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Out walking with your friends, show them this quick way to square numbers that end in 5 using the formula BY ONE MORE THAN THE ONE BEFORE. � 75 2 = 5625 www.classtopper.com ON A WALK 75 2 means 75 x 75. The answer is in two parts: 56 and 25. The last part is always 25. 20
The first part is the first number, 7, multiplied by the number “one more”, which is 8: so 7 x 8 = 56 75 2 = 56 25 7 x 8 = 56 www.classtopper.com � Similarly 85 2 = 7225 because 8 x 9 = 72. Try these: 1) 452 2) 652 3) 952 4) 352 5) 152 For the harmony of the world is made manifest in Form and Number, and the heart and soul and all the poetry of Natural Philosophy are embodied in the concept of mathematical beauty. D’ARCY THOMPSON 21
Page 3 and 4: www.classtopper.com On seeing this
Page 5 and 6: www.classtopper.com caught between
Page 7 and 8: 30 CHECK YOUR BILL 32 CHECK YOUR CH
Page 9 and 10: � Similarly 10,000 - 1049 = 8951
Page 11 and 12: � $10 - $2.30 = $7.70 www.classto
Page 13 and 14: www.classtopper.com You subtract cr
Page 15 and 16: www.classtopper.com 88 - 12 98 - 2
Page 17 and 18: www.classtopper.com Try a few: 1) 1
Page 19: So: � 5 + 3 = 20 + 21 = 41 7 4 28
Page 23 and 24: Diagrammatically: 2 x 8 = 16 32 x 3
Page 25 and 26: � Now suppose we want the digit s
Page 27 and 28: www.classtopper.com So all numbers
Page 29 and 30: www.classtopper.com All sums, even
Page 31 and 32: Now suppose that there is a carry f
Page 33 and 34: � Similarly in 73 - 49 we decide
Page 35 and 36: � Similarly 234 x 7 = 1638 We get
Page 37 and 38: ) Multiply crosswise and add: 2x3 +
Page 39 and 40: Practise a few: 1) 21 2) 23 3) 32 4
Page 41 and 42: � So 72 x 11 = 792 Multiply by 11
Page 43 and 44: www.classtopper.com Divide by 9: 1)
Page 45 and 46: Divide these by 9: www.classtopper.
Page 47 and 48: www.classtopper.com To sum up, for
Page 49 and 50: Page 23 1) 2021 2) 624 3) 4216 4) 2
Page 51: www.classtopper.com ANSWERS Page 45

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