2. Positive and Negative Numbers 0 1 2 3 4 5 X For a long time people had refused to believe in negative numbers. In our time, however, their existence is rarely questioned.. Created by Inna Shapiro ©2007

3. Positive and Negative Numbers 0 1 2 3 4 5 -2 -3-4-5 X Are you ready to take the challenge of the negative numbers?

4. Problem 1 Find the rule and fill empty cells: abc 5-116 32-18-14 -175 -1414 1157

5. Answer abc 5-116 32-18-14 -17512 -14140 1157-68 C = - ( a + b )

6. Problem 2 Pete chose several positive and negative points on the coordinate line. Mary added all these numbers together and got 25. Pete moved all points by 5 units to the left. Mary added the new numbers together and got –35. How many numbers were chosen?

7. Answer The sum was 25, and then it changed to -35. So the difference between the old sum and the new one is 25-(-35)=60 That means that Peter chose 60/5=12 numbers

8. Problem 3 Insert numbers into empty cells so that each of them, starting from the third one, is equal to the sum of two previous numbers. 20

9. Answer 4-22022 -64-22022 10-64-22022 -4226-1610-64-22022 202 -1610-64-22022 26-1610-64-22022 Filling of cells is shown on the schema, starting from the adjacent cells

10. Problem 4 John has 9 cards with numbers -6, -4, -2, -1, 1, 2, 3, 4, 6 on them. Can he choose some cards so that the sum of chosen numbers is equal to –8?

11. Answer He can choose different sets of cards: -6, -2 -6, -2, -1, 1 -6, -2, -4, 4 -6, -2, -1, 1, -4, 4 -6,-4, 2 -6, -4, 2, -1, 1 -6, -4, -2, -1, 2, 3

12. Problem 5 Judy says that she can write 19 numbers in a row, so that the sum of each number with adjacent numbers from the left and from the right is positive, but the total sum of all numbers is negative. Is she right or wrong?

13. Answer Judy is right. Her row is: -7, 4, 4, -7, 4, 4, -7, 4, 4, -7, 4, 4, -7, 4, 4, -7, 4, 4, -7

14. Problem 6 Replace letters with numbers so that the sums of the numbers in any row, any column, or main diagonals are all equal. A8B-14 2C-8-4 -6-2DE 4F-18G

15. Answer The diagonal sum is 4-2-8-14=-20, so A=-20-(4-6+2)=-20 C=-20-(2-8-4)=-10 B=-20-(-20=8-14)=6 D =-20-(6-8-18)=0 E =-20-(-6-2+0)=-12 F =-20-(8-10-2)=-16 G =-20-(4-16-18)=10 -2086-14 2-10-8-4 -6-20-12 4-16-1810

16. Problem 7 Calculate: -100-99-98-……-1+1+2+…+100+101

17. Answer Let us change the order in the sum -100-99-98-……-1+1+2+…+100+101= = (- 100 + 100) + (- 99 + 99) + … + (-1 + 1) + + 0 + 101 = 0+101 So the answer is 101.

18. Problem 8 Calculate 1+2-3-4+5+6-7-8+…+301+302

19. Answer Let us group the numbers: 1+(2-3-4+5)+(6-7-8+9)+…(298-299- 300+301)+302 (2-3-4+5)=0 (6-7-8+9=0) and so on. So the sum is 1+302=303.

20. Problem 9 Jill wrote a long sum: 17=17+16+15+14…+(X+1)+X What was the number X in her sum?

21. Answer X=-16, because 17+16+15+14…+1+0+(-1)+…+(-16)= = 17 + 0 = 17

22. Problem 10 Fill in the cells with 1s and –1s so that the sum of the numbers in any 2x2 square is zero.

23. Answer 11 1 1 1 1 1 1