{"id":8643,"date":"2024-02-15T10:53:57","date_gmt":"2024-02-15T05:23:57","guid":{"rendered":"https:\/\/tsboardsolutions.in\/?p=8643"},"modified":"2024-02-16T17:44:29","modified_gmt":"2024-02-16T12:14:29","slug":"ts-6th-class-maths-solutions-chapter-3-intext-questions","status":"publish","type":"post","link":"https:\/\/tsboardsolutions.in\/ts-6th-class-maths-solutions-chapter-3-intext-questions\/","title":{"rendered":"TS 6th Class Maths Solutions Chapter 3 Playing with Numbers InText Questions"},"content":{"rendered":"

Students can practice TS 6th Class Maths Solutions<\/a> Chapter 3 Playing with Numbers InText Questions to get the best methods of solving problems.<\/p>\n

TS 6th Class Maths Solutions Chapter 3 Playing with Numbers Exercise InText Questions<\/h2>\n

Do This<\/span><\/p>\n

Question 1.
\nAre 953, 9534, 900, 452 divisible by 2? Also check by actual division.
\nAnswer:
\n(i) The given number is 953.
\nThis number is divisible by 2 because it has not any one of the digits 0, 2, 4, 6 or 8 in its units place.
\n\"TS<\/p>\n

\"TS<\/p>\n

(ii) The given number is 9534.
\nThis number is divisible by 2 because it has 4 in its units place.
\n\"TS<\/p>\n

(iii) The given number is 900.
\nThis number is divisible by 2 because it has ‘0’ in its units place.
\n\"TS<\/p>\n

(iv) The given number is 452.
\nThis number is divisible by 2 because it has 2 in its units place.
\n\"TS<\/p>\n

Do This<\/span><\/p>\n

Check whether the following numbers are divisible by 3 ?
\n(i) 45986
\nAnswer:
\nThe given number is 45986.
\nSum of the digits = 4 + 5 + 9 + 8 + 6 = 32
\n32 is not a multiple of 3.
\nSo the given number is not divisible by 3.<\/p>\n

(ii) 36129
\nAnswer:
\nThe given number is 36129.
\nSum of the digits = 3 + 6 + 1 + 2 + 9 = 21
\n21 is a multiple of 3.
\nSo the given number is divisible by 3.<\/p>\n

(iii) 7874
\nAnswer:
\nThe given number is 7874.
\nSum of the digits = 7 + 8 + 7 + 4 = 26
\n26 is not a multiple of 3.
\nSo the given number is not divisible by 3.<\/p>\n

Try These<\/span><\/p>\n

Question 1.
\nIs 7224 divisible by 6 ? Why ?
\nAnswer:
\nThe given number has 4 in its units place.
\nSo it is divisible by 2.
\nThe sum of the digits of the given number is 7 + 2 + 2 + 4 = 15.
\nIt is a multiple of 3.
\nSo the given number is divisible by 3.
\nIf a number is divisible by both 2 and 3 then it is divisible by 6 also.<\/p>\n

\"TS<\/p>\n

Question 2.
\nGive two examples of 4 digit numbers which are divisible by 6.
\nAnswer:
\n9648 and 3756.<\/p>\n

Question 3.
\nCan you give an example of a number which is divisible by 6 but not by 2 and 3, why ?
\nAnswer:
\nA number is divisible by 6 only when it is divisible by 2 and 3.
\nSo, it is not possible to give an example for such number.<\/p>\n

Do This<\/span><\/p>\n

Question 1.
\nTest whether 9846 is divisible by 9 ?
\nAnswer:
\nNumber = 9846
\nSum of the digits = 9 + 8 + 4 + 6 = 27 27
\n\\(\\frac{27}{9}\\) = 3 9
\n\u2234 9846 is divisible 9.<\/p>\n

Question 2.
\nWithout acutal division, find whether 8998794 is divisible by 9 ?
\nAnswer:
\nNumber = 8998794
\nSum of the digits = 8 + 9 + 9 + 8 + 7 + 9 + 4 = 54
\n\\(\\frac{54}{9}\\) = 6
\n\u2234 8998794 is divisible by 9.<\/p>\n

Question 3.
\nCheck whether 786 is divisible by both 3 and 9 ?
\nAnswer:
\nNumber = 786
\nSum of the digits = 7 + 8 + 6 = 21
\n\\(\\frac{21}{3}\\) = 7
\nSo 786 is divisible by 9.
\nBut 21 is not divisible by 9.
\nSo 786 is not divisible by 9.<\/p>\n

Do This<\/span><\/p>\n

Question 1.
\nFind the factors of 80.
\nAnswer:
\nFactors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80.<\/p>\n

Question 2.
\nDo all the factors of a given number divide the number exactly ? Find the factors of 28 and verify by division.
\nAnswer:
\nYes, all the factors of a given number divide the number exactly.
\nFactors of 28 are 1, 2, 4, 7, 14, 28.<\/p>\n

Verification:
\n\\(\\frac{28}{28}\\) = 1, \\(\\frac{28}{14}\\) = 2, \\(\\frac{28}{7}\\) = 4, \\(\\frac{28}{4}\\) = 7, \\(\\frac{28}{2}\\) = 14<\/p>\n

Question 3.
\n3 is a factor of 15 and 24. Is 3 a factor of their difference also ?
\nAnswer:
\nYes. (The difference between 15 and 24 is 9 and 9 is a multiple of 3.)<\/p>\n

\"TS<\/p>\n

Try These<\/span><\/p>\n

Question 1.
\nWhat is the smallest prime number?
\nAnswer:
\nThe smallest prime number is 2.<\/p>\n

Question 2.
\nWhat is the smallest composite number?
\nAnswer:
\nThe smallest composite number is 4.<\/p>\n

Question 3.
\nWhat is the smallest odd composite number?
\nSol.
\nThe smallest odd composite number is 6.<\/p>\n

Question 4.
\nGive 5 odd and 5 even composite numbers.
\nAnswer:
\nThe odd composite numbers are
\n9, 15, 21, 25, 27 etc.
\nThe even composite numbers are
\n4, 6, 8, 10, 12 etc.<\/p>\n

Question 5.
\nIs 1 prime or composite and why?
\nAnswer:
\nThe number 1 has only one factor i.e. (itself). So, 1 is neither prime nor composite.<\/p>\n

Question 6.
\nCan you guess a prime number which when on reversing Its digits, gives another prime number?
\n(Hint : Take a 2 digit prime number)
\nAnswer:
\n13 is a prime number. On reversing its digits it becomes 31, which is also a prime number.<\/p>\n

Question 7.
\nYou know 311 is a prime number. Can you find the other two prime numbers just by rearranging the digits?
\nAnswer:
\nGiven prime number is 311.
\nThe other two prime numbers just by rearranging the digits are 113 and 131.<\/p>\n

Do This<\/span><\/p>\n

From the following numbers identify different pairs of co-primes. 2, 3, 4, 5, 6, 7, 8, 9 and 10.
\nAnswer:
\n(2, 3); (2, 5); (2, 7); (3, 5); (3, 7); (5, 7)<\/p>\n

Do This<\/span><\/p>\n

Question 1.
\nWrite the prime factors of 28 and 36 through division method.
\nAnswer:
\n\"TS
\n\u2234 Prime factors of 36 is 2 \u00d7 2 \u00d7 3 \u00d7 3<\/p>\n

\"TS<\/p>\n

Question 2.
\nWrite the prime factors of 42 by factor tree method.
\nAnswer:
\n\"TS
\n\u2234 Prime factors of 42 is 2 \u00d7 3 \u00d7 7<\/p>\n

Do This<\/span><\/p>\n

Find the HCF of 12, 16 and 28 by prime factorization method.
\nAnswer:
\n\"TS
\nThe common factors of 12, 16 and 28 is 2 \u00d7 2 = 4
\nHence, HCF of 12, 16 and 28 is 4.<\/p>\n

Do This<\/span><\/p>\n

Find the HCF of 28, 35 and 49 by division method^
\nAnswer:
\nFirst find the HCF of any two numbers.
\nLet us find the HCF of 28 and 35
\n\"TS
\nLast divisor is 7
\n\u2234 HCF of 28 and 35 is 7.
\nThen find the HCF of the third numbern and the HCF of first two numbers.
\nLet us find the HCF of 49 and 7.
\n\"TS
\nHCF of 49 and 7 is 7.
\n\u2234 The HCF of 28, 35 and 49 is 7.<\/p>\n

Think, Discuss and Write<\/span><\/p>\n

What is the HCF of any two
\n(i) Consecutive numbers ?
\nAnswer:
\nThe HCF of any two consecutive numbers is 1.<\/p>\n

(ii) Consecutive even numbers ?
\nAnswer:
\n2<\/p>\n

(iii) Consecutive odd numbers ?
\nAnswer:
\n1 (one)<\/p>\n

\"TS<\/p>\n

What do you observe ? Discuss with your friends.
\nAnswer:
\nIt was observed that the HCF of two consecutive numbers and consecutive odd numbers is same, i.e., 1.<\/p>\n

Try This<\/span><\/p>\n

Question 1.
\nfind the LCM of
\n(i) 3, 4
\n(ii) 10, 11
\n(iii) 5, 6, 7
\n(iv) 10, 30
\n(v) 4, 12, 24
\n(vi) 3, 12
\nWhat do you observe ?
\nAnswer:
\n(i) LCM of 3 and 4 = 3 \u00d7 4 = 12
\n(ii) LCM of 10 and 11 = 10 \u00d7 11 = 110
\n(iii) LCM of 5, 6 and 7 = 5 \u00d7 6 \u00d7 7 = 210
\n(iv) LCM of 10 and 30 = 10 \u00d7 1 \u00d7 3 = 30
\n(v) LCM of 4, 12 and 24 = 4 \u00d7 3 \u00d7 2 = 24
\n(vi) LCM of 3 and 12 = 3 \u00d7 4 = 12
\nIt is observed that the LCM of two numbers will be their product, if the given numbers have no common factor except 1.<\/p>\n

Think, Discuss and Write<\/span><\/p>\n

When will the LCM of two or more numbers be their own product ?
\nAnswer:
\nIf the numbers are co-primes or relatively prime numbers then the LCM of two or more numbers be their own product.<\/p>\n

Think, Discuss and Write<\/span><\/p>\n

Question 1.
\nWhat is the LCM and HCF of twin prime numbers?
\nAnswer:
\nLet the twin primes may be (3, 5)
\nLCM of 3, 5 is their product 3 \u00d7 5 = 15
\nHCF of 3, 5 is 1.
\n(for any type of twin prime)<\/p>\n

Question 2.
\nInterpret relationship between LCM and HCF of any two numbers?
\nAnswer:
\nConsider the two numbers be 14 and 21.
\nNow find LCM of 14 and 21.
\n\"TS
\n\u2234 LCM of 14 and 21 = 7 \u00d7 2 \u00d7 3 = 42
\nNow find HCF of 14 and 21.
\n\"TS
\n\u2234 HCF of 14 and 21 is 7.
\nRelation between LCM and HCF of 14 and 21:
\n42 \u00d7 7 = 14 \u00d7 21 = 294
\nProduct of LCM and HCF of two numbers = Product of two numbers.<\/p>\n

\"TS<\/p>\n

Do This<\/span><\/p>\n

Divisibility Rule for 4:<\/p>\n

Question 1.
\nIs 100000 is divisible by 4? Why?
\nAnswer:
\n100000 = 1000 \u00d7 100
\nThe given number is a multiple of 100.
\nWe know, 100 is divisible by 4.
\n\u2234 The given number (i.e., 100000) is divisible by 4.<\/p>\n

Question 2.
\nGive an example of a 2 digit number that is divisible by 2 but not divisible by 4?
\nAnswer:
\n22, 26, 30, 34, 38 98 .
\nAll the above two digit numbers are divisible by 2 but not divisible by 4.<\/p>\n

Do This<\/span><\/p>\n

Question 1.
\nIs 76104 divisIble by 8?
\nAnswer:
\nThe number formed by the last three digits is 104. It is divisible by 8.
\nHence, the given number is divisible by 8.<\/p>\n

Question 2.
\nWrite the numbers that are divisible by 8 and lie between 100 and 200.
\nAnswer:
\n104, 112, 120, 128, 136, 144, 152, 160, 168, 176, 184, 192 are ail divisible by 8.
\nThey lie between 100 and 200.<\/p>\n

Page No. 92 (45)<\/span><\/p>\n

Divisibility Rule for 11:<\/p>\n

Using the division rule of ’11’. Fill the following table.
\n\"TS
\nAnswer:
\n\"TS<\/p>\n

\"TS<\/p>\n

1221 is a Palindrome number, which on reversing their digits gives the same number.
\nThus, every Palindrome number with even number of digits, is always divisible by 11.<\/p>\n

Write a Palindrome number of 6 digits and verify whether it is divisible by 11 or not.
\nAnswer:
\nPalindrome number which on reversing their digits gives the same number.
\nEvery Palindrome number with even number is always divisible by 11.<\/p>\n

\u2234 The 6 digited Palindrome number is 123321. It is divisible by 11.<\/p>\n","protected":false},"excerpt":{"rendered":"

Students can practice TS 6th Class Maths Solutions Chapter 3 Playing with Numbers InText Questions to get the best methods of solving problems. TS 6th Class Maths Solutions Chapter 3 Playing with Numbers Exercise InText Questions Do This Question 1. Are 953, 9534, 900, 452 divisible by 2? Also check by actual division. Answer: (i) … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[15],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/posts\/8643"}],"collection":[{"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/comments?post=8643"}],"version-history":[{"count":4,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/posts\/8643\/revisions"}],"predecessor-version":[{"id":8673,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/posts\/8643\/revisions\/8673"}],"wp:attachment":[{"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/media?parent=8643"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/categories?post=8643"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/tsboardsolutions.in\/wp-json\/wp\/v2\/tags?post=8643"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}