1. Math For People Who Don’t Like Math

2. 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.

3. 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”?
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4. What are the properties of “0”? What is the associative property?
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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?

5. In this world there are an infinite or unending amount of numbers
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.

6. 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?

7. Martians have only two fingers. So how do they count
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.

8. Place Value Place Value is very important in mathematics
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!!!

9. Let’s take a look at place value and number names
Let’s take a look at place value and number names. Read the following numbers aloud. 1) ) 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?

10. 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”.

11. 1) ) 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.)

12. 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.

13. Read all these numbers and notice the commas in them
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.

14. 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.

15. Remember, Do Not Say “and” unless you see a decimal in the number!!
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.

16. 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.

17. 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.
, 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.

18. $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, $0.98

19. Numbers with decimals also have place value
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
is one hundred thousandth
is one millionth and so on and so on…

20. .123 = (one hundred twenty-three thousandths)
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)
= (twelve thousand three hundred forty-
five hundred thousandths)

21. 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.

22. 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.

23. Well, here we are hard at work
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?

24. We can add, subtract, multiply, and divide. That’s all
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.

25. Mathematics is simple, logical, and can be fun
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?

26. 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.

27. Perhaps, you remember having a Popsicle with two sticks
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.

28. 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.

29. 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.

30. We are now going to look at the properties of Zero and One
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.

31. Good old Zero, is very important even though he is nothing
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
Any number minus Zero is itself.
56 – 0 = 56

32. 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.

33. Zero can only do one thing, and that is to hold a place.

34. That makes sense to me, how about you?
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 = 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?

35. 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 = (6+8) = 17
The same thing for multiplying.
(3·6)·2 = ·(6·2) = 36

36. Commutative Property of addition or multiplication.
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 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

37. 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

38. 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.

39. 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.

40. 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.

41. Now, see how easy math can be. You should be a wiz kid now
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!