with it. Find how much milk is needed to make l. ke of dessert. 5. A train covers 220.55 km in 5.5 hours. What is the speed of the train? {Hnfj speed = \"::\" '\"\" ) ltme 6. Mrs Banerjee cuts 781.28 m of ribbon equally into j.6 pieces. What is the length of each Diece? ffi Mixed fruit jam is made out of 2.75 kg of grapes, 1.45 kg of apples and 3 kg of sugar. lf 0.6 kg ofjam is put in one bottle, then how many bottles are needed to store the entire quantity of jam? Target Olympiod 0.9 0.8 o.75 Fill in the empty squares with suitable decimals so that the sum every column, row and diagonal is the same. o.7 1. The place value of 3 in 921.13 is 2. 42.7 x = 4270 3. 9t.2 + 4. 8.81 x 30 = 88.1 x 5. 0.008 x 1= 6. 3.4612 x 1000 = 7. 7.921x O = 7 8. 7000+700+ 170+ 1000 = lf 71.86 x 5 = _, then 0.7 j.86 x 5 = Fill in the boxes using < or > sign. flb. s8.036 e8.306 a. 81.31f 18.131

Percentage observe the following grids. 71 boxes are shaded 28 boxes are shaded 47 boxes are shaded out of 100. This can be out of L00. This can be out of 100. This can be 7t 47 28 written as tO6. written as . written as . lOO 1OO What do vou observe about all the shaded squares in the grid? The squares shaded are out of 1Oo squares. Such fractions are called percentages' Percentage is a way of expressing a number as a fraction with denominator 100' The symbol of percentage is % and read as'per cent', which means per hundred or out of L00. so, the above shaded regions can also be written as 7L%,28% and 47% and read as 71 per cent, 28 per cent and 47 per cent, respectively' Whv do we use Percentages? Let us take an example. Aamna scored 34 marks out of 50 in the first test and 15 marks out of 20 in the second test. Has her performance improved? Let us convert the test marks into percentages. 15 15x5 34 34x2 68 second test: fr = frIJ = 75 rtn 50 2Fir<r rAqt.= -100 = b6e/o - r*= = 50x Thus, her perfo-rmance has improved

j'j.AsHs IAB 4Lj_,UUy objective: To find the sum, difference and product of decimal numbers Materials required: 10 x L0 grid sheet, colour pencils Method: Solve: 0.3 + 0.41 + 0.25 0.3 + 0.4L + 0.25 = 0.30 + 0.41 + 0.25 Colour 30 squares pink, 4L squares blue and 25 squares green. Count all the squares that are coloured. 96 squares out of 100 are coloured, which 96 -is 100 = 0.96 Solve: 0.45 - 0.1 X ,,\\ x XX 0.45 - 0.1 = 0.45 - 0.10 Colour 45 squares pink out of 100 and cancel out 10 squares. Count the remaining squares. We are left with 35 squares out of 100, which is 35= 0.3 5. Therefore, 0.45 - 0.1 = 0.35 100 Solve: 0.7 x 0.5 Colour 70 squares red out of L00, lengthwise (7 columns). colour 50 squares yellow out of 100, breadthwise {5 rows). Count the squares that are common. Colour them orange. 35 squares out of 100 are coloured in orange. I nereTore. u. / x u-5 = u-55

I 1. Convert the following fractions into decimals' 1 7 '\"' 18t-\" a 101: 1, 100 f -10 d 4a.2 ^''4- 20 2. Convert the following decimals into fractions' e. 15.1 a. 18.05 o. +,>2 c.72.025 3. Arrange in ascending order' b.8.71,,8.7,8.A,8.O7 a. 4!.27,4L'L2, 4L.O72, 411'2 4. Arrange in descending order' b. r.02,I.2, r.O02, l.2r a. 15.3, 16 5, !5.8' 16.7 5. Add the following: o. 3!.2+27.9+32.7L a. 4.85 + L4.I2 + 8.2 + 7.129 d. 7.946 + 74.36 + 22.9 + 30.01 c. 5.45 + 3.02 + 8.009 6. Subtract the following: c. I8.I23 - 4.9 d. 71-3'12 a. +.6' z.t tz h. ro-7.257 7. From the sum of 12 2'75 and78'778,take away the sum of 68'04 and 35 271' 8. Find the product. \"d.. 7.12xtZ b. 13.15 x 7 c. 18.21 x 9.5 9.7 x I2.2 e. IS.ZS x 7Lz L L7 .36 x t7.9 9. Divide the following: b. /6.IJ - rJ c. 55.55 i ).f e. 16.25> + t.t a. 25.32 + 4 f. 65.454 + 12 d. 48.L2 + t.2 10. Rahul cycles 8.28 km in 4 5 hours' What is his speed per hour? 1.1. Thereare24bagsofcoffeeinashop lf each bag weighs 0 62 kg' what is the total weight of all the coffee bags? L2. Raj covers 13.26 km by car and 15 km by walking to reach his office Find the total distance to his office. oo

ET A. The decimal point is missing in each of the following numbers. Use the given hints to place the decinial point at the appropriate place. 1. 361. -------+ Number of seconds it takes Mehak to write her name 2. L05 -------+ Length of a new pen in centimetres that Mehak got 3. 330 + Length of an edge of Mehak's maths book in centimetres 4. 24535 Price in rupees of a T-shirt that Mehak got for her birthday 65.. 155 --1173 Mehak is in 5th standard. Her height in centimetres. > Length of Mehak's pencil in centimetres. B. You are given the following 5 digits as shown below. ,1,i.- -rl .,1 2 s Use the digits to form the following decimal numbers. 1. Greatest possible number but less than 60. 2. Least possible number but greater than 30. 3. Number as close as possible to 10. +. tJisreolaced bv !, what would be your answers for questions 1,2 and 3? c. Multiple Choice Questions 0.563 c. 56.3 o. u.u5b5 c. 0.701 1. 8.445 + 0.15 is equal to d. 0.070L 1.01 d. .101 a. 5.63 2. tf 21.03 + 3 is 7.01, what is 2L.03 + 0.3? a.70.L b. 7 .O1. 3. Ll_. LL + LL is equal to b. 10.1 AH'ITIIIITIITTT Ft lrol dd_i I

6 xt ii Let us revise the following terms: AO ii Closed Curve: A curve which starts and ends at the same point. Open Curve: A curve that does not end at the starting point. L_l @ Polygon: A closed plane shape made up of three or more line segments. Circle: A simple closed curve. The distance between the centre meter and any point on the circle is called the radius. Radius The line joining any two points on a circle is called a chord. The chord passing through the centre is called the diameter. [ine: lt extends indefinitely in both directions. ATdB Line Segment: lt has both starting and end points. CD It has a fixed length. Ray: lt has a starting point but no end point. M MNf N It extends indefinitely in one direction. 1. Draw line segments ofthe following measures using a ruler. a. 5cm5mm b. Ll.cmLmm c. gcm6mm

2. Classify as ope n curve or closed curve. d(? i; a' //\\ D. c. /x 1) lj \\t)t ///N -\\ \"o ,A ..o3. ldentify and write the names ofthe following regular polygons. 4. In the given figure, identify and write the name of a. A chord: b. A diameter: c. A radius: Also, draw a circle whose diameter is 12 cm and find its radius. Moths Around Us Venky is making food for his children, Sanjana and Saarika. They are playing in the kitchen with ice cream sticks. Suddenlv Sanjana shouts excitedlV :Sanjana Look! | have made a fish with the ice cream sticks. :Saarika I have also made a fish, but why is my fish so thin? :Sanjana Look! we have made two fish, one is.short and stout and the other is long and thin. Why? They went to their father with their doubts. :Venky That is because ofthe angle between two ice cream sticks. :Saarika What is an angle papa? :Venky Ask your teacher. She will be able to explain it better than I can. Before we learn about angles, we should understand what is a point, a ray, a line and a line segment.

Point, Line, Line Segment and Ray Point A point is a basic unit of geometry. We represent a point by a dot and name it with a capital letter, say A. Some physical examples of point that you see in daily life are tip of a pencil lead, tip of a pin, etc. Can you think of some more examples of a point? Line A line is a collection of points extending endlessly in both the directions along a straight path. AB is a straight line. The arrows in two directions indicate that it goes endlessly in both the directions. so, a line has no starting point and no end point. A line can also be represented by a small letter, say k, l, n, etc. Line Segment A part of a line is called a line segment. lt has a starting point and an end point. We call it by means of its starting point and end point such as line segment PQ and write it as PQ or QP. a Ray A ray is a part of a line which has a starting point but goes endlessly in the other direction. The direction in which the ray goes endlessly and the starting point are clearly indicated in the rav and is written as AB. B Remember Line AB is written as AB (with arrow marks on both sides), line segment AB is written as AB (no arrow marks) and ray AB is written as AB- (arrow mark on one side).

The curtain rods from which curtains hang reminds us of a line segment. Think of more examples from your daily life qhich reminds you of a line, line segment and ray. Angle When two rays meet at a point, an angle is formed. The point where the rays meet is called the vertex and the ravs are called the arms of the angle. The angle formed at O is written as ZPOQ or IQOP where.Z is the symbol for an angle. Measuring Angles The angle between the two arms joining at a point is measured in degrees. A degree is the unit used for measuring angles ouler scate o and it is symbolicallv denoted as \". Inner scale You can use a protractor to measure angles. lt is commonly a semi-circular device. A protractor has two sets of measurements written on it. These are called scales. There is an inner scale and an outer scale, both having measurements from 0. to Lgo. in different directions. There is a baseline and the midpoint of the baseline is called the cenrre. Now let us measure ZCBA. Step 1: Place the protractor over ZCBA such that the centre coincides B with the vertex B of the angle and the baseline lies on the arm AB of ZCBA. Step 2: Note down the measure of the angle against the arm BC counting fhus, ICBA = 44\"

protractor to find the measure of these angles. c. d.. 4\\ -, \"' Dg 2. Draw four different angles with a ruler and measure them with a protractor. Types of Angles Right Angle Look at the angles formed in the following figures. 4I -,,t rl r') : The angle formed while writing the letter L, the angle formed between the minute hand and the hour hand at 3 o'clock, the angle formed at the corners of the blackboard in your class, etc., are all right angles. Right angle measures exactly 90'. ZABC is a right angle. The angles at the corners of your book, the corner of your teacher's table, etc., are all right angles. Think of some more real-life examples of right angles around you. BC Can you think of English letters in which right angles are formed? A few have been done for you. E Complete the list.

Straight Angle An angle measuring 180. is called a straight angle. ZPQR is a straight angle. Look at the following examples. I + Acute Angle An angle which is less than a right angle is called an acute angle. An acute angle is smaller than 90\", but is more than 0\". ZABC is an acute angle. Look at the following examples. t/ Obtuse Angle An angle which is more than a right angle but less than a straight angle is called an obtuse angle. An obtuse angle is smaller than 180' but is more than 90.. ZXYZ is an obtuse ansle. Here are some examples. t Complete Angle An angle that measures 360\" is called a complete angle. ZPOQis a complete angle. See a few examples. J ( o')

l-. Write the type of angle for each of the following angles. '> t' b <' 4\\ LS $,t___ /\" r lr.o\"ern\"u.lrry\".tlnifef\"arengntet yoga asanas. -.^L rbf\\'€' \\qt---1-+ rrtf'+- marked ir €\\-eacn asana. Write a few advantages of doing yoga every day. Construction of an Angle Using a Protractor Example: Draw an angle of measure 50'. Step 1: Draw a ray AB. A rur$qwryry4q'wqilfl lilf '{|til|I||r{rlNrpryq'qul Step 2: Place the protractor on AB such that the baseline coincides with AB and the centre coincides with A. Step 3: Mark a point C on the outer scale, corresponding to the marking of 50' Step 4: Remove the protractor and join A and C. We get ZBAC = 50'.

L. Draw the following angles using a scale and a protractor. f. 725\" a. 30' b. 55\" c.. 110. d. 85. e. 90\" Parallel and Perpendicular lines :r: r: r We know that when two lines meet, an angle is formed. Look at the lines AB and CD. It looks like that they do not intersect. But CD can be extended to meet AB at O, and an angle is formed. lf the angle so formed measures 90\", then the two lines are said to be perpendicular to each other. Let us see a few example below. PQ is perpendicular to AB. The flagpole is perpendicular to the ground JI and the tree trunk is perpendicular to the ground. Now, consider these two lines AB and CD. lf extended, AB and CD do nor meet at all and wherever you measure, the distance between AB and CD will be the same. Such lines are called parallel lines. Two rails of a railway track, a straight road and a ladder are all examples of parallel lines.

1. ldentify and mark parallel and perpendicular lines in the following figures. ..fla. o. 2. ldentify the right angles, acute an_gles and the obtuse angles in the given figure. E llySpl l t ook at the layout of two gardens given below. Name the pairs of parallel and psrpendicular lines in each layout. a.D o. On the occasion of World Environment Day, Ayana and Rohan decided to plant saplings along the boundary of the two gardens. Present your views on World Environment Day emphasizing upon the importance of growing trees. 1. A line is a collection of has a starting point and an end point. 3. A right angle measures 4. An acute angle is than a right angle. 5. An obtuse angle measures than 90\" and less than 6. An angle whose measure is 20\" ls an 7. An angle whose measure is 120\" ls an 8. -Sum of two right angles is a

# [vl_]irv]us uAts \"ry A-UUU Objective: To understand the concept of angles, parallel lines and perpendicular lines Materials required: Notebook, pencil, ruler and protractor Method L. Draw the face of a clock when the angle between the minute hand and hour hand is 120. and write the corresponding time. 30', 50', 90. and 2' Draw a figure using onry rine segments, angres, para|er rines and perpendicurar rines. right angles and obtuse angles in the figure Also count the number of acute angles, drawn. My Proiect tIl 1. Draw angles of the following measures. a. ZPQR where ZQ = 110' b. ZLMN where ZM = 90' c. ZPQR where ZQ = 60' What type of angles do you get? 2. Collect pictures of temples, bridges, towers and other monuments where parallel and perpendicular lines can be found. Stick the pictures on a chart paper with their name, place and year ofconstruction. Markthe parallel and perpendicular lines in each Dicture. Present before your class, the human factors responsible for the damage to our historic monuments. Alsq suggest ways to prevent such damage.

1. Measure the angles marked in the following figures. 2. Classify the following angles as acute angle, obtuse angle, right angle, straight angle and complete angle. D. d.<, /), .> 3. Use a protractor to draw the following angles. a.35\" b. 60\" c. 70\" d. 130\" e. 155' h.30\" f. 90' i. 170. j. 50' A Observe the given figure and answer the following quesuons. A

Wonrsneel 1. Join 1 to 2, 2 to 3, 3 to 4 and 4 to 1. Then join 5 to 6, 6 to 7, 7 to 8 and 8 to 5. Similarly, join 9 to 10, L0 to 11, 11 to 12 and 12 to 9. Similarly, join rest of the points taking four numbers at a time. How manv line segments will be drawn? 'TQ??qe??qqq WT1 T2 T3 14 T5 T6 17 T8 T9 T10 There is a well at the place marked 'W' and LO trees, from T1 to T1O, in a line. Jatin wants to water all the trees. But he can carry water for only one tree at a time. So he plans to come back to the well after watering T1 to take water for T2. lf W to T1 is counted as 1 line segment and T1 to W as another line segment, then how many line segments will Jatin cover by the time he finishes watering all the trees and comes back to the well.

ltl symmetry A ZA shape is symmetrical when one halfofthe shape is exactly S rikethSeyomthmeerhtraYlf li ALine of l\\The line dividing Z the line of symmetrv the symmetrical shape is called 4N \"1. Draw the line(s) of symmetry for the following figures ,* T svmmetry b. 2. Draw the mirror image of the following figures' calculation. b. 10+10=1 a. 8x 4=32 100+10=10 L000+10=100 80x4=320 10,000 +i1100= 800x4=3200 1,00,000 + 10 = 8000 x = 32,000 80,000 x = 3,20,000

Moths Around Us Rahul : What is written on that white van? Father: It is the mirror image of the word AMBULANCE,. Rahul : Father: This is done so that the vehicles ahead can read it as ,AMBULANCE,, the rear view mirror and give way to the ambulance to go fast. Rahul : Where can we use these mirror images? Father: To create patterns and to learn about symmetry. We will discuss this after we reach home, okay! Pattern s You are already familiar with the word pattern and you know how to create patterns, When creating a pattern with designs, the designs repeat. But when we create a pattern using numbers, the numbers may not repeat. Pattern in numbers refers to the logic by which the sequence of numbers is generated. Take a look at the following sequence of numbers. 1.,2, 4, 8, 1,6, 32, ... Here, each number is the double of the previous number. Consider 1, 4,7, L0, L3, ... Here, each number is obtained by adding 3 to the previous number NoW look at the sequence 1, 3,7, IS,3L, ... Are you able to guess what will be the next number? Let us observe the pattern followed below. Ix2+I= 3 3x2+1,=7 7xZ+I=L5 15x2+1=31 So, the next number in the pattern would be 31 x2 + I = 62+ l=63 write the next two terms of the following sequence. a. L,4, L6,64, _, _ b. 1,,4, t3,40, c. 2,3,5,9,17, _, _ d. 3,6, Ls,42,

Square Numbers we can form patterns by arranging dots to form squares of different sides. Count the number of dots in each fieure. 1 9 1,6 We can extend this pattern to obtain a sequence of numbers L, 4, 9, 16, .... Here, each number is obtained by multiplying numbers 1, 2, 3, ... to itself, in oroer. Such numbers are called square numbers. _Write the next two square numbers for the sequence f, 4, g, f6, Triangular Numbers Numbers can be represented in a triangular form also. a aaaa aa 15 a.rj61a0a aaa aaaa The above numbers are called triangular numbers. What will be the next two triangular numbers? Observe that the second triangular number is 3, that is, 1 + 2 (Sum of the first two counting numbers). The third triangurar number is 6, that is, 1 + 2 + 3 (sum of the first tnree counting numbers). Hence, the eighth triangular number will be 1+2+3+4+5+6+7+g=36 Can you find the fifteenth triangular number? Patterns in Calendar We look at the calendar every day flueusf But do you observe any pattern in it? 9u H.T\" f\"Th Fr Sa Take any square (3 x 3) block of dates from a calendar and write a sheet. it on

Example 1: Consider Observe that !6+4=20 18+2=20 16 11 +9=20 Considel Observe that 19 20 27 )+z!=zo 6+20=26 7 +L9=26 L++lZ=ZO Example 2: Consider these column of dates. Column ll Column lll i All these numbers 2 All these numbers 10 All these numbers 9 leave a remainder L7 leave a remainder t leave a remainder IO 2 when divided 24 3 when divided j,,J 1 wten divided 25 5I bY 7. DY I. ^^ rbY /. 30 Take any number from Column I and any number from Column ll. Add the two numbers. You will find the sum in Column lll (Of course, the total should be less than 31, the biggest number in the calendar). For example: 75 + 2 = 17. Find some more interesting patterns and discuss it with your teacher. 1. Write the next two terms in the following sequence. L,3,9,27,8L, _, _ b. t,5,74,30, _, _ c. 5,70, t5,20,2s, _, _ d. 0,3,8, 15,24, _, _ 2. Write the twenty-sixth triangular number. 3. Write the fifteenth square number. 4. Take a square (3 x 3) block of dates inthe current month ofthe calendar and find a pattern in it.

[486.{j!,t.3tnr,::trji .. :. ri . Target Olympiod L. cross out 10 digits from the number 12345123451234512345 so that the remainins number is as large as possible. Keep the order of the digits same. 2. The sum of four 3-digit numbers is 1245. lf each digit in the numbers is replaced by its 9s complement, what will be the total of the new numbers? Hrrt Let the numbers be obc, pqr, xyz and lmn. Let the numbers formed by taking 9s complement of the digits of the original numbers be ABC, PQR, XYZ and LMN, respectively. f hen, d bc + ABC = 999 ; pq r + PQR = gggI xyz + XyZ = ggg and Im n + LM N = ggg Note: Here 'a' and'A' are 9s complement of each other. Therefore, a + 4 = 9. Sum of first 15 odd numbers is 15 x 15 = 225. D. Sum of first 20 odd numbers is 20 x 20 = 4OO. Sum of first 20 even numbers is 20 x 21 = 420. o. Sum of first 30 even numbers is 30 x 31 = 930. 1. Find the sum of the following numbers. First 25 odd numbers : b. First L9 odd numbers : c. First 15 even numbers : First 25 even numbers : 2. Study the following pattern and fill in the blanks. 3 20=

d'i.]A:'j $Ii,eB1 s'1 / Objective: To represent triangular numbers and square numbers Materials required: Colourful circular stickers and chart oaoer Method: stick the circurar stickers on the chart paper to represent trangurar numbers tirl the tenth triangle. Represent square numbers in the same way till the tenth square on the chart paper. show that the combination of two consecutive triangular numbers generates a square number. -1 5 10 and so on ->'l ..... and soon 1A q 1A 'E Prepare a chart on four historicar monuments in India which have beautifur patterns on their exterior and interior write a brief about them. Describe the significance of preservation of historical monumenrs. 1\\5*6'1J/Y+0.141\\Y/536*1+34/\\\\/2\\+21r*, 10/\\\\\\/+\\-+., ./\\/1\\/{+*1.,5\\,0\\//+7*5G\\1/7\\*/ Can you write the next line? The grven information is known as pascal,s traingle. You will learn about pascal's triangle in your higher classes.

SymmetrY Eiffel tower is a symmetrical monument because one half of it is the reflection or the mirror image of the other' Name some other monuments which are symmetrical What is a line of sYmmetrY? tf you fold the first figure along the dotted line, one half will exactly coincide with the other half. Therefore, the dotted line is the line of symmetry' The second figure has two lines of symmetry and the third figure has only one line of symmetrY. How manv lines of symmetry does a square have? 1. Draw the lines of symmetry for the following figures' '€ 2. 3. Make the following figures symmetrical by drawing thei r refl ectron. \"x Y/lb. c. \\Al

Turning Shapes 1 Tile designs can be seen on the floor of houses, restaurants, etc. -n*.The given picture shows the design on a tile. What happens if you turn the design about a fixed point? We can give it either a full turn, half turn or a quarter turn. ,/l\\ Quarterturn \\--0,/ Halfturn Some designs look the same after quarter turn or half turn and some designs change. The above design looks slightly different in each turn. Let us look at a design which remains the same, however vou turn it. Quarterturn It looks the same, doesn,t it? Quarter turn Look at the English letter N. NZ Halfturn What happens when you give it a full turn? Fullturn How many of you have keenly observed the traditional '(o/om' patterns a nd,Rangoll patterns? Quarterturn gsr-g#q.a8 Brse-sni'-9f#f9iFa€ #,\"€ aa{,\\$ Halfturn They look the same after quarter turn or half turn.

The fan given here look the same after a lrd turn. What about this shape? A figure Will it look the same on a which looks the some on lrd turn? f,th turn will_olso look the It will not look the same due to difference in colour. some on {rd turn. fthI nts star shape will look the same on turn. witl this shape look the same on frd turn? frdYes ! As turn is the same as two autn tu.nr. 1. Draw the design for each of the following after quarter turn and half turn. ,+b. 2. The number 88 looks the same after a half turn. Write two 3_digit numbers that same after half turn. look the 3. Write all the English letters which look the same after half turn. \\\\? nl\\ /-\\ .E..r_-_J ,_,F_rb. c. 4. Look at the following shapes. Draw how they will look on Jrd and 1+r\" turn. ti 4,\\\\ V fW)V \\,x._ Creating Patterns The marvellous design of a carpet, the intricate design on a saree are nothing but pafterns created bv repeating a design over and over.

Sometimes, a slight change or a small turn mal(es the pattern more beautiful. 6t'6<6<6< 6s< 6< 6#b6#b66#b dtt),*rsgdp#q),*$9 ldentify and complete the pattern. \" d\"tV fi\\\\ro. 1.. Complete the patterns. ,AVAV. e/J c/J e/l c/0 ,v<A> O U \\r/'1 LS Sumita created the following patterns using waste material. .EEiltrtrtr ***ot-J-tJJ-'l--J..Pick the odd one out and set it right. b =1=**g: , SESOOC \" e&;f6bY6is;Y6;Y6bY6 Create some patterns using waste material.

@l G[D'--.:,':a,\"rl,\"\"u- Create a pattern and ask your friends to complete it. Try to complete the patterns created by your friends. Mlavrutg llgg A-$IIUV Objective: To make a toy windmill and give it a quarter turn, half turn and full turn. Materials required: old newspaper, colours, paper cutter, pin, wooden stick XXX Method: 1. cut out a square sheet of paperfrom an old newspaper and colour it. 2. Fold along the lines as shown and unfold it. Draw a circle in the centre. Nf 3. Cut along the lines till you reach the circumference of the circle and fold one side. 4. Fold allthe corners in the same way as shown. 5. Fix it on the wooden stick with a pin. NoW give it a quarter turn, half turn and full turn and see if these are symmetrical. Discuss your observations in the class. Present your views on advantages of using recycled material. MY Proiect #-- pictures of symmetrical Indian monuments ln your 1,. Stick scrapbook and draw their lines of symmetry' Paste the pictures of animals that are symmetrical in your 2. scrapbook and draw their lines of symmetry Lion-the king of the jungle depicts symmetry' lt is in r€al danger of extinction. Present your views on the reasons for their extinction.

;' 1. Write the number of lines of symmetry of the following figures. i +\\i: '' ,A b sqP^ :LI %'{' i 2. Make the following figures symmetrical by drawing their reflection. d<.al ord c.Q \\ 4 azl : 3. Write the English letters which are symmetrical and draw their lines of symmetry. : : 4. Draw pictures ot any five objects around you that are symmetrical. :: 5. Write the next two numbers in the following sequence. i \" ? A 1n 1q :: h '7 1-1 )-1 \"7 ii c. 2.5. r0, _77. : d. 2,5, 10,50, ::I 6- . -F,ind,.t,he twenty-third triangular number. : i 7. Find the fifty-sixth square number. : trtrtr: 8. Find the pattern in the foilowing block of a calendar. m@tr @@m : J. uv,,,P,srs L,,c Po(Lcrrrr. f _-l, ,b. ,T f | | llr I rf:; ;' oo oo10. Draw a tiling pattern and a border strip of you r choice using geometrical shapes. . -#E-t -

\"WORKSHEE Mr Verma decided to renovate his house by changing the floor tiles. The mason brought a few tiles and told Mr Verma \"Sir, we can join these tiles the way we want and create our own design.\" He created one pattern to show Mr Verma which is given here. Can you help Mr Verma to create some more designs? L23 234 34 L. 1 2 34 2 341 3 4 12 4 L 23 2. 3 1 L3 4 2 24 3 31 2 442 Use your imagination to create your own patterns and colour them. 3. Are the above patterns symmetrical? lf Ves, draw the lines of symmetry. EIHEFIHEITETLEIETFETf,EIf,IE;FTI IIHTH iI IF!tLtA;EtEtFH TH9TTTIIEgHEHTHH T TITggHT

a O I To measure length, we generally use centimetre (cm), metre (m) and kilometre (km) as units, To measure weight (mass), we generally use gram (g) and kilogram (kg) as units. To measure capacity, we generally use litre (L) and millilitre (mL) as unrrs. gd. 1,. Tick the appropriate unit for each of the followins: b. 6s0 g/5s0 kg t L/L mL 15 cm/15 m 5 L/5 mL 2. What unit willyou use to measure the following? a. Length ofa pin b. Weightof a book c. Heightofagirl d. Capacityofa bucket ii is3. The height of one building is 26 m 52 cm and the height of another building ii 32 m 15 cm. Find the difference between the heights ofthe buildings. jl 4. theThe weight of a basket futl of mangoes is 5 kg 250 g. tf the weight of ffiX ii W j. emptybasketis326g,thenfindtheweightofthemangoes. 5. 294L436mLofwateristhereinanoverheadtank.tfl4gL5g4mL 4G ii 6. i=; il tank.of water is added to it, then find the totar quantity of water in the t*_.t converr f he .oltowing: a.54973 mtokmandm b. 59342gtokgandg II c.94L496mLtomL i;

Maths Around Us Rahul's mother is preparing a dish for which she needs the items in the given quantities. sugar-4OO g, water-5OO mL, butter-50 g, egg-1 (slightly beaten), and lemon juice-3o mL Rahul's mother asked him to bring her the required quantities of items. Rahul was ouzzled to see that different quantities have different units. He asked his mother, \"Why are these items written in different units?\" Her mother replied, \"We use different units of measurements depending upon whether we are measuring length, weight or capacity of an object.\" Conversion of Units of Measurement Beside the basic units of measurement such as metre for length, gram for mass and litre for capacity, we have other units as well that help us measure smaller or larger quantities. Kilometre Hectometre Decametre Metre Decimetre Centimetre Millimetre (km) (hm) (dam) (m) (dm) (cm) (mm) 1000 Units of merres Basic L 7 1 100 metres 10 metres Unit of 10 1OO 1OOO Length Length of a metre of a metre of a metre Kilogram Hectogram Decagram cram (g) Decigram Centigram Milligram (dac) (de) (ce) (mc) (kc) (hc) 1t0L 0 T000 Units of Basic -110 of a gram of a gram Weight 1000 grams 100 grams 10 grams unit of Centilitre Millilitre Weight of a gram (ct) tmL) Kilolitre Hectolitre Decalitre titre (tl Decilitre 1-t (kr) (hLt (dat) (dL) loo- 1000 Units of 1000 litres 100 litres 10 litres Basic 1 of a litre of a litre Unit of 10 Capacity Capacity of a litre When we move from a smaller unit to a bigger unit, we divide by 10 for each unit towards its left. +10 +10 +10 +10 +10 +10 Kifl-o-_(k_)__H]e{c-t-o_(_h_)__D_elc{a.-(-d_a)___B_a_sic_ul{-n-_it__D_e_c_i (ldr)---___C_enlrti_(-c'_)__M_illli (m) (nlcl Ll

Example 1: Convert L028 cm into a. decimetre 'i61n?q 1028 cm = = 102.8 dm (We divide by L0 as we are moving 1 unit towards left) b. metre 1.})9 roze.t = i'd? = 10.28 m (We divide by 100, as we are moving 2 units towards left) ' c. kilometre l nta 1028 cm = 16ff;d = 0.01028 km (Moving 5 units towards left) Example 2: Convert a. 120 mL into kL. 11n 'ir - 720 = 0.000120 kL (Since we are moving 5 units towards left) b. 7521 cg to hg. -/15Ez-',r1 ^cg- _= 7527 = 0.7521 hg (Moving 4 units towards left) 10000 Example 3: Convert 1250 mL into litres and kilolitres. I tqn = 1.25 L (since we are moving 3 units towards left) iffi1250 mL = l--rq-n- hr- =10l-0-r0q-0-n00 = 0.00j.25 kL (Moving 6 units towards left) When we move from a bigSer unit to a smaller unit, we multiply by 10 for each unit towards its right. r-*x1_0 __xlLt0-----x1r0 t---txLt0-t x10 x10 Kilo{k} Hecto (hl Deca (dal Basic unit Deci (d) Centi (cl Milli (m) lmlcl Ll Example 1.: Convert 25 hm into cm. 25 hm = 25 x L0000 = 250000 cm (Moving 4 units towards right) Example 2: Convert 3.45 kL into mL. 3.45 kL = 3.45 x 1000000 = 3450000 mL (Moving 6 units towards right)

Example 3: Conve rt a. L5 dag into cg. 15 dag = 15 x 1000 = 15000 cg (Moving 3 units towards right) b. 22.5 hL into 1.. 22.5 hL= 22.5 x L00 = 2250 L (Moving 2 units towards right) 1. convert the following as indicated. D. 416 dag into kilograms J 121 cm into kilometres a. 247 mm into metres f. L248 g into hectograms c. 3042 L into kilolitres e ?qq?.r int^ orrmc 2. Convert the following: 25 hm into millimetres 523 m into centimetres a. 49 km into decimetres f. 34 dal into centilitres c. 18.2 kg into grams e. 12 dg into milligrams 3. Fill in the blanks. daL b. 3498 1= hL = KL 1295 cL = CL d. 748 dm = km= oam c. 5455 kL = Addition and Subtraction rE 5Z 625 Example 1: Add 32 L 625 mL and LL L 380 mL. + 1L 380 We have, 525 mL + 380 mL = L005 mL. 1005 mL can be written as 1000 mL + 5 mL. Write 5 mL in the mL column and carry over 1000 mL as 1L to the Lcolumn. Thus, 32 L 625 mL + 11. L 380 mL = 44 L 5 mL Examole 2: Subtract 420 cm from 7 m. 1:Method Convert higher units into lower units and then subtract. 7m=700cm 700 cm-420 cm = 280 cm = 200cm + 80cm = 2 m 80 cm Ft Thus,7 m -420 cm = 2 m 80 cm I t 30t I

2:Method convert smaller units into higher units and then EE subtract. @, @* 420 cm = 400 cm + 20 cm = 4 m 20 cm t4r2E0 20 cm cannot be subtracted from 0 cm. So, borrow L m from the metre column and regroup O cm to 1oo cm and 7 m to 5 m and then subtract. Thus.7 m -420 cm = 2 m 80 cm Example 3: Two gold bricks were melted. One brick weighed 3 kg 900 g and the other weighed 5 kg 355 g. Find the total weight of the two bricks. During melting, 1 kg 145 g of gold was lost. Determine the weight of gold left after melting. EE 3 900 Weight of first brick +5355 Weight of second brick Total weight of the two bricks Gold lost during melting -rt45 Gold left after melting Thus, the weight of gold left after melting is 8 kg 110 g. Do as directed. a. Add24L42mLand3 kL30 150 mL. b. Subtract 3650 mL from 7 L 500 mL. c. Add 19 km 45 m 40 cm and 85 km 47 m 69 cm. d. Subtract 29 m 34 cm from 40 m. From a can containing 10 litres of milk Mrs Menon used 3.8 litres in the morning and 2.3 litres in the evening. How many hectolitres of milk is left in the can? 28.5 kg of rice, 18.3 kg of pulses and 12.7 kg of wheat are sold in a grocery store. Find the total weight of all the three items. (Give your answer in hectograms)

) A snail travelled 3 m 25 cm on one day and 1 m 75 cm on the second day. How far did the snailtravel? 5. A worm while climbing up a high wall, went up 13 m but slipped back by 3 m 35 cm. How far had the worm reached? 6. shalini's weight is 3500 g greater than her younger brother. The weight of her brother is 35 kg. Find Shalini's weight. 7. Sumit used 2500 mL of water for bathing. lf the total water in the bucket was 6 L 200 mL, then find the water left in the bucket after bathing. L5 Ashutosh and his sister Seema go to Regents Park near their house every morning for workout. Ashutosh runs 2.72 metres in one minute and Seema runs 1.08 metres in one minute. How manv more centimetres does Ashutosh cover in one minute than Seema? Write the benefits of regular exercise in our lives. r. You have a s-litre beaker, a 3-litre beaker and access to unlimited water. How will you exactly measure 4 litres of water? I2. The tail of a fish is as long as its head plus th of its body. lts body is three-fourths of its whole length. lf its head is 4 cm long, what is the total length of the fish? Multiplication and Division ffiE Example 1: Multiply 13 kg 250 g by 9. @ 13 250 Step 1: Multiply the grams column by 9. 9 250gx9g=2kg25og 119 250 Regroup 2 kg to the kg column and write 250 g in the grams column. Step 2: Multiply the kilograms column by 9. 13 kgx9= 117 1* Step 3: Add LL7 kg+2 kg (carry over) = 119 kg Thus, 13 kg 250 g multiplied by 9 is 119 kg 250 g.

2:Example Bharat travels 2 km Z4O m every day. How much distance does he travel in a week? Distance travelled in a day = 2 km 24O m E!E Distance travelled in a week = 2 km 24O m x 7 o 240 7 =15km680m 15 680 Thus, Bharat travels 15 km 680 m in a week. Example 3: The total capacityof6 identical containers of milkisgL. Find the capacity of each container. Total capacity of 6 milk containers = 9 L = 9000 mL .LCapacity of 1 milk contain\"r. = 9003 = 15oo mL =LL500mL Thus, the capacity of each milk container is 1 L 5OO mL. 4:Example Divide 53 m 75 cm by 25. Step 1: Arrange the dividend and the divisor as mcm in simple division sums. z)t t5 It Write 53 in m column and 75 in cm column -50 of the dividend. 2'7 25 goes 2 times in 53. 25 x 2 = 50. Write 50 below 53 and 2 in the quotient column. r 25 53 - 50 = 3. Write 3 as remainder. Step 2: Bring down 7 and write it next to 3 to get 37. 25 goes l time in 37.25 x 1= 25. Write 25 below 37 and 1 in the quotient column. 37 - 25 = 12. Write 1.2 as remainder. Step 3: Bring down 5 and write it next to 12 to get 125. 25 goes 5 times in 125. 25 x 5 = 125. So, write 5 in quotient and 125 below 125 and subtract. Therefore,53 m 75 cm divided by 25 is 2 m j.5 cm.

1. Do as directed. 60 kg 240 g divided by 12 L5 L 200 mL multiplied by L7 c. 328 m 40 cm divided by 8 o. 36 kg 211 g multiplied by 100 2. A pen can hold 10 mL of ink. How many litres of ink is needed to fill lzb oensi 3. Reema bought 2 kg of mango pulp and added 1 kg of sugar to make jam. lf the jam is filled into bottles each of capacity 300 g, then how many bottles would be filled? A lf vou run around a circular park once, you will cover 12.32 metres. How many kilometres will you cover if you run around the park 18 times? 5. 10 cauliflowers weigh 12.78 kg. What is the weight of one cauliflower in grams? L5 Sneha has a habit of eating junk food regularly. Due to this habit, she is gaining 750 g of weight every month and becoming overweight. lf her present weight is 30 kg, what will be her weight in decagrams after a year? Why do you think being overweight is bad? How does it hamper our health? Estimation of Measurements We often estimate measurements to get quick solutions to given problems. An estimated value is close to an exact measurement. The distance from the knuckle to the tip of the thumb of an adult man is almost 3 cm long. ! ., The bottle contains about 1 L of water. J

The weight of the school bag is approximately 700 g. 'fl1. Circle the appropriate measurement. c. *It 500 9/500 mg 400 kgl400 g EIlNlur/-l \\. 1 L/1 mL t2cm/L2mm 25 L/25O mL 2m/2OOm 2. Write true or false. a. Length of a door is about 4 m. b. Capacity of a drop of water is almost 2 L. c. Weight of an apple is approximately 600 g. d. width of a thumb is about L cm. Choose the correct answer to make the following statements meaningful. a. The weight of a book is about 500 g / 500 kg. b. The weight of a bike is about 200 g / 200 kg. c. The height of a building is about 100 cm / L00 m. d. The length of a saree is about 5.5 km / 5.5 m.

Mggnig tleB, AJUUV Objective: To introduce students to metric measures used in day-to-day activities Materials required: A measuring tape, weighing machine, fruit juice cans Method: Divide the class into groups of 5 or 6 students. Ask a student in each group to record the readings for the group. a. NoW ask them to measure the length of the palm of each student in their group. b. Also, make them record the weight of each student. c. Give each student a can of juice and ask them to record the total quantitv of fruit juice drunk by the group. Now ask each group to arrange the lengths, weights and capacities measured in ascending or descending order. Display all the information from the class in the form of a chart. My Proiect L. Make a list of the estimated weight of objects that you use every oaY. E(nx\"atmoip\"let:rnS.ctthoborlebaakgin(wd itahftebor oluknscahnbdrweaitkh)o, uwtabteorokbso)t'tlleun(cwhitbhox water and without water) and so on' Then with the help of your teacher, find their actual weight' Record the difference between the estimated weight and the actual weight. 2. Record the quantity of water used by each member of your family for different activities-bathing, washing, drinking, cooking' etc' Record vour observatlons. Compare your observations with your friend's observations' Do you think conserving water even at the household level can t'\"tpf Sugg\"t, *.ys to reduce wastage of water in our daily life

1.j!. Lhoose the appropriate measurement. One has been done for you. ;:' a. A.,book. weighs 250 kgl25'/0 g. ii b. -A pair of hairclips weigh about 5 g/5 kg. : c.:. Arjun drinks 3 kL/300 mL of milk every day. i O. A pen is about L5 m/15 cm long. : e. The capacity of a water tank is 100 kL/ j.00 mL. : r.: 1250 litres is equal to 7.25 kL/1-2.5 kL. : i C. , 950 cm when written as decametres is 0.95 dam/0.095 dam. 2.: : Madhav carries a suitcase that weighs 12.35 kg and a bag : that weighs 5.28 kg. What is the total weight he is carrying? 3.: A snail climbs 2 m 38 cm up a wall and slides down 1 m 1.5 cm I How many millimetres did it climb? i 4. A kangaroo can cover a distance of 15.25 m in one leap. i How many hectometres will it cover in j.5 leaps? : 5.: An empty box weighs 2.2 kg. Two books weighing 750 g ; each and a painting weighing 535 g are kept inside the i box. What is the total weight of the box in kilograms? :6. Acancontains15 litresof oil. 12.18 litresofoil is used for cooking. How many i decilitres of oil is left in the can? :!- /. tvarcn rne ro owtng: ;: a. u.4zE cm i. 0.121 kL :.: u. u.+zo uL ii. 0.0428 L :l. iii. 0.000121 kL : c. 4028 cm iv 40.28 m i d. t2L L v. 0.00121 kr vi. o.oo428 nr : e- 0.1.21 L :: f. LL.27 ..#.

I aMAnea Perimeter is the sum of the lengths of all sides of a given shape. The perimeter of this figure is 4m+3m+4m+3m=14m m---------------- Area is the amount of space occupied by any shape' Area of a square of side a cm is given by a'? or o x o sq' cm' -4 Area of a rectangle of length I cm and breadth D cm is given by / x D sq cm' The abovefigure is inthe shape of a rectanglewith /= 4 m and b = 3 m' Itsarea is 4 m x 3 m = 12 sq. m. 1. Find the perimeter of the following figures' 3cm b. a. 3cm 1cm

2. Find the approximate area of the following figures if each square has a side of 1 cm. T Moths Around Us Kanika is willing to plant saplings in her entire square field. She wants to fence this square field with a wire so that the saplings do not get harmed. She buys G4 m of wire. Her friend Shahin asks her. \"How many saplings can we plant, if a full grown plant takes 2 m, of area?,, $IKanika replied, \"The length of this field is = 16 m. This means that the area of the field is 16 m x 16 m = 256 m,. Hence, we can ntant -?!ft$ =rZS saptings in this fietd.,, Perimeter The perimeter is the length of the boundary of a closed figure. Let us develop the formulae for finding the perimeter of a rectangle and a square. Perimeter of a Rectangle We already know that, Perimeter of a rectangle = Sum of its four sides = length + breadth + length + breadth A<__/_>n = l+b+l+b 1[------lT = I+l+b+b = 2xl+2xb bb = 2x(t+bl I D Thus, the perimeter of a rectangle = 2 x ll + bl = 2 x (length + breadth) -l-C

Example fLinedn8tthheopftehreimreetcetranogf lae rectangle whose rength is 16 cm and breadth (1) = 16 cm is 8 cm. Ereadth ofthe rectangle (b) = 8 cm a Perimeter = 2x(t+b) I I ,f---r-r-ll= 2x(16cm+8cm) 8cm Thus, the perimeter ofthe rectangle = 2x24cm=4gcm 48- clri is Example 2: frAenrceecdLtaenwnggituthhlaarofbbptah\"\"rrerbkb\"pwd\"aofr,k.,;;;(;./.);lr\"=\"J;3f'Oll.S,isrrmuJ3cU0h.5ofmbaarnbdedbrweairdethis is 2o.s m to be needed? 's Breadth ofthe park (b) = 20.5 m perimeter of the rectangular park = 2x(l+b) = 2x(30.5m+20.5m) = 2xS1.Om = 102.0 m r,h,,u.,.-t t,v^z-m _ wire = 102m ot barbed is n eeded to fence the perimeter of a square park We know that, tl L----8 Perimeter ofa square = sumof itsfoursides lt = side + side + side + side i/ == ;l:-t-\" tll sidesareequar) Ji Thus, the perimeter ------r.c o*r\" .,Example 1: Find the of a square = 4 xs = 4 x side perimeter of o sid\" \"f ,h\" .;:\"..:,1,1 perimeter of the square = 4xside = 4x4cm Thus, the perimeter = 1.6 cm of the square is L6 cm.