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Directed
numbers
Clement
Radcliffe, Contributor
 |
| It's
all smiles during class at Pentab
High School in central Kingston
last week.
- Ian Allen Photo |
I
will begin today's lesson with the solutions
to problems presented last week
1.
82 - 6 2 =
| (a)
2 |
(b)
4 |
(c)
-2 |
(d)
28 |
SOLUTION
It
is best to evaluate the answer as
follows:-
82
- 6 2 = 64 - 36 = 28.
The
answer is (d)
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.
The
answer is therefore (b)
You
could have tested each answer also,
for example, 15 sweets cannot be shared
equally among 10 children.
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 , ÷ ) 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 7 11
SOLUTION:
I
have 7 items but owe 11
I
therefore owe four items which may
be expressed as 7 - 11 = -4
Using
either approach, if necessary, you
should be able to evaluate the following
examples. (1) 15 + 7 = 22
(2) - 6 + 11 = 5
(3) 6 - ( - 4) = 10
(4) - 3 - 6 = -9
(5) - 19 + 12 = -7
(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) - 4 x -3 = 12
(2) -18 ÷ - 3 = 6
(3) 12 ÷ - 4 = -3
(4) -2 x 7 = -14
(5) 2a x -5b = -10ab
(6) 6 x p x q = 6pq
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 do suggest strongly that they 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.
The
method requires that you are comfortable
with finding L.C.M. Please review
if necessary.
The
method is illustrated as follows:
Find
5/6 + 1/4 As the L.C.M of 6 and 4
is 12
N.B.
We have converted 5/6 to 10/12 and
1/4 to 3/12
ie.
Answer is 13/12
Now
please attempt: 2 2/3 - 7/5
In
this case it is recommended that mixed
numbers (2 2/3) be inverted to a fraction.
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 - 5/4 = 5/12
2.
3/4 ÷ 3/4 x
2/1 = 3/4
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, hence I close this
lesson with your homework.
Evaluate
the following:
(i) 2 x 5
(ii) 18 ÷ 3
(iii) 11/12 + 5/6 2/3 (iv)
22 14 + 6
(v) 5a x 4b
(vi)
12/25 x 5/9 ÷ 5/18
*
Clement Radcliffe is principal
of Glenmuir High School in Clarendon.
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