WHY DO STUDENTS CONSIDER MATHS A DIFFICULT SUBJECT
Mathematics is one of the simplest subjects, but students tend to find it
more difficult than any other subject.Some say math is not a readable subject, and some others say it is
meant for solving. I don't know what you have been told by your friends. teachers,
but believe me if you change your mind set about math after reading this
post you will never find math difficult in all your years of study.
Mathematics is mainly comprised of calculations and solving but among those
calculations there are some written words, these words are sometimes few,
maybe about two to ten lines .these words are the key to the door of any
calculation you are learning how to solve, they hold the secrete to/answer to whatever
question you may have about any calculation you are solving.
Unfortunately this is the part students tend to ignore the most; they jump into
the calculation without knowing its origin. Before we continue I will like to
ask you a question, “have you ever separated a fight between two people without
asking them what the problem is? Or have ever started reading a novel from the
back page?"
Yes the answer is capital NO, because-for you to be able to build a house you
must start from the foundation, therefore to solve any problem, you have to
solve the cause if not the problem will be re-established after a short period
of time.
Furthermore, this is how those words you see on your math text book are related
to the calculations themselves. These words are related to the calculations.
THOSE WORDS HOLD THE SOLUTION TO THOSE CALCULATIONS. Therefore to stay on the
safer sides just take your time and read those words.
My dad MR.PATRICK CHUKWUDEOBASI always asks me a constant question each time i
bring a problem in math to him for solution, “have you read the sentences in
this topic ? if no he will ask me go back and read them paragraph by paragraph
but if yes he will ask, where did you get lost,? Then I will show him the paragraph,
do you know the funniest part ,his main purpose is not always to teach me from
where I got lost but to make sure I read those words.
After showing him where I got lost he will start from the beginning of the
topic and read out all those words in full. After reading he will interpret it
to me and that's all, the problem is solved, no magic, only a few practical
work using the guideline given by the text book.
So my there if you really want to be a mathematician, start reading the texts
on any calculation you would like to solve in your math text book because it
holds the key/answer to any question you can ask in math.
BELLOW IS
SOME GUIDELINES THAT YOU CAN FOLLOW WHEN STUDYING MATHS.
- READ: whenever you open a
chapter in math make sure you start from the title of the topic, read them
word by word then enter the first paragraph, also read paragraph by paragraph,
until you finish the words written in that sub topic. This because those
words hold the solution to that topic.
- INTERPRETATION: WHEN YOU ARE
THROUGH READING start afresh from the beginning ,and read this time
interpret the words you read letter by letter ,paragraph by paragraph.
This is because without interpreting the words then and only then can you
solve the problem.
- SOLVE THE EXAMPLES: After you
have interpreted those words the next step is to solve those examples
given by the author of the textbook. Solve them over ad over again only
then will you learn it.
- RULES AND FORMULAS: In your
course of solving those examples there are some formulas or steps/patterns
you may come across do not panic just study them gradually, from their
starting point to the finish point, so that you will learn/master them
without forgetting. do not cram them to prevent losing it in future time,
especially during exams.
- STEPS: After mastering the
formulas the next step is to master the steps i.e. how and when those
formulas are being applied. This part is very important because some
topics don't contain formulas so those steps are the guideline
reader have in solving the questions under that topic. Therefore if you
learn how to make use of those steps, i assure you the sky will be your
stepping stone in mathematics.
- SOLVE THE PROBLEMS: When you
are done perfecting these steps and formulas then the next step is solving
the problems because you are already through with that topic the only
reason why you must solve those problems is to perfect your knowledge the
more.
- APPLY YOUR KNOWLEDGE: Knowledge
is termed not complete unless shared, so therefore to complete the process
of the knowledge acquisition simply apply your knowledge or share it. see[HOW
TO APPLY KNOWLEDGE ]
AS WE COME
TO THE END OF THIS ARTICLE MAY YOU BE BLESSED AS YOU READ?
THANKS.
NUMBER SYSTEM
Before we proceed we will
shortly see the number base. Number base
is simply a system of counting, in which certain units make up a unit make up a
bundle and the placing of the unit shows its values. [I.e. place value].
Usually we
count in base ten that is why we find it very difficult to count in other
bases. There are some rules to follow while counting in other bases; those
rules must be obeyed to the very last if you intend to learn the topic number
system in mathematics.
NOTE: The
highest digit in a number system is the base-1, thus the highest digit in base
ten is 10-1 = 9 and this is applicable to other bases.
BASE
TEN: 0 1 2 3 4 5 6 7 8 9
BASE NINE: 0 1 2 3 4 5
6 7 8
BASE
EIGHT: 0 1 2 3 4 5 6 7
BASE
SEVEN: 0 1 2 3 4 5 6
BASE SIX: 0 1 2 3 4 5
Note that while solving problems under number base; it
is advisable that the base being used should always be written in words not in
figures to avoid confusions.
Examples;
144eight not 1448
during placing values, the base is considered
Example; 2546eight
Here are the place values of the above figure
[2x83]+ [5x82] + [4x81]
+ [6x80]
2[8x8x8] +
5[8x8] + 4[8] + 6[1]
Note number base is calculated in their powers
More examples of place value are;
574seven = [5x72] + [7x71]+
[4x70]
23145four = [3x44] + [3x43]
+ [1x42] + [4x41] + [5x40]
Binary system or base two is a method
of counting, which is very important because of its use in computer technology.
Below are some methods of counting numerals in base two.
Base ten Base two 
0 0 
1 1
2 10
3 100
4 101
The above
just shows the converted base ten to base two
Binary system or base two is a method of counting,
which is very important because of its use in computer technology. Below are
some methods of counting numerals in base two.
Numbers can be converted from one
base to another through few steps; number can be converted from base 10 to
other bases, through long division method or from other bases through
successive multiplication or other methods. Numbers can also be converted from
one base to another through some simple steps;
This process is made possible through
successive division of the base Ten number by another base, which you wish to
convert to, and also record the remainders until you get the final figure which
is 0 is reached. After which you write down your remainders starting from the
bottom of the line.
Examples
Convert 216ten to base six
6
216
6 36 REMAINDER 0
6 6 REMAINDER 0
6 1
REMAINDER 0
6 0 REMAINDER 1
Thus 216ten =1000six
2. Convert to
base 8 11ten
8 11
8 1 remainder 3
8 0 remainder 1
Thus 11 ten =13 eight
NOTE: whenever you get to the point
where you cannot divide a number with another again e.g. 1/6 i.e. 1 divided by
6. What you can do is to write 0 and write its remainder as the number above
it. Use the arrows as a guideline
To convert from other bases to base
ten you either use the successive multiplication method or you consider the
power multiplication.
POWER MULTIPLICATION METHOD
In this method every single digit is multiplied by the power
of its place value.
Examples; 134five = [1x52]
+ [3x51] + [1x50]
1x25 +
3x5 + 1x1
25
+ 15 + 1
44ten
SUCCESSIVE MULTIPLICATION
134FIVE = [1X5+3] = 8
[8X5+4] =44ten
CONVERTION OF NUMBERS FROM ONE NUMBER BASE TO
ANOTHER
This simply implies the process
involved when converting a number from one base to another base which is not
base ten. It comprises two steps, the first step consists of the conversion of
the given number base to base ten, while the second step involve the conversion
of the base ten to the required base.
Example [1]
Convert 134five to base two
SOLUTION
STEP 1; Convert to base ten: 134five
=
[1x52] + [3x51] + [[4x50]
1x25 + 3x5 + 4x1
25 + 15 + 4
44ten
STEP 2; Convert the base ten to base two [which is the
required base]
2 44
2 22 remainder 0
2 11 remainder 0
2 5
remainder 1
2 2 remainder 1
2 1 remainder 0
2 0
remainder 1
Thus 44ten =101100two
That is 134five = 101100two
EXAMPLE 2: IF 3245SIX = xnine find x
SOLUTION
STEP1: CONVERT TO BASE
TEN
3245SIX =
[3 X 6 +2] =20
[20 X 6 + 4] = 124
[124 X 6 +5] =749
STEP2: CONVERT THE BASE TO BASE NINE
9 794
9 83 REMAINDER 2
9 9 REMAINDER 2
9 1
REMAINDER 0
9 0 REMAINDER 1
Thus 3245six=794=1022CONVERSION OF DECIMAL NUMBER BASE TO BASE TEN
Before we can convert a
decimal number base to base ten, we first express each digit as a power of its
base, then we change the powers of the decimal part to fraction.
This process involve four steps;
conversion of the integer part then followed by the converting the decimal part
to fraction then add. A decimal fraction contains two parts; the integer part [whole
number] and the decimal part [fraction part]. See the illustration bellow
4.0123
Integer part decimal part
EXAMPLE 1: Convert
101.001two to base ten.
solution
First step: conversion of the integer part.
1 x 22 + 0 x 21 + 1x 20 [any number raised to power 0 is 1].
1 x 4 + 0 x 1 + 1 x 1
4 +
0 + 1 = 5ten
second step: conversion of the decimal part. [.011].
0
X 2-1 + 1 X 2-2 + 1 X 2-3
0 X 
+ 1 X 
+ 1 X 
[If you don’t know how to
convert negative index to fractions. then see indices]
+ 1 X + 1 X [If you don’t know how to
convert negative index to fractions. then see indices]
0
+ 1 X 
+ 1 X 
0 + +
+ 1 X 0 +
+
[The reason why the powers of the decimal part started
with -1 and contains a negative sign is because while counting, after we count
0 the next number is 1 followed by 2. For the negative sign, it is there
because the number is a decimal number. If you watch you will notice that the
last power of the integer part ended with 0 so then next 0 will start with 1.]
Next
we add; + [find the L.C.M]
+ [find the L.C.M]
2
+ 1 8
[If you don’t know how to add
fractions or subtract them. see fractions]
Thus: + = 
.
+ = .
THIRD STEP: convert the
fraction to decimal.
This can be done through the long division
process and through the use of a calculator.
0.375
8 30
-24
60
-56
Thus: =0.375
FOURTH STEP: Add the integer to the decimal. I.E
5 + 0.375 =
5.375
Thus: 101.001two
= 5.375ten
EXAMPLE TWO: convert 1.101two to
base ten.
FIRST STEP: Convert the integer part. Which is 1.
THUS: 1 x 20
1 x
1 =1
STEP TWO: convert the decimal part to fraction and
add. .101
1 X 2-1 + 0 X 2-2 + 1 X 2-3
1 X 1/2 + 0 X 1/
+ 1 X 
+ 
+
ADD
+ [FIND THE
L.C.M]
4
+ 1
8
THUS: + = 
+ = 
THIRD STEP: Convert the fraction to decimal. 0.625
8
50
- 48
20
-16 
40 
FOURTH
STEP: Add the integer part to the decimal. I.E
1 + 0.625 = 1.625
Thus: 1.101two
=1.625ten
Numbers can be added in bases that are not
base ten; Numbers can be added in base two, three, and five. e. t. c. the only
difference between the addition in base
ten and that of other bases is that when
adding and you are required to carrying over or borrow, instead of borrowing 1
and calling it 10, we borrow 1 and call it the base why are adding. E.g. if we
are adding in base five then, we borrow 1 and call it 5.
EXAMPLE 1: 318 + 24 in base 10
Solution
3 1 8
+ 2 4
3 4 2
8 + 4 = [12 but we will write 2 and carry 1. This is
because the numbers 12 contains only one 10’s and remains two so we write two
and carry one.]
Thus 1 + 1 + 2 = 4 [write only 4 because 4 does not
contain any 10 in it.]
Finally bring down or write 3 because it is not up to
10.
Therefore 318 + 24 = 342
BUT
In base five; 318 + 24
3 1 8
+ 2 4 
312
8 + 4 = 12[12
but we will write 2 and carry 2, This is because the number 12 contains only
two 5’s and remains two so we write two and carry two.]
Thus: 2 + 1 + 2 = 5(we write one because the number 5
contains only a single 5, so we write 1.)
Finally we write three because 3 is not up to 5.
This process is applicable to all types of number
bases.
EXAMPLE 1: ADD 314 + 24 IN BASE FIVE.
SOLUTION
3 1 4
+ 2
4 
3 4 3
4 + 4 = 8 BUT eight contains only 1 five and remains 3
so we write three and carry one.
Thus: 1 + 1 + 2 = 4. Write 4 because it is not up to
five.
Write 3.because it is not up to five.
Thus: 314five + 24five = 343five
EXAMPLE 2: FIND THE MISSING FIGURE;
1 3 0
2
+ 1 2
3
Z Z
Z Z
10112FOUR
SOLUTION
First add 1302 + 123
1
3 0 2
+
1 2 3
2 0 3 1
2
+ 3 =5.five contains one four and one remainder. So we write 1 and carry 1
Thus: 1 + 0 + 2 = 3. Write three because it does not
contain any four.
3 + 1 = 4. Write 1 because the number 4 only contains
1 four.
1 + 1 = 2. Write 2 because it does not contain any
four.
Thus: 1302 + 123 = 2031
SECOND STEP: Subtract your answer from the given one.
I.E: 10122 – 2031
1
0 1 2 2four
- 2 0 3 1four
2 
0 3 1
0 3 1
2– 1 = 1.write 1 because it is not up to four.
2– 3 = 3. 2 – 3 is not possible so we have to borrow 1
and call it four thus: 4 + [2 – 3] = 3
0 – 0 = 0
0 – 2 = 2.0
– 2 IS not possible so we borrowed one and called it four, thus: 4 + 0 – 2 = 2
To subtract
numbers in other bases is similar to that of addition, the only difference is
that we are subtracting not adding.
ILLUSTRATIONS
3 1 8
- 
24
in base 10
24
in base 102 9 4
8 – 4 =
4.Write 4. Because it is not up to 10
1 – 2 = 9. 1
– 2 is not possible so we borrowed 1 from 3 and called it 10.
Thus: 10 + 1
– 2 = 9.
Finally
write 2. Because we have already borrowed 1 from 3 so it has to remain 2.
THUS: 318 –
24 = 294ten
IN BASE 5
3 1 8
2 4
2 4 4
8 – 4 =
4.write 4 because it is not up to five.
1 – 2 = 4.1
– 2 is not possible, so we borrowed 1 from 3 and called it five.
Thus: 5 + 1
– 2 = 4.
Finally bring
down 2.
Thus: 318 –
24 = 244.
EXAMPLE 1: 317 – 265 IN BASE EIGHT.
SOLUTION
3 1 7
-2 6 5
32
7 - 5 =2.Write
2 because it is not up to eight.
1 – 6 = 3.1
– 6 is not possible so we borrow one from 3 and call it eight.
Thus:8 + 1 –
6 = 3.
2 – 2 = 0
Thus 317 –
265 = 32 in base eight.
EXAMPLE
2: 11111 – 1010 IN BASE
TWO.
SOLUTION
1 1 1 1 1
1 0 1 0
1 0 1 0 1
1 – 0 =
1.Write 1 because it is not up to two.
1 – 1 =
0.write it down.
1 – 0 = 1.write
it down.
1 – 1 =
0.write it down.
Finally
write down 1.
Thus: 11111
– 1010 = 10101two
This process
is not different from the previous methods we used in addition and subtraction,
so follow the steps and you will learn.
ILLUSTRATIONS
31 4
* 24
1 2 5 6
+ 6 2 8 
7
5 3 6
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