I first learned Algebra using the classic textbook by William Hart. It didn't make a lot of sense then since I was more fascinated with the concepts of Physical science rather than abstract mathematics. I wasn't patient enough then to do exercises. It was only when I started working on Calculus that I developed the discipline of going though each exercise. I am however grateful for this book, my high school Algebra teacher and my tutor for developing the basic mathematical skills I would need later on in life.
Today we tackle Exercise 1 from Hart's College Algebra. This covers very basic concepts of operations involving signed integers so solutions will be simple. Nevertheless, I hope this will be helpful to the mathematical novice.
Have fun!
Exercise 1
Basic rules
- Odd number of negative factors , product is negative
-Even number of negative factors, product is positive
- For division, negatives cancel if they are both on the numerator and the denominator.
-For Absolute values, just ignore the sign and write the number.
Compute each product:
1. 8x (-3) = -24
2.(-2)(5) = -10
3. 7 x 0 = 0
4. 6x(-3)=-18
5. -(-5) = 5
6. +(-3) = -3
7. +(-1) = -1
8. -(+8) = - 8
9. (-9)(-5) = 45
10. (+5)(-7)= -35
11. (-4)(+3) = -12
12. (-133)x0 = 0
13. (-7)(-4)(6) = 168
14. 4(-2)(-7)(-3) = -168
15. 3(5)(2)(-4) = -120
16. -4(-5)(6)(-3) = -360
17 (-5)(-3)(0)(-4) = 0
18. 5(-2)7(-3)(-4) = -840
19. (-5)(-3)(-4)(-2) = 120
20. (-1)(-1)(-1)(-1) = 1
21.(-1)(-1)(-1)(-1)(-1) = -1
22. -1.57(-2.31) = 3.6267
23. -3.2(-4.7) = 15.04
24. 3(-1.42)(2.5) = 10.65
State the absolute value of the number
25. 17 = 17
26. -46 =46
27. -33 = 33
28. - 3/4 = 3/4
29. -1.48 = 1.48
Read the symbol and specify its value
30. | 7 | = 7
31. | -36 | = 36
32. | -9 | = 9
33. | -5/3 | = 5/3
34. | -1.3 | = 1.3
35. Find the product of -2,-5 and -2.3 = -23
36. Find the product of 5.3, -4 and 2 = - 42.4
37. Compute 4abc if a = -3, b = -4 and c = -2.
4abc = -96
38. Compute 3xyz if x = -2, y = 10 and z = 5.3
3xyz = -318
39. Compute 2abxy if a = - 3, b = 4, x = - 3, and y = 5
2abxy = 360
Find the negative of each number
40. -3 = 3
41. 6 = -6
42. -2/3 = 2/3
43. -8 = 8
44. 16.7 = -16.7
45. 0 = 0
Express the quotient as a positive or negative integer or a fraction
46. +16/+8 = +2
47. -16/8 = -2
48. 15/-3 = -5
49. -48/12 = - 4
50. -42/-6 = - 7
51. -36/-18 = +2
52. -28/7 =-4
53. +39/-3 = -13
54. -14/-10 = 7/5
55. +12/-36 = -1/3
56.-16/28 = -8/14
57. 0/-39 = 0
Today we tackle Exercise 1 from Hart's College Algebra. This covers very basic concepts of operations involving signed integers so solutions will be simple. Nevertheless, I hope this will be helpful to the mathematical novice.
Have fun!
Exercise 1
Basic rules
- Odd number of negative factors , product is negative
-Even number of negative factors, product is positive
- For division, negatives cancel if they are both on the numerator and the denominator.
-For Absolute values, just ignore the sign and write the number.
Compute each product:
1. 8x (-3) = -24
2.(-2)(5) = -10
3. 7 x 0 = 0
4. 6x(-3)=-18
5. -(-5) = 5
6. +(-3) = -3
7. +(-1) = -1
8. -(+8) = - 8
9. (-9)(-5) = 45
10. (+5)(-7)= -35
11. (-4)(+3) = -12
12. (-133)x0 = 0
13. (-7)(-4)(6) = 168
14. 4(-2)(-7)(-3) = -168
15. 3(5)(2)(-4) = -120
16. -4(-5)(6)(-3) = -360
17 (-5)(-3)(0)(-4) = 0
18. 5(-2)7(-3)(-4) = -840
19. (-5)(-3)(-4)(-2) = 120
20. (-1)(-1)(-1)(-1) = 1
21.(-1)(-1)(-1)(-1)(-1) = -1
22. -1.57(-2.31) = 3.6267
23. -3.2(-4.7) = 15.04
24. 3(-1.42)(2.5) = 10.65
State the absolute value of the number
25. 17 = 17
26. -46 =46
27. -33 = 33
28. - 3/4 = 3/4
29. -1.48 = 1.48
Read the symbol and specify its value
30. | 7 | = 7
31. | -36 | = 36
32. | -9 | = 9
33. | -5/3 | = 5/3
34. | -1.3 | = 1.3
35. Find the product of -2,-5 and -2.3 = -23
36. Find the product of 5.3, -4 and 2 = - 42.4
37. Compute 4abc if a = -3, b = -4 and c = -2.
4abc = -96
38. Compute 3xyz if x = -2, y = 10 and z = 5.3
3xyz = -318
39. Compute 2abxy if a = - 3, b = 4, x = - 3, and y = 5
2abxy = 360
Find the negative of each number
40. -3 = 3
41. 6 = -6
42. -2/3 = 2/3
43. -8 = 8
44. 16.7 = -16.7
45. 0 = 0
Express the quotient as a positive or negative integer or a fraction
46. +16/+8 = +2
47. -16/8 = -2
48. 15/-3 = -5
49. -48/12 = - 4
50. -42/-6 = - 7
51. -36/-18 = +2
52. -28/7 =-4
53. +39/-3 = -13
54. -14/-10 = 7/5
55. +12/-36 = -1/3
56.-16/28 = -8/14
57. 0/-39 = 0
