Math Problem Help - Inequalities

Inequalities was a very confusing topic for me when I first learned Algebra.  The key to it really is to remember that < means less than  and > is less than.  Here's my solution to Exercise 4 of College Algebra by Hart.

Math Problem Help : Dealing with Grouping 3

We continue with how to deal with grouping in mathematical equations.  This is a continuation of my solutions for exercise 3 of College Algebra by Hart.

Math Problem Help : Dealing with Grouping part 2

In this post, we will be continuing our work on grouping. Specifically, we will work on problems that involve the removal of grouping in equations.  A key thing to remember if a negative number goes before a parenthesis, we are to multiply it to the numbers inside.

Math Problem Help(Algebra) - Dealing with groupings part 1

Today we deal with groupings.  It is not uncommon for the mathematically challenged to be confused when parenthesis are put on some terms of an equation.  The key to solving your problem is to deal with the operations inside the parenthesis first.  A good acrostic to remember is PMDAS - Parethesis, Multiply, Divide, Add, Subtract telling us what operations to do first.  Below is the first installment of solutions to Exercise 3 of College Algebra by William Hart. 

Math Problem Help (Algebra)- Operations Involving Signed Numbers 2

Today we continue our journey into the exciting field of mathematics.  While a lot of us may have had bad experiences with math, we cannot deny that it is exciting in that the very laws of the physical universe are  somehow coded in mathematical language.  So we will, retake baby steps in Algebra in the hope that it will create in us a new found joy in Mathematical thinking.

In Arithmetic, we dealt with addition, subtraction, multiplication and division of positive numbers.In this post, we will tackle the addition of signed numbers. Here are some things to consider when working with signed numbers:

1. ) When two numbers have the same sign then you are supposed to add them and retain the sign they carry.  Ex. -28 -9 = -37

2.) When two number have opposite signs, then you get the difference and adapt the sign of the bigger number. Ex. -13 + 5 = -8

3.) Adding or subtracting by 0 results in the identity of a number. Ex, 0 -25 = -25

4.) The negative of a negative is a positive. Ex. -(-3) = +3

5.) It is helpful to associate terms of like signs together before doing the operation.
Ex. -10+17-8+14=-10-8+17+14= -18 + 31 =   13

6.) When solving for products or quotients of two numbers, like signs result in a positive number. Opposite signs result in a negative number .

Below are my solutions to Exercise 2 of College Algebra by William Hart.

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