8th Class Maths 15th Lesson Playing with Numbers InText Questions and Answers<\/h3>\n
Do this<\/span><\/p>\n Question 1. Question 2. Question 3. Question 4. Question 5. Question 6. Question 7. Question 8. Question 9. Question 10. Question 11. Question 12. Question 13. Question 14. Question 15. Question 16. Question 17. Question 18. Question 19. Question 20. Question 21. Question 22. Question 23. Question 24. Question 25. Question 26. Question 27. Question 28. Question 29. Question 30. Try these<\/span><\/p>\n Question 1. Question 2. Question 3. Question 4. Question 5. Question 6. Question 7. Question 8. Question 9. Question 10. Question 11. Question 12. Question 13. Question 14. Question 15. Think, Discuss and Write<\/span><\/p>\n Question 1. Question 2. Question 3. Question 4. Question 5. AP State Syllabus 8th Class Maths Solutions 15th Lesson Playing with Numbers InText Questions AP State Syllabus\u00a0AP Board 8th Class Maths Solutions Chapter 15 Playing with Numbers InText Questions and Answers. 8th Class Maths 15th Lesson Playing with Numbers InText Questions and Answers Do this Question 1. Write the place value of numbers underlined.\u00a0 \u00a0 …<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[6],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/8016"}],"collection":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/comments?post=8016"}],"version-history":[{"count":0,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/8016\/revisions"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/media?parent=8016"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/categories?post=8016"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/tags?post=8016"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\nWrite the place value of numbers underlined.\u00a0 \u00a0 \u00a0(Pg. No: 312)
\ni) 2<\/span>98<\/span>79\u00a0 \u00a0ii) 103<\/span>44<\/span>\u00a0 \u00a0iii) 98<\/span>725<\/span>
\nAnswer:
\ni) 2<\/span>98<\/span>79
\nPlace value of 8 = 8 \u00d7 100 = 800
\nPlace value of 2 = 2 \u00d7 10,000 = 20,000
\nii) 103<\/span>44<\/span>
\nPlace value of 4 = 4 \u00d7 1 = 4
\nPlace value of 3 = 3 \u00d7 100 = 300
\niii) 98<\/span>725<\/span>
\nPlace value of 5 = 5 \u00d7 1 = 5
\nPlace value of 8 = 8 \u00d7 1000 = 8,000<\/p>\n![\"AP](\"https:\/\/apboardsolutions.guru\/wp-content\/uploads\/2020\/12\/AP-Board-Solutions.png\")
<\/p>\n
\nWrite the following numbers in expanded form,\u00a0 \u00a0 \u00a0 \u00a0 (Pg. No: 313)
\ni) 65\u00a0 \u00a0 ii)\u00a0 \u00a0 74\u00a0 \u00a0 iii) 153\u00a0 \u00a0 iv) 612
\nAnswer:
\nNumber Expanded form
\ni) 65 = 60 + 5 = (6 \u00d7 101<\/sup>) + (5 \u00d7 100<\/sup>)
\nii) 74 = 70 + 4 = (7 \u00d7 101<\/sup>) + (4 \u00d7 100<\/sup>)
\niii) 153 = 100 + 50 + 3 = (1 \u00d7 102<\/sup>) + (5 \u00d7 101<\/sup>) + (3 \u00d7 100<\/sup>)
\niv) 612 = 600 + 10 + 2 = (6 \u00d7 102<\/sup>) + (1 \u00d7 101<\/sup>) + (2 \u00d7 100<\/sup>)<\/p>\n
\nWrite the following in standard notation.\u00a0 \u00a0 \u00a0 \u00a0(Pg. No: 313)
\ni) 10 \u00d7 9 + 4\u00a0 \u00a0 \u00a0ii) 100 \u00d7 7 + 10 \u00d7 4 + 3
\nAnswer:
\nExpanded form General form
\ni) 10 \u00d7 9 + 4 = 90 + 4 = 94
\nii) 100 \u00d7 7 + 10 \u00d7 4 + 3 = 700 + 40 + 3 = 743<\/p>\n
\nFill in the blanks.\u00a0 \u00a0 \u00a0 \u00a0(Pg. No: 313)
\nAnswer:
\ni) 100 \u00d7 3 + 10 \u00d7 ——— + 7 = 357 (5)
\nii) 100 \u00d7 4 + 10 \u00d7 5 + 1 = ——— (451)
\niii) 100 \u00d7 ——— + 10 \u00d7 3 + 7 = 737 (7)
\niv) 100 \u00d7 ——— + 10 \u00d7 q + r = \\(\\overline{\\mathrm{pqr}}\\) (p)
\nv) 100 \u00d7 x + 10 \u00d7 y + z = ——— (\\(\\overline{\\mathrm{xyz}}\\))
\nDo you know?<\/p>\n
\nThe number 8281807978777675747372717069686766656463626160595857565554535251504948474645444342414039383736353433323130292827262524232221201918 1716151413121110987654321 is written by starting at 82 and writing backwards to 1 and see that it is a prime number.\u00a0 \u00a0 \u00a0 \u00a0 (Pg. No: 313)
\nAnswer:
\nNo.of digits in the given number are 155.<\/p>\n<\/p>\n
\nWrite all the factors of the following numbers.\u00a0 \u00a0 \u00a0 \u00a0(Pg. No: 314)
\na) 24\u00a0 \u00a0 b) 15\u00a0 \u00a0c) 21\u00a0 \u00a0d) 27\u00a0 \u00a0e) 12\u00a0 \u00a0f) 20\u00a0 \u00a0g) 18\u00a0 \u00a0h) 23\u00a0 \u00a0i) 36
\nAnswer:
\na) Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
\nb) Factors of 15 = 1, 3, 5, 15
\nc) Factors of 21 = 1, 3, 7, 21
\nd) Factors of 27 = 1, 3, 9, 27
\ne) Factors of 12 = 1, 2, 3, 4, 6, 12
\nf) Factors of 20 = 1, 2, 4, 5, 10, 20
\ng) Factors of 18 = 1, 2, 3, 6, 9, 18
\nh) Factors of 23 = 1, 23
\ni) Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36<\/p>\n
\nWrite first five multiples of given numbers\u00a0 \u00a0 \u00a0(Pg. No: 314)
\na) 5\u00a0 \u00a0b) 8\u00a0 \u00a0c) 9
\nAnswer:
\na) Multiples of 5 = 5, 10, 15, 20, 25
\nb) Multiples of 8 = 8, 16, 24, 32, 40
\nc) Multiples of 9 = 9, 18, 27, 36, 45<\/p>\n
\nFactorize the following numbers into prime factors.\u00a0 \u00a0 (Pg. No: 314)
\na) 72\u00a0 \u00a0 b) 158\u00a0 \u00a0c) 243
\nAnswer:
\na) 72 = 2 \u00d7 2 \u00d7 2 \u00d7 3 \u00d7 3
\nb) 158 = 2 \u00d7 7 \u00d7 9
\nc) 243 = 7 \u00d7 7 \u00d7 7<\/p>\n
\nCheck whether the following given numbers are divisible by 10 or not.\u00a0 \u00a0(Pg. No: 315)
\na) 3860\u00a0 \u00a0b) 234\u00a0 \u00a0c) 1200\u00a0 \u00a0d) 103<\/sup>\u00a0 \u00a0e) 10 + 280 + 20
\nAnswer:
\na) 3860, c) 1200, d) 103, e) 10 + 280 + 20 are divisible by ’10’.
\n[\u2235 the units digit of above numbers is ‘0’]
\nb) 234, is not divisible by 10.
\n[\u2235 its unit digit is 4]<\/p>\n
\nCheck whether the given numbers are divisible by 10 or not.\u00a0 \u00a0 (Pg. No: 315)
\na) 1010<\/sup>\u00a0 \u00a0b) 210<\/sup>\u00a0 \u00a0c) 103<\/sup> + 101<\/sup>
\nAnswer:
\na) 1010<\/sup> = 10000000000
\nb) 210<\/sup> = 1024
\nc) 103<\/sup> + 101<\/sup> = 1000 + 10 = 1010
\n\u2234 a) 1010<\/sup>, c) 103<\/sup> + 101<\/sup> are divisible by ’10’.
\n[\u2235 Their units digits are ‘0’.]
\nb) 1024 is not divisible by 10.
\n[\u2235 Its units digit is 4.]<\/p>\n<\/p>\n
\nCheck whether the given numbers are divisible by 5 or not\u00a0 \u00a0 \u00a0 (Pg. No: 315)
\na) 205\u00a0 \u00a0b) 4560\u00a0 \u00a0 c) 402\u00a0 \u00a0 d) 105\u00a0 \u00a0 e) 235785
\nAnswer:
\na) 205, b) 4560, d) 105, e) 235785 are divisible by 5.
\n[\u2235 The units digit of the above numbers are either 0 (or) 5.]
\nc) 402 is not divisible by 5.
\n[\u2235 Its units digit is 2.]<\/p>\n
\nCheck whether the given numbers which are divisible by 3 or 9 or by both,\u00a0 \u00a0 \u00a0 (Pg. No: 318)
\na) 3663\u00a0 \u00a0 b) 186\u00a0 \u00a0 c) 342\u00a0 \u00a0 d) 18871\u00a0 \u00a0 e) 120\u00a0 \u00a0 f) 3789\u00a0 \u00a0 g) 4542\u00a0 \u00a0 h) 5779782
\nAnswer:
\n![\"AP](\"https:\/\/apboardsolutions.guru\/wp-content\/uploads\/2021\/03\/AP-Board-8th-Class-Maths-Solutions-Chapter-15-Playing-with-Numbers-InText-Questions-1.png\")
<\/p>\n<\/p>\n
\nCheck whether the given numbers are divisible by 6 or not.\u00a0 \u00a0 \u00a0 (Pg. No: 320)
\na) 1632\u00a0 \u00a0 b) 456\u00a0 \u00a0 \u00a0c) 1008\u00a0 \u00a0 \u00a0d) 789\u00a0 \u00a0 \u00a0e) 369\u00a0 \u00a0 f) 258
\nAnswer:
\n![\"AP](\"https:\/\/apboardsolutions.guru\/wp-content\/uploads\/2021\/03\/AP-Board-8th-Class-Maths-Solutions-Chapter-15-Playing-with-Numbers-InText-Questions-2.png\")
<\/p>\n
\nCheck whether the given numbers are divisible by 6 or not.\u00a0 \u00a0 \u00a0(Pg. No: 320)
\na) 458 + 676\u00a0 \u00a0 b) 63<\/sup>\u00a0 \u00a0 c) 62<\/sup> + 63<\/sup>\u00a0 \u00a0 d) 22<\/sup> \u00d7 32<\/sup>
\nAnswer:
\n![\"AP](\"https:\/\/apboardsolutions.guru\/wp-content\/uploads\/2021\/03\/AP-Board-8th-Class-Maths-Solutions-Chapter-15-Playing-with-Numbers-InText-Questions-3.png\")
<\/p>\n<\/p>\n
\nCan you arrange the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 in an order so that the number formed by first two digits is divisible by 2, the number formed by first three digits is divisible by 3, the number formed by first four digits is divisible by 4 and so on upto nine digits?
\nSolution: The order 123654987 looks promising check and verify.\u00a0 \u00a0 \u00a0(Pg. No : 320)
\nAnswer:
\n![\"AP](\"https:\/\/apboardsolutions.guru\/wp-content\/uploads\/2021\/03\/AP-Board-8th-Class-Maths-Solutions-Chapter-15-Playing-with-Numbers-InText-Questions-4.png\")
\n\u2234 This number can\u2019t continue upto ‘9’.
\n\u2192 123654987
\n![\"AP](\"https:\/\/apboardsolutions.guru\/wp-content\/uploads\/2021\/03\/AP-Board-8th-Class-Maths-Solutions-Chapter-15-Playing-with-Numbers-InText-Questions-5.png\")
\n\u2234 The given number 123654987 is not divisible by all the numbers like 2, 3, 4, 5,……… 9.<\/p>\n
\nCheck whether the given numbers are divisible by 4 or 8 or by both 4 and 8.
\na) 464\u00a0 \u00a0 b) 782\u00a0 \u00a0 \u00a0c) 3688\u00a0 \u00a0 d) 100\u00a0 \u00a0 \u00a0e) 1000\u00a0 \u00a0 f) 387856\u00a0 \u00a0 g)44<\/sup>\u00a0 \u00a0 \u00a0h) 83<\/sup> (Pg. No: 321)
\nAnswer:
\nIf a number is divisible by 4 then the last two digits of the number must be divisible by 4.
\nIf the last 3 digits of a number is divisible by 8 then it is divisible by 8.
\n![\"AP](\"https:\/\/apboardsolutions.guru\/wp-content\/uploads\/2021\/03\/AP-Board-8th-Class-Maths-Solutions-Chapter-15-Playing-with-Numbers-InText-Questions-6.png\")
<\/p>\n<\/p>\n
\nCheck whether the given numbers are divisible by 7. (Pg. No: 322)
\na) 322\u00a0 \u00a0 \u00a0b) 588\u00a0 \u00a0 \u00a0c) 952\u00a0 \u00a0 \u00a0d) 553\u00a0 \u00a0 e) 448
\nAnswer:
\n![\"AP](\"https:\/\/apboardsolutions.guru\/wp-content\/uploads\/2021\/03\/AP-Board-8th-Class-Maths-Solutions-Chapter-15-Playing-with-Numbers-InText-Questions-7.png\")
\nAll the given numbers are divisible by ‘7’.<\/p>\n
\nCheck whether the given numbers are divisible by 11.\u00a0 \u00a0 (Pg. No: 323)
\ni) 4867216\u00a0 \u00a0 \u00a0 ii) 12221\u00a0 \u00a0 \u00a0iii) 100001
\nAnswer:
\nIf the difference between the sum of digits of odd places and even places is divisible by 11, then entire number is divisible by 11.
\n![\"AP](\"https:\/\/apboardsolutions.guru\/wp-content\/uploads\/2021\/03\/AP-Board-8th-Class-Maths-Solutions-Chapter-15-Playing-with-Numbers-InText-Questions-8.png\")
<\/p>\n
\nTake different pairs of numbers and check the above four rules.\u00a0 \u00a0 \u00a0 (Pg. No: 325)
\nAnswer:
\na) Consider a factor of 36, say 9.
\nFactors of 9 are 1,3,9.
\n\u2234 36 is divisible by 1, 3, 9.
\n\u2234 36 is also divisible by all the factors of 9.
\nb) Let us consider a number 60. It is divisible by 5 and 6. It is also divisible by 5 x 6 = 30 Where 5, 6 are co-primes.
\nc) Take two numbers 25, 30. These numbers are both divisible by 5.
\nThe number 25 + 30 = 55 is also divisible by 5.
\nd) Take two numbers 36, 54. These numbers are both divisible by 9.
\nTheir difference i.e., 54 – 36 = 18 is also divisible by 9.<\/p>\n
\n144 is divisible by 12. Is it divisible by the factors of 12? Verify.\u00a0 \u00a0 \u00a0(Pg. No : 325)
\nAnswer:
\nFactors of 12 = 1, 2, 3, 4, 6, 12.
\nIf 12 is a factor of 144 then 144 is divisible by all the factors of 12.<\/p>\n
\nCheck whether 23<\/sup> + 24<\/sup> + 25<\/sup> is divisible by 2. Explain.\u00a0 \u00a0 \u00a0 \u00a0(Pg. No : 325)
\nAnswer:
\n23<\/sup> + 24<\/sup> + 25<\/sup> = 8 + 16 + 32 = 56 is an even.
\n\u2234 56 is divisible by 2.<\/p>\n<\/p>\n
\nCheck whether 33 – 32 is divisible by 3. Explain\u00a0 \u00a0 (Pg. No : 325)
\nAnswer:
\n33 – 32 = 27 – 9 = 18 \u2192 1 + 8 = 9 \u21d2 \\(\\frac{9}{3}\\) (R = 0)
\n\u2234 It is divisible by ‘3’.<\/p>\n
\nCheck the result if the numbers chosen were\u00a0 \u00a0 \u00a0 \u00a0(Pg. No : 328)
\ni) 37\u00a0 \u00a0 ii) 60\u00a0 \u00a0 iii) 18\u00a0 \u00a0iv) 89
\nAnswer:
\ni) If the digits are interchanged in 37 then it becomes as 73.
\n\u2234 37 + 73 = 110 \u2192 \\(\\frac{110}{11}\\) (R = 0)
\nIt is divisible by ’11’.
\n![\"AP](\"https:\/\/apboardsolutions.guru\/wp-content\/uploads\/2021\/03\/AP-Board-8th-Class-Maths-Solutions-Chapter-15-Playing-with-Numbers-InText-Questions-9.png\")
<\/p>\n
\nIn a cricket team there are 11 players. The selection board purchased 10x + y T-shirts to players. They again purchased \u201810y + x’ T-shirts and total T-shirts were distributed to players equally. How many T-shirts will be left over after they distributed equally to 11 players ? How many each one will get?\u00a0 \u00a0 \u00a0(Pg. No : 328)
\nAnswer:
\nNo.of players in the team = 11
\nNo.of T- shirts are purchased at first = 10x + y
\nNo. of T – shirts are purchased for the 2nd time = 10y + x
\nSum of the T – shirts = (10x + y) + (10y + x)
\n= 11x + 11y = ll(x + y)
\n\u2234 11(x + y) T – shirts are distributed among 11 players then each will get ll(x + y)
\n\\(\\frac{11(x + y)}{11}\\) = x + y
\nRemaining T – shirts = Purchased T – shirts – 11 (No.of T-shirts got by each)
\n= 11(x + y) – 11(x + y)
\n= 0<\/p>\n<\/p>\n
\nIn a basket there are \u201810a + b’ fruits (a \u2260 0 and a > b). Among them \u201810b + a’ fruits are rotten. The remaining fruits distributed to 9 persons equally. How many fruits are left over after equal distribution? How many fruits would each child get?\u00a0 \u00a0 \u00a0 (Pg. No: 328)
\nAnswer:
\nNo. of fruits in a basket = 10a + b
\nNo. of fruits are rotten = 10b + a
\nRemaining fruits to be distributed = (10a + b) – (10b + a)
\n= 10a + b – 10b – a
\n= 9a – 9b = 9(a – b)
\n\u2234 9(a – b) fruits are distributed among ‘9’ Children
\nthen each will get = 9(a – b) \u00f7 9 = \\(\\frac{9(a – b)}{9}\\) = (a – b)
\nNo. of fruits left over after distribution
\n= Total no. of fruits distributed – No.of fruits got by each
\n= 9(a – b) – 9(a – b) = 0<\/p>\n
\nCheck in the above activity with the following numbers.\u00a0 \u00a0 \u00a0 (Pg. No: 329)
\ni) 657\u00a0 \u00a0 ii) 473\u00a0 \u00a0 \u00a0iii) 167\u00a0 \u00a0 iv) 135
\nAnswer:
\n![\"AP](\"https:\/\/apboardsolutions.guru\/wp-content\/uploads\/2021\/03\/AP-Board-8th-Class-Maths-Solutions-Chapter-15-Playing-with-Numbers-InText-Questions-10.png\")
<\/p>\n
\nIf 21358AB is divisible by 99, find die values of A and B.\u00a0 \u00a0 \u00a0(Pg. No: 331)
\nAnswer:
\nIf 21358AB is divisible by 99, then it is divisible by 9 and 11.
\nIf 21358AB is divisible by 9 then the sum of the digits is divisible by 9.
\n2 + 1 + 3 + 5 + 8 + A + B = 9 \u00d7 3 say
\n\u21d2 19 + A + B = 27
\n\u21d2 A + B = 27-19 = 8
\nA + B = 8 …… (1)
\nIf 21358AB is divisible by ‘ll’ then the difference of sum of even and odd digits will be divisible by’ll’.
\n2 1 3 5 8 A B
\n\u2234 (2 + 3 + 8 + B) – (1 + 5 + A) = 11 \u00d7 1 say
\n\u21d2 13 + B – 6 – A = 11
\n\u21d2 B – A = 11 – 7 = 4 ……. (2)
\nFrom (1) & (2) A = 2, B = 6
\n\u2234 The required number is 21358AB = 2135826 which is divisible by 99.<\/p>\n<\/p>\n
\nFind the values of A and B of file number 4AB8 (A, B are digits) which is divisible by 2, 3, 4, 6, 8 and 9.\u00a0 \u00a0 \u00a0 \u00a0(Pg. No: 331)
\nAnswer:
\nGiven number is 4AB8.
\n4AB8<\/span> \u2192 \\(\\frac{8}{2}\\) (R = 0) so, it is divisible by ‘2’.
\n4AB8 \u2192 If it is divisible by ‘3’, sum of all the digits should be a multiple of ‘3’. .
\n\u2234 4 + A + B + 8 = 3 or 6 or 9 or 12 or 15 …….
\n![\"AP](\"https:\/\/apboardsolutions.guru\/wp-content\/uploads\/2021\/03\/AP-Board-8th-Class-Maths-Solutions-Chapter-15-Playing-with-Numbers-InText-Questions-11.png\")
\n4AB8 \u2192 If it is divisible by 9, sum of all the digits should be a multiple of ‘9’.
\n\u2234 4 + A + B + 8 = 9 or 18 or 27 or 36
\n\u21d2 A + B + 12 = 9 \u222318\u2223 27\u2223 36 ……. (3)
\nFrom (1) & (3)
\nA + B + 12 = 9 or 18 say
\nIf A + B + 12 = 9
\nA + B = 9 – 12 = -3
\nIt is impossible
\nIf A + B + 12 = 18
\nA + B = 18 – 12 = 6
\n\u2234 A + B = 6
\nIf A = 4 & B = 2
\n4AB8 = 4428<\/span>
\n4AB8 \u2192 4428 \u2192 \\(\\frac{428}{8}\\) (R \u2260 0)
\n\u2234 A = 4 & B = 2 are not possible.
\nIf A = 2& B = 4
\n4AB8 \u2192 4248<\/span> \u2192 \\(\\frac{248}{8}\\) (R = 0)
\n\u2234 A = 2 and B = 4<\/p>\n<\/p>\n
\nBy using the above method check whether 7810364 is divisible by 4 or not.\u00a0 \u00a0 \u00a0 \u00a0 (Pg. No: 333)
\nAnswer:
\nGiven number = 7810364
\n![\"AP](\"https:\/\/apboardsolutions.guru\/wp-content\/uploads\/2021\/03\/AP-Board-8th-Class-Maths-Solutions-Chapter-15-Playing-with-Numbers-InText-Questions-12.png\")
\nSum of product of place values and remainders of place values = 0 + 0 + 0 + 0 + 0 + 12 + 4
\n\u2192 \\(\\frac{16}{4}\\) (R = 0)
\n\u2234 7810364 is divisible by ‘4’.<\/p>\n
\nBy using the above method check whether 963451 is divisible by 6 or not.\u00a0 \u00a0 \u00a0(Pg. No: 333)
\nAnswer:
\nThe given number = 963451
\n![\"AP](\"https:\/\/apboardsolutions.guru\/wp-content\/uploads\/2021\/03\/AP-Board-8th-Class-Maths-Solutions-Chapter-15-Playing-with-Numbers-InText-Questions-13.png\")
\nSum of product of place values and remainders of place values
\n= 36 + 24 + 12 + 16 + 20 + 1 \u2192 \\(\\frac{109}{6}\\) (R \u2260 0)
\n\u2234 963451 is not divisible by ‘6’.<\/p>\n
\nIn the division 56 Z \u00f7 10 leaves remainder 6, what might be the value of Z.\u00a0 \u00a0 \u00a0(Pg. No: 315)
\nAnswer:
\nLet 56Z, Z = 0, 1,2, 3, 4, ….. , 9 say.
\nTo obtain remainder ‘6’ when divided by 10, Z = 6
\n\\(\\frac{566}{10}\\) = \\(\\frac{560+6}{10}\\)
\nRemainder is 6.
\n![\"AP](\"https:\/\/apboardsolutions.guru\/wp-content\/uploads\/2021\/03\/AP-Board-8th-Class-Maths-Solutions-Chapter-15-Playing-with-Numbers-InText-Questions-14.png\")
\n\u2234 Z = 6<\/p>\n<\/p>\n
\nIf 4B \u00f7 5 leaves remainder 1, what might be the value of B?\u00a0 \u00a0 (Pg. No : 316)
\nAnswer:
\nIf 4B is divided by 5 then remainder should be ‘1’,
\n\u2234 B = {0, 1, 2, ….. , 9}
\ni.e., 40, 41, 42, …… , 49
\nFrom the above numbers we have to take 41 and 46.
\n41 and 46 are divided by 5 and leaves the remainder 1.
\n\u2234 B = {1, 6}<\/p>\n
\nIf 76C \u00f7 5 leaves remainder 2, what might be the value of C?\u00a0 \u00a0 \u00a0(Pg. No: 316)
\nAnswer:
\nTo get remainder 2, when 76C is divided by 5 take C = {0, 1,……, 9}.
\nIf C = 2, 7 then
\n76C = 762 or 767 are divided by 5 leaves the remainder 2.<\/p>\n
\n\u201cIf a number is divisible by 10, it is also divisible by 5.\u201d Is the statement true? Give reasons.\u00a0 \u00a0 \u00a0(Pg. No : 316)
\nAnswer:
\nThe given statement is true.
\n\u2235 When a number is divisible by ’10’, then its units digit should be ‘0’.
\nSimilarly the units digit of a number is 5 or 0, then it is divisible by 5.
\n\u2234 The number which is divisible by 10 is also divisible by 5.<\/p>\n
\n\u201cIf a number is divisible by 5, it is also divisible by 10.\u201d Is the statement is true or false? Give reasons.\u00a0 \u00a0 \u00a0(Pg. No : 316)
\nAnswer:
\nThe given statement is false.
\n\u2235 If a number is divisible by 5, then its units digit must be ‘5’ or ‘0’. But in case of 10, it . must be ‘0’ only.
\n\u2234 The number which is divisible by ‘5’ is need not be divisible by ’10’.<\/p>\n
\nCheck whether the given numbers are divisible by 4 or 8 or by both 4 and 8.\u00a0 \u00a0 \u00a0(Pg. No : 321)
\na) 42<\/sup> \u00d7 82<\/sup> b) 103<\/sup> c) 105<\/sup> + 104<\/sup> + 103<\/sup> d) 43<\/sup> + 42<\/sup> + 41<\/sup> – 22<\/sup>
\nAnswer:
\n![\"AP](\"https:\/\/apboardsolutions.guru\/wp-content\/uploads\/2021\/03\/AP-Board-8th-Class-Maths-Solutions-Chapter-15-Playing-with-Numbers-InText-Questions-15.png\")
<\/p>\n<\/p>\n
\nTake a four digit general number, make the divisibility rule for \u20187\u2019.\u00a0 \u00a0 \u00a0(Pg. No : 322)
\nAnswer:
\nLet the 4 – digited number be ‘abcd’ say.
\nThe remainders when divided by ‘7’,
\n![\"AP](\"https:\/\/apboardsolutions.guru\/wp-content\/uploads\/2021\/03\/AP-Board-8th-Class-Maths-Solutions-Chapter-15-Playing-with-Numbers-InText-Questions-16.png\")
\n\u2234 If (6a + 2b + 3c + d) is divisible by 7 then the 4 – digited number be divisible by ‘7’.<\/p>\n
\nCheck your rule with the number 3192 which is a multiple of 7.\u00a0 \u00a0 \u00a0 (Pg. No : 322)
\nAnswer:
\nThe given number is 3192
\n\u21d2 a = 3, b = 1, c = 9, d = 2
\n6a + 2b + 3c + d = 6 \u00d7 3 + 2 \u00d7 l + 3 \u00d7 9 + 2.
\n= 18 + 2 + 27 + 2
\n= 49 \u2192 \\(\\frac{49}{7}\\) (R = 0)
\n\u2234 3192 is divisible by 7\u2019according to my law.<\/p>\n
\n1) Verify whether 789789 is divisible by 11 or not.\u00a0 \u00a0 \u00a0(Pg. No: 323)
\n2) Verify whether 348348348348 is divisible by 11 or not.
\n3) Take an even palindrome i.e. 135531 check whether this number is divisible by 11 or not.
\n4) Verify whether 1234321 is divisible by 11 or not.
\nAnswer:
\n![\"AP](\"https:\/\/apboardsolutions.guru\/wp-content\/uploads\/2021\/03\/AP-Board-8th-Class-Maths-Solutions-Chapter-15-Playing-with-Numbers-InText-Questions-17.png\")
<\/p>\n<\/p>\n
\nCheck whether 1576 \u00d7 1577 \u00d7 1578 is divisible by 3 or not.\u00a0 \u00a0 \u00a0(Pg. No : 325)
\nAnswer:
\nThe given number is 1576 \u00d7 1577 \u00d7 1578.
\nThe product of any 3 consecutive numbers is divisible by ‘3’.
\nEx : 4 \u00d7 5 \u00d7 6 = 120 \u2192 \\(\\frac{120}{3}\\) (R = 0)
\n\u2234 1576 \u00d7 1577 \u00d7 1578 is divisible by \u20193\u2019.<\/p>\n
\nCheck the above method applicable for the divisibility of 11 by taking 10-digit number.\u00a0 \u00a0 \u00a0(Pg. No : 326)
\nAnswer:
\nThe largest 10 – digited number = 9,99,99,99,999
\nD C B A
\n\u2234 9\/999\/999\/999
\n\u21d2 B + D = 9 + 999 = 1008
\nA + C = 999 + 999 = 1998
\n\u2234 (A + C) – (B + D) = 990 \u2192 \\(\\frac{990}{11}\\) (R = 0)
\n\u2234 The largest 10 – digited number should be divisible by 11 according to this method.<\/p>\n
\nTake a three digit number and make the new numbers by replacing its digits as (ABC, BCA, CAB). Now add these three numbers. For what numbers the sum of these three numbers is divisible?\u00a0 \u00a0 \u00a0 (Pg. No : 329)
\nAnswer:
\n![\"AP](\"https:\/\/apboardsolutions.guru\/wp-content\/uploads\/2021\/03\/AP-Board-8th-Class-Maths-Solutions-Chapter-15-Playing-with-Numbers-InText-Questions-18.png\")
<\/p>\n
\nIf YE \u00d7 ME = TTT find the numerical value of Y + E + M + T.
\n[Hint: TTT = 100T + 10T + T = T(111) = T(37 \u00d7 3)]\u00a0 \u00a0 \u00a0 (Pg. No: 332)
\nAnswer:
\nTTT = 100T + 10T + T
\n= T(111)
\n= T(37 \u00d7 3)
\n\u2234 YE \u00d7 ME = T(37 \u00d7 3)
\n\u2234 T ={1, 2, 3, ….., 9}
\nBut T = {3, 6, 9} are multiples of 3.
\nT(37 \u00d7 3) = 3(111), 6(111), 9(111) are divisible by 3.
\n\u2234 YE \u00d7 ME = 333\u2223666\u2223999
\nYE \u00d7 ME = 999 = 27 \u00d7 37
\n\u2234 Y = 2, M = 3, E = 7, T = 3
\n\u2234 Y + E + M + T = 2 + 3 + 7 + 3 = 15<\/p>\n<\/p>\n
\nIf cost of 88 articles is A733B, find the values of A and B.\u00a0 \u00a0 \u00a0 \u00a0(Pg. No: 334)
\nAnswer:
\nIf A733B is divisible by 88 then it is divisible by 8 \u00d7 11.
\nDivisibility of 11:
\n\u21d2 A733B \u2192 (A + 3 + B) – (7 + 3) = 0
\n\u21d2 A + B = 7 ……. (1)
\nDivisibility of 8:
\n\u21d2 A733B \u21d2 \\(\\frac{33B}{8}\\)
\n\u2234 \\(\\frac{336}{8}\\) (R = 0) (If B = 6 then it is divisible by 8)
\n\u2234 B = 6 ……. (2)
\nFrom (1), (2)
\n\u2234 A = 1, B = 6<\/p>\n
\nCheck whether 456456456456 is divisible by 7, 11 and 13.\u00a0 \u00a0 \u00a0(Pg. No: 334)
\nAnswer:
\n\u2234 The given number = 456456456456
\n456456456456 = 456 (1001001001)
\n= 456 \u00d7 (7 \u00d7 11 \u00d7 13) \u00d7 (1000001)
\n\u2234 456456456456 is divisible by 7, 11 and 13.<\/p>\n
\nFind the digit in the units place of a number if it is divided by 5 and 2 leaves the remainders 3 and 1 respectively.\u00a0 \u00a0(Pg. No: 316)
\nAnswer:
\nIf a number is divided by 5 and 2 leaves the remainders 3 and 1 respectively, then its units digit be 3.
\nEx: \\(\\frac{13}{5}\\) \u21d2 (R = 3), \\(\\frac{13}{2}\\) \u21d2 (R = 1)
\n\\(\\frac{23}{5}\\) \u21d2 (R = 3), \\(\\frac{23}{2}\\) \u21d2 (R = 1)
\n\u2234 The unit’s digit of a required number be 3.<\/p>\n<\/p>\n
\nTake a two digit number reverse the digits and get another number. Subtract smaller number from bigger number. Is the difference of those two numbers is always divisible by 9?\u00a0 \u00a0 \u00a0 (Pg. No : 328)
\nAnswer:
\n![\"AP](\"https:\/\/apboardsolutions.guru\/wp-content\/uploads\/2021\/03\/AP-Board-8th-Class-Maths-Solutions-Chapter-15-Playing-with-Numbers-InText-Questions-19.png\")
<\/p>\n
\n1) Can we conclude 102n<\/sup> – 1 is divisible by both 9 and 11? Explain.\u00a0 \u00a0 \u00a0(Pg. No: 333)
\n2) Is 102n+1<\/sup> – 1 is divisible by 11 or not? Explain.
\nAnswer:
\n![\"AP](\"https:\/\/apboardsolutions.guru\/wp-content\/uploads\/2021\/03\/AP-Board-8th-Class-Maths-Solutions-Chapter-15-Playing-with-Numbers-InText-Questions-20.png\")
<\/p>\n<\/p>\n
\nVerify a5<\/sup> + b5<\/sup> is divisible by (a + b) by taking different natural numbers for \u2018a\u2019 and ‘b’.\u00a0 \u00a0 (Pg. No : 334)
\nAnswer:
\n![\"AP](\"https:\/\/apboardsolutions.guru\/wp-content\/uploads\/2021\/03\/AP-Board-8th-Class-Maths-Solutions-Chapter-15-Playing-with-Numbers-InText-Questions-21.png\")
\n\u2234 a5<\/sup> + b5<\/sup> is divisible by (a + b).
\n\u2234 (a5<\/sup> + b5<\/sup>) is divisible by (a + b) for all the values of a, b.<\/p>\n
\nCan we conclude (a2n+1<\/sup> + b2n+1<\/sup>) is divisible by (a + b)?\u00a0 \u00a0 \u00a0 (Pg. No : 334)
\nAnswer:
\n![\"AP](\"https:\/\/apboardsolutions.guru\/wp-content\/uploads\/2021\/03\/AP-Board-8th-Class-Maths-Solutions-Chapter-15-Playing-with-Numbers-InText-Questions-22.png\")
\na2n+1<\/sup> + b2n+1<\/sup> is divisible by (a + b) for all the values of ‘n’.<\/p>\n","protected":false},"excerpt":{"rendered":"