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Unit – HCF & LCMSubunit – LCM Concept CornerScene – Pankaj go every 6th day to swimming & every 4th day to tabla class . Today he go to bothlaces then again what day he go to both places.See any thing remainde you ? You also take help ofcalender again how can solve this?any other method? Day for swimming are 6 th, 12th, 18th,.and so ontable of 6 – 6,12, 18, 24, For tabla class days 4th,8th,12th,16th,.and so onTable of 4 – 4, 8, 12, 16, 24, 6See care fully pankaj go to both swimming & tabla class on same day which are12,24.and like that Which is first day for both activity exactly 12th day 12 is smallest & same number which is in both table 4 & 6 12 is a smallest number which is divisible by both 4& 6 Hence least common multiple LCM of 4& 6 is 12 . I understood Least multiple of two or mote number is LCM of that given numbers. Given numbets wrtten in their multiple or their table and then their smallest common multiple iscalled LCM Two or more than two numbers having LCM is always greater than that numbers List method Facorization method or division metod are used to determine LCM Given two or more numbers if Greater number is divisible by smaller number then greaternumber is LCMfor example 4,12,36 then 36 is divisible by all 4,12,36 then LCM is 36.LCM product of common,& uncommon factors Practice cornerNow we determine LCM of 4& 9 by using list method ,prime factor method & division method& then we see answer by all method !List Method – Table of 4 – 4, 8,12, 16, 20, 24, 28, 32, 36, 40, 44, 48,52,56,60,64,68,72 Table of 9 – 9,18, 27, 36, 45, 54, 63, 72, 81,90, 99,--Common numbers of 4th & 9 th table – 36, 72, least common multiple is 36. hence LCM of 4 & 9 is 36.

Prime factor method –prime factors of 4 , Prmime factor of 9 Common factor of prime factor of 4 & 9 has no common factors.Produc of uncommon factors of 4 & 9 isLCM Product of common prme factors & uncommon prime factorsDivision method – See the adjoining method take a prime factor of 4 & 9 upto 1then take product of common and uncommon factor we get LCM this method isknown as division method Solve this –1) Find LCM of 8&12 by list method2) What is LCM of 3,9,&27 without using factorization -----------3) Find LCM of 5,6&7 by using division method Quick HelpDiksha app link –See video of LCMhttps://diksha.gov.in/play/content/do 31327270197864038416463

I UnderstandPractice

Area – knowledge and operation on numbersSubunit – Introduction of rational numbersUnit – Operation on rational numbersDay - 9thConcept CornerScene: shamal bring a big cake and make ‘Cut into 8 equal part 2 part eat by shamal.Two part eatby her younger brother. 1 part each eat by her mother & father.one part each eat by her grandpa &grandmawe write part of cake eaten by each person mathematicallyEqual part of cake – 8eaten by shamal -Eaten by younger brother -Eaten by mother -Eaten by father -Eaten by grandma-Eaten by grandpa Think & markAt correct place Can we cut a cake in 0 equal parts ?See maths funmeansyes/ nomeans4/0 is not possible as 0 0 not equal 4 That means no number is divided by 0In case of cake we write all numbers in form but we can’t write q 0 We Write 2 in form as Also -5 inform But 2 or -5 cannot be write as 2/0 or -5/0 2is whole number while -5 is integer I understand12) Number which can be written as p/q form & q is not equal to 0 iscalled rational number All natural, whole,integer,decimal numbers canbe written in the form of rational numbers but denominator is not 013) All fractions are rational numbers but all rational numbers may ormaynot be rational numbers Eational numbers are negative or positive. Practice cornerSee these example which are rational numbers .These example are not rational numbers.These example are not fraction, ,,etc., - , 6, 12, -18, 2.1 etcetc.

Let’s SolveNumber12-7/917/08/9-Mark thisRationalat correct places.Not rational Small HelpDiksha app link Rational number video.https://diksha.gov.in/play/content/do 31327270259433472016527FractionNot fraction

Subunit – addition & subtraction of rational numbers Day - 10thConceptCornerScene 1 – Ayush compete journey in two stages He complete 2/6 part journey yesterday & 4/6 partjourney today .So how much part journey completed in two day.!Part of journey by Ayush yesterday 2/6Part of journey by Ayush today 4/6For total journey we adding . Scene 2 - Suraj take 5/2 sugar & Sohel take 5/2 sugar How many Kg sugar they both takeSugar bought by Suraj 5/2 kgSugar bought bySohel 7/3 kgSugar bought by both kgScene3 – Sagar baught gold16/7 gm Sangita baught gold12/5gm How many more gram gold baughtby sangita thn sagarGold baught by saSagar 16/ 7gmGold baught by Sangita 12/5 gmMore gold baught by sangita than Sabgar gm I understood1) When addition or subtraction of rational numbers whose denominator areequal we only add or subtract numerator2) When denominator are different then equal denominator by taking LCM.3) When we add or subtract decimal fraction then adding or subtractinginteger 7 add or subtract fraction by decimal method Practice Corner – Compete following activity.1)2)

Let’s Solve –Solve the following addition / subtraction1) 2) 3) 4) Quick HelpDiksha app link – Addition & subtraction of rational numbershttps://diksha.gov.in/play/collection/do 312528209295843328153323?contentId do 3130003206227312641121

Subunit – product of rational numberDay - 11th Concept Corner 5 times of 3/4 is equal to? for solving this example help of addition & multiplication 5 times of 3/4 hence we take 3/4 five times we write in the form of addition. as Also we write in the form of multiplication – Method by taking multiplication is very easy Now see next example.rational numbers is always negativeIn this example product of negative & positive How can you solve ?. In this example rational numbers multiplications ofnumerator & multiplication of Denominator I understood1) Multiplication of rational number at numerator product of numerator &at Denominator product of denominator2) When product of negative & positive rational numbers we follow rulesof sign3) When division of rational number taking reciprocal of divisor & andthen product4) While division we follow rules of sign same as for integers.𝟏 . What is the answer of this question means that divide 𝟐 in two equal parts byfigure we can observe it clearly. 𝟏𝟐rational number we see1 wholeHalf of half is one fourth h Similarly let’s solve following exampleलक्षात घ्या – Practice Corner–दोन परिमेय संखयांचा भागाकाि कितानापरिमेय संखयेचactivityी गुणाकािव्यस्त संखया घेवनू गुणाकाि केला आहे .Completetheभाजकfollowing1)

2)Let’s Solve –Solve following multiplication & Division1) 𝟏𝟐𝟖2) 𝟗𝟐𝟑𝟕 𝟖 3) What is -5 times of 4/9?4) Divide 2/3 in -1/5 equal parts then each part is Quick helpDiksha app link Video link for multiplication & division of rational number1) https://diksha.gov.in/play/collection/do 312528209295843328153323?contentId do 31300032079723724811002) https://diksha.gov.in/play/collection/do 312528209295843328153323?contentId do 3130007804581642241248

Area – knowledge and operation on numbersSubunit – introduction of indicesUnit – IndicesDay - 12thConcept Corner Let remember Find the following product.1)(2)(3) Check whether your answer is correct or not1)4(2)(3)Very good ! Now we see another method for writing when one number is multiplied by itself Now see understand and write the answer at the blank spacesYou write 4 in the blank spaces correct but why? Because in first place you multiply 2 by two times hence 2 is written on head of 2 multiply 2 by three times hence 3 is written on head of 2 multiply 2 by Four times hence 4 is written on head of 2Yes understood a number is multiply by itself in how many times can be written on head of thatnumber in number 2 is a base & number 3 on head is index in this number 6 is base & 5 is index ,6 is multiply by 6 in 5 times its product form is The number which can be form by base & power is called Indices number I understood A number is multiplied by itself in one or number of times thenthat number of times is called index or power of that numbers Base & index we get indices Index form of numbers means number multiply with itself Practice corner let’s try to understand1)2)3) Try to understand following1)2)

Let’s Solve Write tickmark & crossmark at correct placesnumberfalsetruenumberfalsetrueQuick helpDiksha app link – Index number Videohttps://diksha.gov.in/play/collection/do 312528209295843328153323?contentId do 3130003210636247041101

Area – Number work and operations on numberSubunit – Rules of Indices Unit – IndicesDay - 13thConcept CornerLet's observe the following math fun.𝟑𝟐 𝟑𝟑 𝟑 𝟑 𝟑 𝟑 𝟑 In this example, the number 𝟑𝟐 was initially written as a multiplicationform and the number 𝟑𝟑 was also written as a multiplication form and then the multiplication of all 3’swas presented in one place Now try to write the multiplicative number here as index form !𝟑 𝟑 𝟑 𝟑 𝟑 Make sure that you have written35 in the blank space . Have you done? . Very nice Now itcan be written together as follows.𝟑𝟐 𝟑𝟑 𝟑𝟓 means 𝟑𝟐 𝟑𝟑 𝟑𝟐 𝟑 𝟑𝟓 𝟑𝟓Similarly we can write 𝟑𝟓 𝟑𝟑 𝟑𝟑 𝟑 𝟑 𝟑 𝟑 𝟑𝟑 𝟑 𝟑 𝟑 𝟑 𝟑𝟐 in short 𝟑𝟓 𝟑𝟑 𝟑𝟐Now observe the given pattern and write what number will appear in the blank space. Have you tried? . Write the number that comes in the blank space. The number 1 appears in the blank space. As the index is decreasing by one then itsvalue becoming half of previous one. Here 8, 4 and 2. Thus 2 will be followed by 1. In the case of any other index form of the number you will find the same result. . Now I know The following rules are used to calculate the value of indexnumber . We call them laws of indices : Practice Corner -Study the examples in the table below and write the correct number in the blanks.1) 𝟓𝟒 𝟓𝟑𝟓𝟒 𝟓𝟕2) 𝟗𝟓 𝟗𝟐𝟗𝟓 𝟑3) ( 𝟑𝟒 )𝟓 𝟑𝟒 𝟓 𝟑4) 𝟏𝟐𝟎5) 𝟏𝟏 𝟐𝟏𝟏 𝟐 𝟏𝟏𝟏

Let’s solve1)𝟏𝟑𝟓 𝟏𝟑𝟖-Solve the following examples using laws of indices. 2) ( 𝟒)𝟗 ( 𝟒)𝟒 𝟒3) (𝟒 𝟐 ) 4) 𝟏𝟐𝟑𝟒𝟎 5) 𝟖 𝟑 Quick helpDiksha app link – Laws of Indices – Watch the given video.https://youtu.be/sbftWkb3CmE

Area – AlgebraUnit – Algebraic Expressions and Operations on themSubunit – Algebraic Expressions-IntroductionDay - 14thConcept CornerLet’s recall1. How many mangoes will be 2 mangoes and 3 mangoes together? --- There will be 5 mangoes2. How many fruits will there be with 2 mangoes and 3 chickoos? -There will be 5 fruits.That's right.If we use the letter x for 1 mango, note that 2 mangoes and 3 mangoes together will be 5 mangoes.This can be written as 𝟐𝒙 𝟑𝒙 𝟓𝒙Now let us use the letter x for 1 mango and the letter y for 1 chikoo. because mango and chikoo aredifferent fruits so the letters used for them will also be different. Now let's do addition of 2 mangoesand 3 chickoos as follows. 𝟐𝒙 𝟑𝒚Note that the above addition will not be 5xy. 𝑳𝒆𝒕 𝒖𝒔 𝒄𝒂𝒍𝒍 𝒕𝒉𝒆 𝒆𝒙𝒑𝒓𝒆𝒔𝒔𝒊𝒐𝒏 𝒇𝒐𝒓𝒎𝒆𝒅 𝒃𝒚 𝒏𝒖𝒎𝒃𝒆𝒓𝒔 𝒂𝒏𝒅 𝒍𝒆𝒕𝒕𝒆𝒓𝒔 𝟐𝒙 𝒂𝒏𝒅 𝟑𝒚 𝒂𝒔 𝒕𝒉𝒆𝒂𝒍𝒈𝒆𝒃𝒓𝒂𝒊𝒄 𝒆𝒙𝒑𝒓𝒆𝒔𝒔𝒊𝒐𝒏′. 𝑯𝒆𝒓𝒆 𝒕𝒉𝒆 𝒏𝒖𝒎𝒃𝒆𝒓𝒔 𝟐 𝒂𝒏𝒅 𝟑 𝒂𝒓𝒆 𝒄𝒐𝒆𝒇𝒇𝒊𝒄𝒊𝒆𝒏𝒕𝒔 𝒂𝒏𝒅 𝒕𝒉𝒆𝒍𝒆𝒕𝒕𝒆𝒓𝒔 𝒙, 𝒚 𝒂𝒓𝒆 𝒄𝒂𝒍𝒍𝒆𝒅 𝒗𝒂𝒓𝒊𝒂𝒃𝒍𝒆𝒔. Now I know!1) The term formed after multiplying numbers by letters is calledalgebraic term.2) Numbers are called coefficients and letters are called variables.3) Expressions are named after the number of terms they have.Expressions with one term are called monomials, those with twoterms, binomials, with three terms, trinomials and if they have morethan three terms, they are called polynomials4) Terms which have the same variables with the same powers are called‘like terms’5)6)7) Practice Corner8) Given algebraic9)expressions are monomials: - 𝟑𝒙 , 𝟒𝒚, 𝟖𝒛𝟐 etc. Given algebraic10)expressions are binomials: 𝟑𝒙 𝟐𝒚, 𝟓𝒛 𝟗𝒑 etc.11)‘like terms’. Given algebraic expressionsare trinomial: 𝟑𝒙 𝟐𝒚 𝟗𝒛, 𝟓𝒛 𝟗𝒑 𝟕𝒒 etc. The terms in the given pair are the like terms.𝟒𝒙𝟐 𝒚 व 𝟗𝒙𝟐 𝒚 , 𝟑𝒛 व 𝟓𝒛 etc.Note that all the above expressions are also polynomial .Let’s solve –Mark in front of the type of correct polynomial in the following table.Algebraic expression𝟒𝒙𝒚𝒛𝟔𝒚 𝟗𝒛𝟖𝒂 𝟗𝒃 𝟕𝒄Monomialbinomialtrinomial

Write any like term for the following algebraic term. 1) 𝟒𝒙𝒚 Quick help(2) 𝟐𝒙𝟑 𝒚 (3) 𝟗𝒑𝒒𝟑 𝒓 Diksha app link – Watch the video on algebraic expression .https://youtu.be/ffLLmV4mZwU

Area – AlgebraUnit – Algebraic Expressions and Operations on themSubunit – Addition & Subtraction of Algebraic ExpressionsDay - 15th Concept Corner 3 Chikoo and 5 Chikoo together make 8 Chikoos. Let's solve this additionusing the following methods. We will use the letter x for a chikoo.𝟑𝒙 𝟓𝒙 𝟖𝒙 After selling 3 dozen mangoes out of 10 dozen mangoes,7 dozen mangoesremains, using the variable y for 1 dozen mangoes we can write this subtractionas follows.𝟏𝟎𝒚 𝟑𝒚 𝟕𝒚 Let us write the total number of 2 chikoo and 3 mangoes using the letter x forchikoo and the letter y for mango.2x 3y Note that : Here the addition will not be 5xy . Now I know! In algebraic expressions additions and subtractions aremade only of like terms of expressions. When there are no like terms, the addition or subtractionis written using variables as it is . Practice Corner : Study examples of addition and subtraction in the following table .Let’s solve -𝟒𝒙𝒚 𝟗𝒙𝒚 𝟏𝟑𝒙𝒚𝟒𝒑 𝟑𝒑 𝟏𝒑Solve the examples of addition and subtraction in the following table .𝟕𝒑𝒒𝒓 𝟐𝒑𝒒𝒓 𝟏𝟐𝒛 𝟏𝟎𝒛𝟖𝒙 𝟑𝒚𝟐𝟕𝒎𝒏 𝟐𝟎𝒎 Quick helpDiksha app link – Addition and subtraction of algebraic expressions - watch the video .https://youtu.be/kuntXMSMYrE

Area – AlgebraUnit – Algebraic Expressions and Operations on themSubunit – Multiplication of Algebraic ExpressionsDay - 16th Concept CornerLet’s recall. –1) Multiplication is repeated addition of the same number or expression.2) According to the laws of indices ,when the indices with the same base aremultiplied then we add the indices in the resultant product and the indicesare subtracted in division. 2 times 2x ? For this we will add it up twice and see what the answer is.𝟐𝒙 𝟐𝒙 𝟐 𝒕𝒊𝒎𝒆𝒔 𝟐 𝒙 𝟒𝒙 Now if we take 3xy ; 4 times, you will have noticed that 12xy will come.From this,𝟒 𝟑𝒙𝒚 𝟏𝟐𝒙𝒚 𝟐𝒙 𝒕𝒊𝒎𝒆𝒔 𝟒𝒙 𝒘𝒊𝒍𝒍 𝒃𝒆 𝒎𝒖𝒍𝒕𝒊𝒑𝒍𝒊𝒆𝒅 𝒖𝒔𝒊𝒏𝒈 𝒕𝒉𝒆 𝒍𝒂𝒘𝒔 𝒐𝒇 𝒊𝒏𝒅𝒊𝒄𝒆𝒔𝟐𝒙 𝟒𝒙 𝟐 𝟒 𝒙 𝒙 𝟖𝒙𝟐 Now let's see how multiplication will work if there are different variables.Such as 𝟑𝒙𝒚 𝟐𝒑𝒒 𝟑 𝟐 𝒙𝒚 𝒑𝒒 𝟔𝒙𝒚𝒑𝒒 Now I know!1) While multiplying algebraic expressions, multiply thecoefficients by the coefficients and multiply the variablesby the variables.2) If there are variables, multiply the indices by using therule of multiplication of index.3) If there are no like terms, in multiplication they all writethe same in multiplication form. Practice cornerStudy the following Products.(2) 𝟓𝒙 𝟔𝒙𝒚 𝟑𝟎𝒙𝟐 𝒚(1) 𝟓 𝟔𝒙𝒚 𝟑𝟎𝒙𝒚 Let’s Solve blanks.(3) 𝟑𝒙𝒛 𝟒𝒚 𝟏𝟐𝒙𝒚𝒛Study the following multiplication and write the correct number in the(1) 𝟏𝟐 𝟑𝒙 𝟑𝟔(2) 𝟒𝒙 𝟐𝒙 𝟖

(3) 𝟓𝒙𝒚 ( 𝟐)𝒛 𝒙𝒚𝒛(4)𝟏𝟎𝟎𝒙𝟑 𝟐𝒙𝟑 𝒚 𝟐𝟎𝟎(5)(5) 𝟏𝟎𝒍𝒎𝒏 𝟑𝒍𝒎 (6)(6) 𝟗𝒚 𝟑𝒙𝒚 𝟐𝟕 Quick HelpDiksha app link – Video Link for : Multiplication of Algebraic Expressionshttps://youtu.be/YqnsUf40gNI

Area – Applied mathematicsUnit – Direct Proportion and Inverse ProportionSubunit – Direct Proportion and Inverse ProportionDay - 17th & 18thConcept CornerEvent - Children of Mangal Society are going from house to house on the occasion ofGaneshotsav and collecting donations. The number of houses they visited and the donationreceived from each house are given in the table below. Let's understand that.Number of houses visitedDonation from each household (in rupees)23005750101500Observe the above table carefully , write the correct answers to the following questions.1. The amount of donation increases / decreases as the number of houses increases.My Answer - ---2. How much is the donation from one house?My Answer - Let's check the answers given are correct or not .1. The amount of donation increases / decreases as the number of houses increases.My answer - increases.2. How much is a donation from one house fee?My answer - Rs. 1502. The secrete /hidden mathematics behind this –The ratio of the number of houses visited and the donaton collected from each house 𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 ��𝒏 ��𝟏 𝟑𝟎𝟎 𝟕𝟓𝟎 𝟏𝟓𝟎𝟎 𝟏𝟓𝟎That is, the ratio of the number of houses to each donation collected is constant. which is ,1:150 Now look at the example in the table below.Number of pages read per dayThe days it takes to finish reading a book204010805160Got it? Let's find , What is the total number of pages in the book to read the book completely?Exactly 800The secrete /hidden mathematics behind this – As the number of pages read per day decreases, the number of days it takes to finishreading a book increases. 𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒑𝒂𝒈𝒆𝒔 𝒓𝒆𝒂𝒅 𝒑𝒆𝒓 𝒅𝒂𝒚 𝒅𝒂𝒚𝒔 𝒓𝒆𝒒𝒖𝒊𝒓𝒆𝒅 𝟐𝟎 𝟒𝟎 𝟏𝟎 𝟖𝟎 𝟓 𝟏𝟔𝟎 𝟖𝟎𝟎 That is, the product of the number of pages and the number of days required is constant.

1.2.3.4. Now I knowAn increase or decrease in one quantity increases or decreases in another quantitybased on it, Such a proportion is called as direct proportion.If the given quantities are in direct proportion then their ratio is always constant.An increase in one quantity leads to a decrease in another quantity based on it or adecrease in one quantity leads to an increase in another quantity . Such a proportionis called inverse proportion.If the given quantities are inverse proportion, then their product is always constant. Practice Corner

Part three - Solved Activity/ Demo Part Four - Practice Part Five - little help, DIKSHA Video Link/E-Content/QR Code . In kabaddi match when match is lost, then each lost loss of 5 marks loss & when match is win then gain of 10 marks. One team lost 3 match & gain 4 match then what is total marks of that . 2) HCF of 9 & 15 by using prime .