{"id":82356,"date":"2022-01-31T16:59:51","date_gmt":"2022-02-01T04:59:51","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=82356"},"modified":"2024-02-27T12:45:46","modified_gmt":"2024-02-27T07:15:46","slug":"__trashed-396","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-material\/cbse-notes\/class-5\/maths\/__trashed-396\/","title":{"rendered":"NCERT Solutions for Class 5 Maths Chapter 7 Can You See The Pattern?"},"content":{"rendered":"

NCERT Solutions for Class 5 Maths Chapter 7 Can You See The Pattern?<\/h2>\n

<\/b><\/span><\/p>\n

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NCERT Textbook Page 103<\/strong><\/span>
\nLook for a Pattern<\/strong>
\n1.Mark that picture which is breaking the rule. Also correct it.<\/strong><\/span><\/p>\n

Ans.<\/strong><\/span> (a) In this pattern the sixth figure from the left is breaking the rule.
\nCorrect figure is as follows:
\n(b)The sixth figure from left is breaking the rule.
\n(c)The second figure from left is breaking the rule. Correct figure is as follows:
\n(d)The fourth figure from left is breaking the rule. Correct figure is as follows:<\/p>\n

Magic Squares<\/strong>
\nDo you remember magic triangles? Come now, let\u2019s make some magic squares.<\/strong><\/span>
\n 1.Fill this square using all the numbers from 46 to 54.<\/strong><\/span>
\n Rule: The total of each line is 150<\/strong><\/span><\/p>\n

Ans.<\/strong><\/span> In the third row, we have
\n52 + 47 =99
\nAnd 150-99 =51
\nSo, we can fill 51 in the first box of the third row.
\nNow, in the first column, we have 46 + 51 =97
\nAnd 150-97 =53
\nSo, we can fill 53 in the first box of the first column.
\nIn the first row, we have
\n53 + 49 = 102
\nAnd 150 \u2013 102 = 48
\nSo, we can fill 48 in the second box of the first row.
\nIn the second column, We have
\n48 + 52 =100
\nAnd 150-100 =50
\nSo, we can fill 50 in the second box of the second column. In the third row, we have
\n49 + 47 =96
\nAnd 150 \u2013 96 = 54
\nSo, we can fill 54 in the second box of the third column.<\/p>\n

2.Fill this square using all the numbers from 21 to 29. Rule: The total of each side is 75.<\/strong><\/span>
\nAns.<\/strong><\/span> In the first row:
\nThe required number =75 \u2013 (26 + 22)
\n=75 \u2013 48 = 27
\nIn the first column:
\nThe required number=75 \u2013 (26 + 28)
\n=75 \u2013 54 = 21
\nIn the second row:
\nThe required number=75 \u2013 (21 + 25)
\n=75 = 75 \u2013 46 = 29
\nIn the third row:
\nThe required number=75 \u2013 (28 + 24)
\n=75 \u2013 52 = 23
\nHence, the complete magic square is as follows:<\/p>\n

NCERT Textbook Page 104<\/strong><\/span>
\nMagic Hexagons<\/strong>
\n1.Leek at the patterns of numbers in hexagons. Each side has 2 circles and 1 box. You get the number in each box by multiplying the numbers in the circles next to it.<\/strong><\/span><\/p>\n

Look at the number 65 in the box.
\nWhich are the circles next to it?
\nCan you see how tite rule works?
\nUse the same rule to fill the hexagons below:<\/p>\n

 <\/p>\n

2.Now you also make your own magic hexagons.<\/strong><\/span>
\nAns.<\/strong> <\/span>Some of the magic hexagons are given below:<\/p>\n

NCERT Textbook Page 105<\/strong><\/span>
\nNumbers and Numbers<\/strong><\/p>\n

1.Are they equal?<\/strong><\/span>
\nAns.<\/strong><\/span>Yes they are equal.<\/p>\n

2.Fill in the blank spaces in the same way.<\/strong><\/span>
\nAns.<\/strong><\/span><\/p>\n

3.Now look this<\/strong><\/span><\/p>\n

Ans.<\/strong><\/span><\/p>\n

Left Right\u2014Same to Same<\/strong>
\n1.Can you see something special about 121?<\/strong><\/span>
\nAns.<\/strong><\/span> The number reads the same in backward and forward.<\/p>\n

2.What, it\u2019s just a number!<\/strong><\/span>
\nAns.<\/strong> <\/span>Oh, yes! It is 1, 2, 1 from right to left also.
\nTake a number, say : 43
\nNow turn it back to front : 34
\nThen add them together : 77
\n77 is one such special number. There are many such numbers. Take another number : 48
\nNow turn it back to front : 84
\nThen add them together : 132<\/p>\n

3.Is this a special number? No! Why not?<\/strong><\/span>
\nAns.<\/strong> <\/span>Because it is not the same after reversing it.
\nOK, carry on with the number : 132
\nAgain turn it back.to front : 231
\nThen add the two together : 363
\nAh 1 363 is a special number.
\nAns.<\/strong><\/span> Yes, it is a special number.
\nSo we see that to get special numbers we sometime need more steps. Now you try and change these numbers into special numbers:
\n(\u0430)28<\/strong><\/span>
\nAns.<\/strong><\/span> 82
\n110 This is not a special number; so let us do more steps Oil
\n121 This is a special number<\/p>\n

(b)132<\/strong><\/span>
\nAns.<\/strong> <\/span>231
\n363 This is a special number<\/p>\n

(c) 273<\/strong><\/span>
\nAns.<\/strong><\/span> 372
\n645 This is not a special number; so let us do more steps 546
\n1191 This is not a special number; so let us do more steps 1911
\n3102 This is not a special number; so let us do more steps 2013
\n5115 This is a special number<\/p>\n

4.Now let\u2019s use words in special way.<\/strong><\/span><\/p>\n

Did you notice that it reads the same from both sides; right to left and left to right?<\/strong><\/span>
\n Now try and use words in a special way.<\/strong><\/span>
\nAns.<\/strong><\/span> Some such examples are given below:
\nBACON NO CAB
\nBAR CANOE ON A CRAB
\nDENNIS SINNED
\nEVIL OLIVE<\/p>\n

NCERT Solutions for Class 5 Maths Chapter 7 Page 107<\/strong><\/span>
\nCalendar Magic<\/strong>
\nLook at the calendar below:
\nLet us mark a 3 x 3 box (9 dates) on the calendar and see some magic<\/p>\n

Take the smallest number:3
\nAdd 8 to it: +8
\n= 11
\nMultiply by 9:x 9
\nTotal: 99
\n99 is equal to the sum of all these numbers.
\nNow you choose any 3\u00d73 box from a calendar and find the total in the same way. Play this game with your family.
\nLet us take 4
\nAdd 8 to it +8
\n= 12
\nMultiply it by 9
\n= 9 x 12 = 108
\nThis is equal to the sum of these 9 numbers.
\nTo get the answer even faster multiply the middle number by 9, i.e. 12 x 9 = 108.<\/p>\n

NCERT Solutions for Class 5 Maths Chapter 7 Page 108<\/strong><\/span>
\nSome More Number Patterns<\/strong>
\n1.Take any number. Now multiply it by 2, 3, 4\u2014\u2014\u2014\u2014- at every step. Also add 3 to it at each step. Look at the difference in the answer. Is it the same at every step?<\/strong><\/span>
\n 12 x 2 + 3 = 27<\/strong><\/span>
\n 12 x 3 + 3 = 39<\/strong><\/span>
\n 12 x 4 + 3 = 51<\/strong><\/span>
\n 12 x 5 + 3 =63<\/strong><\/span>
\n 12 x + 3 =\u2014\u2014\u2014\u2014\u2014-<\/strong><\/span>
\n \u2014\u2014\u2014\u2013x 7 + 3 =\u2014\u2014\u2014\u2014<\/strong><\/span>
\nAns.<\/strong><\/span>12 x 6 + 3 = 75
\n12 x 7 + 3 = 87
\n12 x 8 + 3 =99
\n12 x 9 + 3 =111 .
\nIn every case the difference between consecutive numbers is 12<\/p>\n

2.Now try doing it with some other number and also take a different number to add at each step.<\/strong><\/span>
\nAns.<\/strong> <\/span>Let us take another number to see the pattern;
\n15 x 2 + 5 =35
\n15 x 3 + 5 = 50
\n15 x 4 + 5 =65
\n15 x 5 + 5 =80
\n15 x 6 + 5 = 95
\n15 x 7 + 5 = 110
\n15 x 8 + 5 = 125
\nWe can see the difference between two subsequent numbers is 15<\/p>\n

3.Look at the numbers below. Look for the pattern. Can you take it forward?<\/strong><\/span>
\n (9-1) \u00f78 =1<\/strong><\/span>
\n (98 \u2013 2) \u00f78 = 12<\/strong><\/span>
\n (987 \u2013 3) \u00f78 = 123<\/strong><\/span>
\n (9876 \u2013 4) \u00f78 = \u2026\u2026\u2026\u2026.<\/strong><\/span>
\n (98765-4) \u00f78 = \u2026\u2026\u2026\u2026<\/strong><\/span>
\n (\u2026\u2026\u2026\u2026. -\u2026\u2026\u2026\u2026.. ) \u00f78 =\u2026\u2026\u2026\u2026.<\/strong><\/span>
\n (\u2026\u2026\u2026\u2026\u2026.. -\u2026\u2026\u2026\u2026)\u00f78 = \u2026\u2026\u2026\u2026\u2026<\/strong><\/span>
\nAns.<\/strong><\/span>The above pattern is not correct. The correct pattern is as follows:
\n(9876 \u2013 4) \u00f78 = 1234
\n(98765-5)\u00f78 =12345
\n(987654 \u2013 6) \u00f78 =123456
\n(9876543 \u2013 7) \u00f78 =1234567<\/p>\n

NCERT Solutions for Class 5 Maths Chapter 7 Page 109<\/strong><\/span>
\nSmart Adding<\/strong>
\n1.What if someone gives you to add ten numbers together?<\/strong><\/span>
\nAns.<\/strong><\/span> Multiply 10\/2 by (10 + 1) = 5 x 11 = 55
\n1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 =55
\n11 + 12 + .. .. + .. .. + .. .. + .. .. + .. .. + .. .. + .. .. + 20 =155
\n21 + .. .. + .. .. + .. .. + .. .. + .. .. + .. ,. + .. .. + .. .. + 30 = \u2026.
\n31 + .. .. + ., .. + .. .. + .. .. + .. .. + .. .. + .. .. + ., .. + 40 =\u2026.
\n41 + .. .. + ., .. + .. .. + .. .. + .. .. + .. .. + .. .. + .. .. + 50 = \u2026.
\n51 + .. .. + ., .. + .. .. + .. .. + .. , . + . , .. + .. .. + .. .. + 60 =555
\n61 + .. .. + .. .. + .. .. + .. .. + .. .. + .. .. + .. .. + .. .. + 70 = \u2026.<\/p>\n

2.Did you notice some pattern in the answers?<\/strong><\/span>
\nAns.<\/strong> <\/span>Yes, I have noticed some pattern; sum of 1 to 10 is 55, sum of 11 to 20 is 155, sum of 21 to 30 is 255 and so on.
\n1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 =55 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 = 155
\n21 + 22 + 23 + 24 + 25 + 26 + 27 + 28 + 29 + 30 = 255
\n31 + 32 + 33 + 34 + 35 + 36 + 37 + 38 + 39 + 40 = 355
\n41 + 42 + 43 + 44 + 45 + 46 + 47 + 48 + 49 + 50 = 455
\n51+ 52 + 53 + 54 + 55 + 56 + 57 + 58 + 59 + 60 = 555
\n61 + 62 + 63 + 64 + 65 + 66 + 67 + 68 + 69 + 70 = 655<\/p>\n

Fun with Odd Numbers<\/strong>
\nTake the first two odd numbers. Now add them, see what you get.<\/strong><\/span>
\n Now, at every step, add the next odd number.<\/strong><\/span>
\n 1 + 3 = 4 =2 x 2<\/strong><\/span>
\n 1+3+5=9=3 x 3<\/strong><\/span>
\n 1 + 3 + 5 + 7 = 16 =4 x 4<\/strong><\/span>
\n l+3 + 5 + 7 + 9 = \u2026 =\u2026 x \u2026<\/strong><\/span>
\n 1 + 3 + 5 + 7 + 9 + 11 = \u2026=\u2026 x \u2026.<\/strong><\/span>
\n 1 + 3 + 5 + 7 + 9 + 11 + 13 = \u2026 = \u2026 x \u2026<\/strong><\/span>
\n 1.How far can you go on?<\/strong><\/span>
\nAns.<\/strong><\/span> Complete patterns are as follows:
\n1+3 + 5 + 7 + 9 = 25=5 x 5
\n1 + 3 + 5 + 7 + 9 + 11 = 36 = 6 x 6
\n1 + 3 + 5 + 7 + 9 + 11 + 13 = 49 =7 x 7
\nThis process can go on and on.
\nThe sum of first \u2018n\u2019 odd numbers can be given by \u2018n x n\u2019<\/p>\n

NCERT Solutions for Class 5 Maths Chapter 7 Page 110<\/strong><\/span>
\nSecret Numbers<\/strong>
\nBanno and Binod were playing a guessing game by writing clues about a secret number. Each tried to guess the other\u2019s secret number from the clues.
\n1. Can you guess their secret numbers?<\/strong><\/span>
\nAns<\/strong><\/span>.<\/p>\n