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BOMDAS
Clement Radcliffe,Contributor
As
we continue our review of directed
numbers, I will share with you the
answers to the problems given for
homework last week.
Evaluate
the following:
(i)
-4 x -3 = 12
(ii)
-21 / 7 = -3
(iii)
11⁄12
+ 5⁄6
- 2⁄3
The
solution to (iii) is based on the
conversion of the three fractions
to the same denominator. This denominator
is the LCM of the existing denominators
12, 6 and 3.
(Please
note that the LCM of 12, 6 and 3 is
12)
11⁄12
+ 5⁄6
- 2⁄3
=
( (11 x 1) + (5 x 2) - (2 x 4) )/12
= ( 11 + 10 - 8 )/12 = 13⁄12
(iv)
-8-7 + 6 = -9
(v)
3a x -6b = -18ab
(vi)
12⁄25
x 5⁄9
/ 5⁄18
12⁄25
x 5⁄9
/ 5⁄18
=
12⁄25
x 5⁄9
x 18⁄5
= 24⁄25
If
the above posed no difficulty, then
you are ready to consider exam-type
questions.
Application
of the Four Arithmetic Operations
to Vulgar Fractions
In
applying the four basic operations
to vulgar fractions, students are
required to observe the correct law
with respect to applying the order
of the operations as follows:
B
- Brackets
O
- Of (Multiply)
M
- Multiply
D
- Divide
A
- Add
S
- Subtract
BOMDAS
identifies the order in which the
operations should be carried out and
must always be obeyed. If an expression
has multiple operations, then the
operations within the brackets are
evaluated first, if they exist. Multiplication
or 'of' is done before division, while
division is done before addition and
so on.
Let's
practise the use of BOMDAS.
Practice
1
Calculate
the value of 11⁄2
+ 5 x 2 / 12⁄3
Convert
to common fractions
= 3⁄2
+ 5 x 2 / 5⁄3
Using
BOMDAS , we do the multiplication
first:
3⁄2
+ 10 / 5⁄3
We
then do the divsion:
3⁄2
+ (10 x 3⁄5)
=
3⁄2 +
6
= 71⁄2
(b)
Practice 2
4
x ( (21⁄3
+ 1⁄2)
)We first do the brackets (despite
the fact we are required to add):
...
( (21⁄3
+ 1⁄2)
) = 7⁄3
+ 1⁄2.
Using the LCM of 2 and 3, that is
6 we get
=
( (2 x 7) + (3 x 1) )/6
=
( 14 + 3 )/6 = 17⁄6
To
complete the problem, we now multiply:
( (4 x 17⁄3)
) = 68⁄3
= 34⁄6
= 111⁄6
(c)
Practice 3
Calculate
the value of: ( ( 61⁄3
- 15⁄6)/(11⁄2
x 22⁄3)
)
Using
BOMDAS, we first note that the line
represents brackets and so the numerator
may be evaluated first.
(
(61⁄3
- 15⁄6
= 19⁄3
- 11⁄6)
=
( (2 x 19) - (1 x 11) )/6
=
(38 - 11)/6 = 27⁄6
Evaluating
the denominator:
11⁄2
x 22⁄3
3⁄2
x 8⁄3
= 24⁄6
= 4
Dividing:
= 27⁄6
/ 4 = 27⁄6
x 1⁄4
= 9⁄8
Points
to note
- In
solving a problem such as Practice
3, you may first evaluate either
the numerator or the denominator.
You may verify this by finding the
solution beginning with the denominator.
- Finding
the LCM CORRECTLY is a very important
step in the solution. If you have
difficulty with this step
you should resolve these at this
time.
- As
Practice 3 requires the exact value,
you are not allowed to express the
fraction in decimal form. If this
is done, then your answer would
be different from 9 and you 8 may
be penalised.
- Your
working must be always clearly shown
in logical sequence as presented
above.
Let
us now work the following together:
Using
a calculator, or otherwise, determine
the exact value of (3.9)2
- (6.24 - 2.3).
Solution:
(3.9)2 - (6.24 - 2.3)
Using the recommended approach, we
first evaluate the brackets.
(3.9)2
= 15.21 and (6.24 - 2.3) = 3.94
=
15.21 - 3.94 = 11.27
Ans
= 11.27
Please
be reminded that it is important to
get the first question on the exam
paper correct. It
naturally
builds your confidence. Always remember
to apply BOMBAS. Even if the individual
operations
are done correctly, the appropriate
order is required to get the correct
answer.
I
close this week with the following:
1.
Calculate the value of 51⁄2
x 2⁄3
- 1⁄4.
2.
Evaluate 9/10 ÷ (2/5 + 4/15
x 3/10)
3.
Simplify (31⁄3
- 15⁄8)
4.
Find the value of 35.75 - (2.34)3
5.
Find the value of ( 4 1⁄3
- 1 5⁄6
) / ( 21⁄2
x 22⁄3
)
Clement
Radcliffe is an independent contributor.
Send questions and comments to kerry-ann.hepburn@gleanerjm.com
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