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Maths Fundamentals (for MA11)
Andrew Roberts
4th November 2003
Arithmetic
Whilst this document will not delve into the most basic arithmetic (tens and
units, etc.), people often forget how to correctly calculate with negative num
bers.
m

(

n
) =
m
+
n
(e.g., 10

(

5) = 15)
m
×
n
=

(
m
×
n
)
(e.g., 10
×
5 =

50)

m
×
n
=

(
m
×
n
)
(e.g.,

10
×
5 =

50)

m
×
n
=
m
×
n
(e.g.,

10
×
5 = 50)
m
÷
n
=

(
m
÷
n
)
(e.g., 10
÷
5 =

2)

m
÷
n
=

(
m
÷
n
)
(e.g.,

10
÷
5 =

2)

m
÷
n
=
m
÷
n
(e.g.,

10
÷
5 = 2)
And ﬁnally, let’s not forget the golden rule when multiplying numbers by
zero:
n
×
0 = 0.
Fractions
For the addition and subtraction of fractions, always remember that the de
nominator (bottom) must be the same for each fraction involved. Then, simply
apply the following (for subtraction, simply substitute the pluses for minuses):
n
p
+
m
p
=
n
+
m
p
(e.g.,
2
7
+
3
7
=
2+3
7
=
5
7
)
Unfortunately, you will not always be given fractions with a common de
nominator. It will therefore be necessary to perform some extra calculations
to get the expression into the required format, before addition/subtraction can
take place.
1
3
+
2
9
1
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View Full DocumentIn the above example, the lowest common denominator is 9. The fraction on
the right can be left as we found it, as its denominator is already 9. To convert
the lefthand fraction, we simply multiply the top and bottom numbers by some
constant that will result in the new denominator being 9. In this case, we must
multiply by 3. The addition can then be carried out as normal:
1
3
+
2
9
=
1
×
3
3
×
3
+
2
9
=
5
9
The next eventuality is when neither dominator shares a common factor.
The trick then is to multiply the two denominators together, with the result
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