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Exercise 2.1 1. The form of the equation given. Find the

equation Next, using inductive reasoning, and check the accuracy of the answers provided by the method of calculation

1) (1×9 )+2=11

(12×9 )+3=111

(123×9 )+4=1,111

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2) 1=11+2=31+2+3=61+2+3+4=10

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3) 1=11+3=41+3+5=9

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4) 1+10=111+10+100=1111+10+100=1111

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5) 11×11=121111×111=12321

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1,111×1,111=1,234,321

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6) 9×9=8199×9=891999×9=8,991

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7) 9×9=81909×9=8,18190,909×9=818,181

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8) (1×8 )+1=9(12×8 )+2=98(123×8 )+3=987

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9) (9×1 )−1=8(9×21 )−1=188(9×321 )−1=2,888

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10) 1,089×1=1,0891,089×2=2,1781,089×3=3,267

1,089×4=………… .. 1,089×5=…………….

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1,089×6=…………….

1,089×7=……………. 1,089×8=……………. 1,089×9=…………….

1.By using the inductive reasoning find the next sequence

1. 12,22,32,42, ……………. 6. -15,-5,15, ……………. 2. 12,10,8,6, ……………. 7. 1,-1,-3,-5, ……………. 3. 5, 3,-1,-3, ……………. 8.-5,-3,-1,1, ……………. 4. 1,-1,1,-1,,1, ……………. 9. 1,6,11,16,25, ……………. 5. 1,4,9,16,25, ……………. 10. 8 ,14 ,20,26 , …………….

2. The multiplier effect of the following. It has been noted on the multiplier and the multiplier effect. And can provide conclusive or not1×9=9 6×9=54 11×9=99

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×9=18 7×9=63 12×9=108

3×9=27 8×9=72 13×9=117

4×9=36 9×9=81 14×9=1265×9=45 10×9=90 15×9=135

……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….3. The multiplier effect of the following numbers 142,857 x 1 = 142,857142,857 x 2 = 285,714142,857 x 3 = 428,571142,857 x 4 = 571,428

1.A note about the numbers instead of the multiplier effect, however

……………………………………………………………………………………………..……………………………………………………………………………………………..

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2.142 857 with a multiple of 5 and 6 have the same format as above

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3.The product obtained by multiplying 142,857 by the seventh and eighth on the conclusion of the above is true or not.

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4.Consider the following multiples 37×3=11137×6=22237×9=33337×12=444

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1) It should be noted, however, about the multiplier and the multiplier effect of the above.…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………

2) use inductive reasoning to find the multipliers that have a multiplier effect. 555 , 666, 777, 888 ,999 ……………………………………………………………………………………………………………………………………………………………………………………

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5) The form of the equation given. Find the equation Next, using inductive reasoning, and check the accuracy of the answers provided by the method of calculation1) (9×9 )+7=88

(98×9 )+6=888

(987×9 )+5=8888

(9,876×9 )+4=88,888

…………………………………………………….

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2) 34×34=1,156 334×334=111,556 3 ,334×3,334=…………………

…………………………………………………….3) 2=4−2

2+4=8−2

2+4+8=16−2

2+4+8+16=32−2

…………………………………………………….

4) 3=3 (2)2 3+6=6(3)2 3+6+9=9(4)2 3+6+9+12=12(5)2

…………………………………………………….5) 5(6)=6(6−1)

5 (6 )+5(36)=6(36−1)5 (6 )+5 (36 )+5 (216)=6(216−1)

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…………………………………………………….

6) By using the inductive reasoning find the value of the following1) 1 + 2 + 3 + … + 150

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2) 1 + 2 + 3 + … + 300

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3) 1 + 2 + 3 + … + 500 ………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………

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4) 1 + 2 + 3 + … + 1,000 …………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………

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7) By using the inductive reasoning find the value of the following 1) 2 + 4 + 6 + … + 100

…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………

2) 1 + 2 + 3 + … + 125 ……………………………………………………………………………………………………………………………………………………………………………………

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3) 1 + 2 + 3 + ... + n, where n is the number of counts is odd.

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8. The ancient Greeks wrote of 1,3,6,10,15,21 Please use the following symbol

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Based on the Triangle Write the triangle next two numbers .

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3) Considering that the number 72 is a triangle or not . …

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9) Use inductive reasoning to determine the following conclusions .(ใชก้ารใหเ้หตผุลแบบอุปนัยในการตรวจสอบขอ้สรุปต่อไปน้ี) 1 ) The product of two numbers , any number divided by two is always perfect

ผลคณูของจำานวนนับสองจำานวนใด ๆ จะหารด้วย 2 ลงตัวเสมอ

…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………

2) Count any more than four will be written as the sum of the numbers on a combination of two or more than double the number at any time

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(จำานวนนับใด ๆ ท่ีมากกวา่ 4 จะเขยีนในรูปการบวกของจำานวนนับท่ีเรยีบติดกันสองจำานวนหรอืมากกวา่สองจำานวนได้เสมอ เชน่ 5=2+3

6=1+2+3 14=2+3+4+5)…………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………

3) Two counts of any kind will always be an even number . (กำาลังสองของจำานวนนับใด ๆ จะเป็นจำานวนคู่เสมอ)

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10). .Photos from the patterns Write the Next Picture

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Exercises 2.2 Determine whether reasonable or not

จงตรวจสอบวา่ผลสรุปต่อไปนี้สมเหตสุมผลหรอืไม ่โดยใช้แผนภาพ

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