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Fundamental
concepts
Clement Radcliffe, Contributor
Having
reviewed important aspects of the structure of the CSEC examinations, I will now
consider some fundamental concepts of mathematics. These should have been done
in the lower forms (Grades 7 - 9), but are worth reviewing. Prior
to doing so, please let us together determine the solutions to last week's homework.
1. 4²
- 2² =
(a)
2
(b) 4
(c) 12
(d) 14 SOLUTION
It is
best to evaluate the answer as follows: 42
- 22 = 16 - 4 = 12. The answer is (c) 2.
The least number of sweets which can be shared equally among 5, 10 or 15 children
is: (a)
15
(b) 30
(c) 45
(d) 60 SOLUTION
The
least number to be divided equally among the three numbers is the highest common
factor (HCF). The HCF of 5, 10 and 15 is 30. Therefore, the answer is (b). You
could have tested each answer also. For example, 10 sweets cannot be shared equally
among 15 children. This is also the case for 45. 3.
2/5 expressed as a percentage is: (a)
5%
(b) 20%
(c) 25%
(d) 40% SOLUTION
2/5
expressed as a percentage is 2/5 x 100 = 40%. The answer is therefore (d) 4.
23. 98 x 0.5 is approximately equal to: (a)
0.12
(b) 1.2
(c) 12
(d)
120 SOLUTION
23.
98 is approximately 24 24
x 0.5 = 12. The answer is therefore (b) Now
let us continue this week's lesson by reviewing the topic DIRECTED NUMBERS.
I do
believe that it is worth emphasising the importance of this topic, as weakness
in this area will affect your ability to solve problems involving the application
of the four arithmetic operations (+, -, x, y) to real numbers. Your
performance in a wide variety of topics, including many in algebra, could also
be significantly affected. The number line is quite useful in helping students
to understand this topic. The following method is also recommended: EXAMPLE:
Evaluate 8 - 11 SOLUTION:
I have 8 items but owe 11 I,
therefore, owe three items which may be expressed as 8 - 11 = -3 Using
either approach, if necessary, you should be able to evaluate the following examples.
(1)
13 + 9 = 22
(2) -3 + 11 = 8
(3) -19 + 2 = -17
(4) 8 - (-4) = 12
(5)
-3 - 9 = -12
(6)
5 - 8 -3 = -6 Let
us now proceed to look at the multiplication and division of integers. Review
the following examples with a view to identifying obvious patterns. (1)
-2 x -3 = 6
(2)
-18 y -2 = 9
(3)
12 y -3 = -4
(4) -2 x 8 = -16
(5) 3a x -5b = -15ab
(6) 3 x p x q = 3pq From
the examples given above, the following should be noted: Positive
x Positive = Positive
Negative x Positive = Negative
Positive x Negative
= Negative
Negative x Negative = Positive This
above pattern is also true when dividing. I strongly suggest that this be committed
to memory. More importantly, you should ensure that all future calculations satisfy
these rules. Let
us now review the addition and subtraction of fractions. This is usually the first
question on the paper. It is in your best interest to begin on a successful note.
Practice is, therefore, key. ADDITION
AND SUBTRACTION OF FRACTIONS The
method requires that you are comfortable with finding LCM. Please review if necessary.
The
method is illustrated as follows: Find
5/6 + 1/4 As the LCM of 6 and 4 is 12 
Now
let us attempt the following together: 2
2/3 - 7/5 In
this case it is recommended that mixed numbers 2 2/3 be inverted to a fraction.
 2
2/3 - 7/5 = 8/3 - 7/5
The
LCM of 3 and 5 is 15. 
The
multiplication and division of fractions are also important fundamental concepts.
Please review the following, noting that the rules relating to positive and Negative
numbers are also applicable: 1.
1/3 x - 5/3 = - 5/9 2.
- 3/4 - 1/2 = -
3/4 x - 2/1 = 3/2 3.
1/6 x 7/3 5/12 =
1/6 x 7/3 x 12/5 = 14/15 Constant
practice is crucial to your success in mathematics, so I will end this lesson
with your homework. Evaluate
the following: (i)
-5 x -3
(ii)
-21 3 (iii)
11/12 + 5/6 - 2/3 (iv)
-8 -10 + 6 (v)
5a x -6b (vi)
12/25 + 5/9 5/18 Clement
Radcliffe is the principal of Glenmuir High School in May Pen. | 
