Download Math For People Who Don`t Like Math

Math For People Who
Don’t Like Math
Questions for Contemplation
The following questions are the basis of
a true understanding of mathematics.
To be “good” in math, you must own the
answers to these questions.
These are a review of what you
already know.
•
•
•
•
•
•
•
How many numerals are there in the universe?
How many operations can you perform with these?
What is absolute value?
What is a whole number?
What is a fraction?
What is a decimal?
What are the properties of “1”?
continued next page
continued
•
•
•
•
•
•
•
•
What are the properties of “0”?
What is the associative property?
What is the commutative property?
What is the distributive property?
What are the Number Families?
What are rational numbers?
What are integers?
Why do I need to know all this stuff?
In this world there are an infinite or unending
amount of numbers. However, all the zillions
of number are a composite of only 10 numerals.
What are those numerals?
Mathematics doesn’t seem so intimidating once
you realize that there are only 10 numerals
with which we must deal with.
You have known those numbers since you were
just a toddler and sang songs like “Ten Little
Indians”.
Can you explain how you make the number “10”
out of the numerals “0, 1”
We use the place value system to make the
number “10”. We put the 0 in the ones place
and the 1 in the tens place to represent the
number “10”.
What if you didn’t have 10 numerals? Could we
use the place value system to make numbers
with 2 or 3 digits?
Martians have only two fingers. So how
do they count?
The Martians count just as we do. They
start with 1, 2, and then they have no
more numerals, so the next number is 10.
We count 1,2,3,4,5,6,7,8,9 and then we
say the next number which is a
combination of 0 and 1. That number is
10. It is the same for Martians.
What number would come after 10 on
Mars? Why eleven of course, and then
12. Now we have run out of numerals
again, so what is the next number? You
are right, it is 20.
Place Value
Place Value is very important in
mathematics. We have to understand
that each place has a name, and there
are punctuation marks in mathematics
that help us read the numbers easily
and correctly. Let’s take a look!!!
Let’s take a look at place value and
number names. Read the following
numbers aloud.
1) 457 2) 5,789 3) 45,900 4) 650,002
What punctuation mark did you notice in
the numbers above? What does that
mark do? Does it help you say the
number?
1) 457 2) 5,789 3) 45,900 4) 650,002
The only punctuation mark that
you see in the numbers above is a
comma. The comma marks the
thousands place in the numbers
above. The comma does help us
read the number. When we see
one comma in a number, we know to
say “thousand”.
1) 457 2) 5,789 3) 45,900 4) 650,002
Do you see a decimal in any of the
numbers? No. Is there a decimal
in these numbers? There is a
decimal in every number. In a
whole number such as (457), the
decimal is to the right of the (7),
but we don’t write it. It is
understood that we know the
decimal is there (457.)
In a number representing an amount of money,
we are used to seeing the decimal, and we
always say “and” when we read the amount
($45.89).
When reading numbers, you only say the word
“and” when there is a decimal written in the
number. In the numbers above you should
have read forty-five dollars “and” eighty-nine
cents.
Read all these numbers and notice the
commas in them. What does the comma
tell us to say?
5) 345,678,000
6) 290,000,009
7) 809,340,889
The second comma tells us to say
million. It is easy to read numbers
when we use the punctuation marks.
Read these numbers.
8) 6,998,000
9) 2,045,900,000
10) 10,987,801,000,000
The third comma tells us to say billion.
The fourth says a trillion. Remember,
to break the number apart and then say
what the comma tells you to say. For
example – 495,000 – say four hundred
ninety five (one comma) thousand.
Knowing the place value represented by
the commas in mathematics will help you
to read numbers easily. Let’s practice
•
•
•
•
•
•
•
•
456
3,981
85,703
901,845
2,009,567
34,672,005
902,999,000
9,345,602,781
Remember, Do Not
Say “and” unless
you see a decimal
in the number!!
Also, you must
remember what
the commas say in
a number.
The Decimal
Now it is time to take a brief look at the
decimal. We aren’t going to go too deeply
into this topic at this point, but for now we
must understand how to read a decimal
correctly.
Remember, we have the numerals
0,1,2,3,4,5,6,7,8,9 from which we can
write any number. So, for now we will
start with 0 and look at a number line.
0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1, 2, 3, 4, 5, 6, 7…
• The numbers between 0 and 1 represent a part of the
whole number 1.
• Between every whole number there are parts of that
number.
• We can divide a number into 10ths, 100ths, or even
1,000,000ths. The parts of a number are designated
by the decimal. We are most familiar with decimals in
money.
$5.00; $678.95; .50 or 50 cents.
The decimal is a punctuation mark for
mathematics and it tells us to say “and”.
Read these numbers.
$6.90
$3,980.12
$0.98
Numbers with decimals also have place
value. Let’s take a look at decimal
numbers and learn to say them
correctly using place value.
•
•
•
•
•
•
.1 is one tenth
.01 is one hundredth
.001 is one thousandth
.0001 is one ten thousandth
.00001 is one hundred thousandth
.000001 is one millionth and so on and so
on…
When we read decimal numbers it is important
to read the number first and then say the
place value. Let’s read some decimal numbers
together. Remember read the number first!
.1 = (one tenth)
.12 = (twelve hundredths)
.123 = (one hundred twenty-three thousandths)
.1234 = (one thousand two hundred thirty-four
ten thousandths)
.12345 = (twelve thousand three hundred fortyfive hundred thousandths)
Absolute Value
What is the absolute value of a number?
Well the simplest way to remember
absolute value is that it is that number.
If the number has a decimal (.45), is a
fraction (½), or is a negative number
(-348), the numerals still have the
absolute value of that number. By
definition, absolute value is how far a
number is from zero on the number line.
Absolute value is the number that the
numeral represents.
If you really think about it, all we do with
numbers is count them! We count how
many we have, how many we need, how
many more, how many less, how many in a
dozen and how much of each.
If you think about mathematics in this light,
you have been doing it well for a long time,
since kindergarten.
Well, here we are hard at work. We are
doing mathematical operations on whole
numbers, fractions, and decimals. Do
you know the names of the operations
we can perform on these numbers?
We can add, subtract, multiply, and
divide. That’s all!!!
There are only ten numerals on which
we can perform these four algorithms
or functions. So, as you can see,
mathematics is not the big mystery
that some people make it.
Mathematics is simple, logical, and can
be fun. Anyone can do mathematics
well, if they memorize a few rules and
use them consistently. Let’s move on to
bigger and better things, shall we?
What are fractions?
When most people hear the word
“FRACTION” they run the other way, or
say “I just can’t do fractions!” Actually,
you have been doing fractions since you
were a small child. Watch and see how I
know you have.
Perhaps, you remember having a Popsicle
with two sticks. Chances are that if you had
a little brother, sister, or friend, you would
have to share that Popsicle, and your mom
broke it into two parts. That my friend, is a
fraction. When you break a whole into parts,
you have created a fraction or part of that
whole.
Let’s take a brief look at fractions
You can break a whole number into
parts just like breaking the
Popsicle or slicing a pizza. When
you write a fraction, the two
numbers represent the number of
divisions and the parts that are
present or missing.
Let’s look at ¾ (three-fourths).
The number of divisions is four (4) and the
number of pieces present is three (3). We
have 3 out of 4 pieces or ¾.
It is important to reduce all fractions to the
lowest terms when possible.
Each part of the fraction has a name. The
top number is the numerator (remember,
the number of pieces). The bottom
number is the denominator because it
denotes the number of pieces in which we
have divided the whole.
We are now going to look at the
properties of Zero and One. These
properties are crucial in understanding
and being able to do mathematics well.
Good old Zero, is very important even
though he is nothing. Zero is a place
holder. A zero in the wrong place will
make the entire answer incorrect.
Here are some things to remember
about zero
Any number plus Zero is
itself.
56 + 0 = 56
Any number minus Zero
is itself.
56 – 0 = 56
Zero Continues…
What happens when you multiply a number by
Zero. Nothing, the answer is Zero
23 · 0 = 0
Okay, so what happens if you divide by Zero? Same
thing, nothing, the answer is undefined (Zero)
23/0 = 0
Can you divide a number into Zero? Well, I guess you
can, but the answer is (guess what?) Zero. (undefined)
0/23 = 0
Remembering these facts about Zero will help you to be a
better mathematics student.
Zero can only do one thing, and
that is to hold a place.
Let’s take a look at the number 1, and
see if we can learn some rules to help us
use the number 1 correctly.
One plus a number is always the next
highest number. 5 + 1 = 6
Any number minus one is always the
next lowest number. 5 – 1 = 4
What happens when you multiply by
one? It’s always itself. 5 x 1 = 5
What happens when we divide a
number by one? Yeah, you guessed
it, it’s always itself. 5/1 = 5
That makes sense to me, how about
you?
What, more rules? Yes I am
afraid so.
Associative Property of
Addition and Multiplication.
When you add or multiply three or
more numbers, you may group them
however you like and they still add
up to the same answer.
(3+6)+8 = 17 3+(6+8) = 17
The same thing for multiplying.
(3·6)·2 = 36 3·(6·2) = 36
This next property will come in very
handy as you work more complicated
mathematics and algebra problems.
Commutative Property of addition or
multiplication.
You can add two or more numbers in any order and
they still add up to the same answer.
2+5 = 7 and 5+2 =7 3+4 = 7 and 4+3 = 7
Yes, multiplication works the same too!
2·3 = 6 and 3·2 = 6
2·3·4 = 24 and 4·3·2 =24
One last property and we are done
for now.
Distributive Property
This property allows you to multiply a number across
an expression or distributes that number among
the rest.
8·(3+4) = 56 is the same as (8·3) + (8·4) = 56
Sometimes you may see this expression written as
8(3+4) = 56
Number Families
In mathematics, we give names to certain
sets of numbers or number families. We
have already discussed two of these
families; counting numbers ( also called
natural numbers) and whole numbers. Let’s
look at all of them in ascending order.
Counting numbers…1, 2, 3, 4, 5, 6, 7, 8, 9
Whole numbers…0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Rational numbers… ½, ¾ ,1, 2, 3, -4, 5, 6
Integers…-3, -2, -1 ,0 ,1 ,2 ,3
We have now discussed most of the number
families and the algorithms (addition,
subtraction, multiplication, and division). You
have the fundamentals now, so let’s do some
problems and see just what great
mathematicians we have become.
Integers
What are they and what do we do with them?
Integers are the set of all positive and negative
numbers.
-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5
Positive numbers are all numbers (greater than) > 0
Negative numbers are all numbers (less than) < 0
You can do all four operations with integers,
but there are rules for each operation that
you must follow in order to get the correct
answer. For now we only need understand
the set of integers. Later we will study
the rules and how they are applied.
Now, see how easy math can
be. You should be a wiz kid
now. Being “good” at math
only takes a few steps along
with a few rules and the
results will be astounding!