Math Problem Help( Algebra) - Operations involving signed numbers from College Algebra by William Hart

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
    
 

How to Improvise : Mirroring Exercise

Albert Einstein once defined Insanity as doing the same things over and over again but expecting different results.  The reality is that in our daily lives, insanity seems to be the norm. Whether its Business or at Home we find ourselves doing the same things over and over again, following the same line of thinking that got us into the problem in the first place.  It is a challenge for everyone to go off tangent and approach a situation for a different angle.

As a Physicist and Engineer, I had to face similar situations that would have led to dead end scenarios.  I am thankful for my Ballet training, having equipped me with a set of mental tools to develop my creativity. I had an easier time thinking of crazy ideas because of creative experiences I've had in the past. 

A pivotal moment in my dance training was when I took a course in Improvisation under Agnes Locsin, Cultural Center of the Philippines Awardee for Dance.  It was here that I learned to explore the use of my body and find new approaches to its use.  Specifically, I learned how I can move my arms and my legs in novel ways that were beautiful to behold and felt good to me, the performer.

Do you need to have any dance training to improvise and explore the use of your body? No. As a matter of fact, those who do not have any dance training are able to explore better because they do not have any movement biases.  It is more challenging for me to teach ballet dancers Improvisation because they are so concerned about technique. 

So how does one start improvisation. One way is to write your name with a specific part of your body. ( I will save this interesting exercise for another post. ) Another way, is by Mirroring.  In this exercise, 2 performers face each other with one designated as leader and the other as follower.  The leader moves a part of his/her body slowly with the follower copying the movement just like a mirror image.  Being challenged by my students ballet mindset, I started the exercise by having the leader do 2 movement phrases of 8 counts each, which I just improvised.  The follower was to do the usual following as the leader did my phrases. This was all done to establish the experience of being leader and follower among the dancers.

Having established the relationship between follower and leader, I then had the latter create her own phrase.  AS expected, her fear of technical incorrectness led her to make conservative hand moments. At this point, I directed the leader to go to a door frame in the studio and try to make movement that related to the frame.  I told her to explore moving at different levels.  My only constraint was for her to move in a  slow, steady manner. After she found her movement phrases, I had the leader go back to her pair and introduced the additional constraints of not turning her back to the follower. I had the leader 16 counts of her own movement before eliminating my movement phrases.  It was a pleasant suprise for my dance to have created her own movement. After completing the exercise. I had the leader/follower roles switched.  Below is a video clip showing the mirroring exercise done by my students for Acts Manila @ Life N Arts Sta Rosa Laguna.

A Review of Stephanie Meyer's The Host ( Novel )

I recently finished The Host and found it to be very engaging. I find most interesting the internal dialogue between the lead character Wanda and the owner of the body she inhabits, Melanie.  Here's a short video review of Stephanie Meyer's The Host. Enjoy...

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Biometric Voter Registration Process Philippines

The deadline for Biometric voter registration in the Philippines is coming up in the next few days.  As the COMELEC's campaign slogan goes, No Bio...No Boto...This just emphasizes the importance of this process to ensuring our voice as citizens are heard.  In general the process was smooth except for the volume of people that were queuing up for registration.  The process goes in 4 steps are shown in the infographic below. I've also put a short video to take you through the Registration Process.

 

Hope this helps you out in the next few days. 

 #Hope4Change #Election2016 #GodBlessThePhilippines #NoBioNoBoto

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