AB 57. AB 58. AA × 6 × AB × A C68 6 A B C A B and B – A = 1 59. AB 60. 8ABC 61. If 2A7 ÷ A = 33, – B 7 –ABC5 then find the 4 5 D488 value of A. 62. 212 x 5 is a multiple of 3 and 11. Find the value of x. 63. Find the value of k where 31k 2 is divisible by 6. 64. 1y3y6 is divisible by 11. Find the value of y. 65. 756 x is a multiple of 11, find the value of x. 66. A three-digit number 2 a 3 is added to the number 326 to give a three-digit number 5b9 which is divisible by 9. Find the value of b –a. 67. Let E = 3, B = 7 and A = 4. Find the other digits in the sum BASE +B A L L G AM E S 68. Let D = 3, L = 7 and A = 8. Find the other digits in the sum + AS + A BULL 69. If from a two-digit number, we subtract the number formed by reversing its digits then the result so obtained is a perfect cube. How many such numbers are possible? Write all of them. 70. Work out the following multiplication. 12345679 × 9 Use the result to answer the following questions.
- (a)What will be 12345679 × 45?
- (b)What will be 12345679 × 63?
- (c)By what number should 12345679 be multiplied to get 888888888?
- (d)By what number should 12345679 be multiplied to get 999999999? 71. Find the value of the letters in each of the following: (i) PQ (ii) 2 L M × 6 + LM1 QQQ M18 72. If 148101B095 is divisible by 33, find the value of B. 73. If 123123A4 is divisible by 11, find the value of A. 74. If 56x32y is divisible by 18, find the least value of y. 1. Polygonal Numbers Study the patterns given below and extend it. We already know about square numbers. * * * * * * * * * * * * * * 1 4 9 Draw two more. Here for the first square number, use 12; for the second square number, use 22. To find the third square number use 32 and so on. Write the nth square number. Now let’s move to triangular numbers. * * * * * * * * * * * * * * * * * * * * 1 3 6 10 Find the next triangular number. n × (n + 1) To find the nth triangular number we use the formula Are you familiar with pentagonal numbers? First three are given to you. Write the next one * * * * * * 1 * * * * * * * * * 5 * * * Draw the dot patterns for the next pentagonal number. Count the number of dots inside the entire shape and write the number under the shape. 2. Put tick mark in the appropriate boxes if the given numbers are divisible by any of 2, 3, 4, 5, 6, 8, 10, 11 numbers. S.No. Number Divisible by 2 3 4 5 6 7 8 9 10 11 1. 40185 2. 92286 3. 56390 4. 419562 5. 10593248 3. Cross Number Puzzle Fill in the blank spaces in the cross number puzzle using following clues. Down (a) 59 ______ 63 ÷ 33 (b) 81 ______ 42 ÷ 6 (c) 7 ______ 6988 ÷ 11 (d) 37604 ______ 5 ÷ 15 (e) 56 ______ ÷ 10 Across (f) 90 ______ 815 ÷ 15 (g) 3514 ______ ÷ 12 (h) 4 ______ 07 ÷ 7 (i) 8 ______ 558 ÷ 6 (j) 6 ______ 5 ÷ 55 MATHEMATICS Rough Work UNIT-13 Rough Work PLAYING WITH NUMBERS 419 MATHEMATICS Rough Work
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(a) What will be 12345679 × 45?
(b) What will be 12345679 × 63?
(c) By what number should 12345679 be multiplied to get 888888888?