Introduction to Factor

 You maybe feeling curious about what exactly are Factor, Prime factor, Prime number and other related words, here I will explain the detail of all of those, so keep on reading for better understanding.
 I promise I would not mess up, promise me you will understand it and even share it over and over to everybody you know.

Prime number is a number that is divisible by exactly two positive whole number: 1 and that number itself.
Composite number is a number that is divisible by at least three numbers.

FACTOR

Their is a very deep relationship between factor and division which I will uncover later, so please be calm.

Let say, 4 multiply by 5 the result is 20 (check multiplication for detail), these two number that are multiply together are factor for the result (20). 

 4 * 5 = 20 

In the quick explanation above:

• 4 and 5 are factor to 20.
• 4 and 5 are smaller number than 20.
• 20 is bigger than those because they are it multiple.
• 20 is a multiple of 4 and also a multiple of 5.

   5 is a factor of 20

  20 is a multiple of 5

Note: Two factor are multiplied to equal a product (Multiple)

Relationship between factor and division

 Truly their is really true relationship but their is a vise verser friendship in their life circle. 

 Following the quick explanation above.

 Let say, 20 divided by 5 equal 4, 20 divided by 4 equals 5. 

 20 / 5 = 4, 20 / 4 = 5    (check division of number for detail),

• 20 is divisible by 5 and 4.
• 5 and 4 is a divisor of 20.

Conclusion: Thanks for taking your time to read this we will later write a new post on how to find a prime number, prime factor, factor of a specific number.

Please comment if their is any question or you want us to explain something about the topic being explain in this post.

How Numbers are Round Off

How Numbers are Round off

Working with longer number may likely to get you in confusion, rounding number and eliminating some is the best path mathematician do follow. Also when working with some problems you may be asked to round off your answer.

Rounding number helps you change some of it digit to place-holding zeros or change a difficult number to an easier one. Stick to the information below to avoid some mistakes.

Rounding to the nearest ten

When rounding a two-digit numbers to the nearest ten, bring it up or down to the nearest number which ends in 0

Examples

    1. 45 → 40
    2. 54 → 50
    3. 22 → 20
    4. 75 → 80
    5. 73 → 70
    6. 92 → 90.
Higher than or equal to 95
    7. 95 → 100
    8. 97 → 100
    9. 98 → 100
    10. 96 → 100.

No matter higher the number ends. Except for numbers higher than 95`s which round up to 100.

Rounding to the nearest hundred

To round number to the nearest hundred and beyond the focus on the hundreds digit and the digit immediate right of the hundreds digit, change all other digits to the right of these two-digit to 0`s.

Examples

    1. 899 → 900
    2. 354 → 400
    3. 540 → 500
    4. 795 → 800
    5. 952 → 1000.

Note: if the number immediate the hundreds digit is five or higher (5, 6, 7, 8, 9) change it to 1 and add it to the hundreds digit, but if it four or lower (4, 3, 2, 1 ) it will be 0.

Rounding to the nearest thousand

Underline the thousand digit and the digit immediate right, change all the other digit to zero (digit greater than or equal to 5 changes to 1 and add to the thousands digit, digit less than or equal to 4 changes to 0).

Examples

    1. 4,372 → 4,000
    2. 7,535 → 8,000
    3. 6,683 → 7,000
    4. 78,521 → 79,000
    5. 7,891 → 8,000.

Rounding to the nearest million

Rounding to million also follows the same rule only you focus on the millions digit and the digit immediate the millions.

Examples

    1. 1,234,567 → 1,000,000
    2. 85,923,531 → 86,000,000
    3.2,535,253 → 3,000,000.

Problem easier with Approximating value

After you have bet down rounding, Approximating number is simple, it saves much of your time while calculating and allow you to avoid complicated calculation. Approximately equal to( ≈ ) is used instead of equal sign =. In some cases, if you approximate a given numbers before calculating the real answer, it could result in the round off answer, but sometimes it works. I will only advise you to approximate at the end of your answer especially if you are told to do so in the question.

Examples:

    1. 722 + 506 + 383 + 1,279 + 91 + 811,
round this number down, 
700 + 500 + 400 + 1300 + 90 + 800
≈ 3,800.

But if you add without rounding the answer is 3,792, which is not a bad answer (because if you round the answer you will still get 3,800).

Also, check this out.
879 x 618  if round off, it changes to 900 x 600. Which equals 540,000 (good answer, you will think it is) but if you did not round off before the multiplication takes place, the answer will be 543,222.

You can see that...

A Little advice on approximating number that can help, not getting round off answer.
 Don`t round too many numbers in the same direction.
Don`t multiply or divide rounded numbers.

Division of Number

Division

The last of the four operators is division, which literally means splitting thing up. For instance, your father may have given you and your brothers some amount of money to share among yourself. Let say you have three brothers with you, which makes you all four in number. If your father gives you twelve dollars ($12). How will you share it?
$12 ÷ 4 = 3, that means each of you will get $3 each.

TIPS:

• Division has more than one sign, representing it present (fraction slash /, fraction bar    ̶, fraction is related to division).
• When dividing numbers, the first number is called the dividend and the second number is called the divisor, the result is the quotient.
• You can use multiplication table for division; it only cost you to reverse the other of multiplication.

For example, in the multiplication table we learn that 2 × 7 is 14.

So, 14 ÷ 2 = 7, 14 ÷ 7 = 2.

How larger numbers are divides

Example 1.

Dividing larger numbers against one-digit number, dividing 860 ÷ 5.

Unlike other operations, dividing number moves from left to right, so, in this question I will start at the hundreds column.

• First  8 ÷ 5 = 1 (with remainder)
• 1 × 5 = 5 (the 1 from the dividing, multiply by the divisor (5)).
• Write the answer below 8.
• Subtract the 8 and the 5, which equals 3.
• Bring down the 6 to make the number equals 36.
• 5 goes in 36 = 7 (with remainder).
• 7 multiply by 5 = 35.
• Subtract 35 from 36, which equals 1
• Bring down the 0, to make it 10.
• 5 go in 10 = 2.
• 2 × 5 = 10
• Write the 10 below the other 10.
• Subtract the 10 and the 10, which result 0.

We got no more number to bring down, so, finish solving problem.860 ÷ 5 = 172.

Example 2.

Dividing that remains. 77 ÷ 3. Following the above steps.

• There is no number to bring down
• The number that remains below is 2, which is the remainder.

77 ÷ 3 = 25 r 2.

NOTE: When you are dividing number, that the divisor is larger than the dividend. You always get a quotient of 0 with a remainder as the number you started with. For instance,

• 1 ÷ 2 = 0 r 1 (or 0.5 in decimal).
• 3 ÷ 4 = 0 r 3.

What do you feel learning this,

Share me you knowledge on this topic, let me know how much you gain.

Multiplication made simple

Multiplication

The third in the kingdom of mathematics is multiplication "getting a number in times of another". Suppose you have three friend and you want to give each one of then two pieces of cookies, you may want to make the calculation to know how many cookies you have to buy. Three friends times two cookies. That means you will have to buy eight cookies for you three friends (I am also your friend, buy 18 cookies because I will take 10 cookies! I love it! ).

When multiplying numbers.

• The two numbers that you are multiplying are called the factors and their is always product.
•  First number is the multiplicand and the second number is the multiplier.
• Multiplication is represented with a (×) or dot in some advance math.
• Putting number in parentheses also means multiplication "2(3) means 2 x 3", but if addition or subtraction or division, is place before the parentheses it not multiplication "2 + (3) means 2 + 3".

You don`t have to memorize the multiplication table, you just have to understand it.

You may be wondering while I have removed the 0, 1, and 2, I always remember what my teacher told me.

• Any number multiply by 0 is always 0 (try 999,999)
• Any number multiply by 1 is that number itself (try 123,445).
• To get the multiples of two add 2 to the preceding number, read more on that at the article understanding of number sequences.

NOTE: Now what remain is from 3 to 9. You may feel like completing the table, but how! Here is what to do. Let say the 3 row for example, multiply 3 by 3 which it result is 9, if you want to get the remaining number keep adding 3 to get the next as show in the table above. 

How larger numbers are multiply

Learning multiplication table is very important, because it will be useful in multiplying larger number.

To multiply larger number, you have to stack them on top of other (I have explain that while explaining addition and subtraction).

Examples:

1. Suppose you want to multiply 23 * 4 (two-digit number against one-digit number), don`t forget to put a line underneath after the stacking, as show below.

       2. Also let multiply 63 times(*) 7, after stacking, multiply 7 times 3 which is 21, write down the 1 at the units digit after the underneath line, put the 2 above the 6, multiply 7 by 6 it result 42, because 6 and 7 are the last number to multiply you don`t have to keep any number. Add the 42 with the 2 you write at the top of the 6, 42 + 2 = 44, now write the 44 under at the tens and the hundreds (4 at the tens, 4 ate the hundreds) see the below image.

To multiply a two-digit number by two-digit number, first stack the number on top of each other.

  3. multiply 38 by 27.

Note: when multiply 2 with 8 I start writing down the product at the bottom of the second number below the top number (the tens digit number). And later add the top number with the bottom number.

Number line

Number line

The diagram  above illustrate the structure of number in number line, which sometimes use to show how number get bigger in one direction and smaller in the other direction.

Adding and Subtracting with number line, may seen confusing but keep the two rule below.

• The number goes up as you go right (+)
• The number goes down as you go left (-)

Example 1: 3 + 4 means, you start at 3 and jumps up 4 spaces to 7 (3+ 4 =7) as show in the  diagram below.

Example 2 : 9-2 means, start at 9 and jump down 2 spaces (9 -2=7) as show in the diagram below.

You can even be more advance with number line, if you try to solve some equation like this 3 +1 -2 + 4 - 3 - 2 (start at 3, up 1, down 2, up 4, down 3, down 2).

Do these:

•  2 - 7 + 2 + 4  
• 1 + 4 - 4 + 3
• 2 + 5 + 5 + 6 -5  and comment your answer...

Negative number line

You may have meet someone telling you, you can`t take away more than you have, but the true is you can indeed take away more than you have, which result in negative number (7-10 = -3).

Adding and subtracting negative number on number line is somehow mismatch, but if you stay calm it`s easy to understand. Say you have 2 Naira and you owe your best friend 5 Naira, if you pay him with the 2 Naira, now you are still owing him 3 Naira(which is -3 subtracting 3 Naira from your money which you don`t have that time) as show below.

start at 2 and go down 5 times as illustrate above.

Multiplying Negative and Positive number with number line. suppose you want to multiply any number by 2, circle every other number starting from 0 as show below (multiply of 2).

Now let calculate 2 × 2 which is equal to 4.

You start moving from 0 through it right and keep resting on the circled number till you do it two (2) times.

 (multiplying by 3, 4 ,5)try these and comment your answer ().

Negative number (-2 * 2)

circle from 0 to the left as show above and count the circled number till you count 2 times

also -2 * -2 =? (negative number against negative number).

Note: if you want to multiply something like (-2 * -2 or other number provided that they both have a negative sign in front), start at 0 and circle the number through the right, count from 0 two  (2)times to the right (for equation -2 × -2).

Note: Take a sheet of paper and do some of this type of equation then comment, to know if it`s understandable.

Dividing with number line, to divide a number against another on a number line, you write the bigger number (like 0, 1, 2 ...) starting at 0 on the number line.

Suppose you are to calculate 4 / 2 after you have follow the step above (diagram),  just split it in 2 (because it is dividing against 2)

Do these 

• 5 ÷ 10 
• 6 ÷ 3

☺Funny: Tape rule ruler are of number line... 

Tape rule

Don`t forget top comment if there is any question.

Subtraction of Number

Subtraction of Number

Is the second operation you will discover (addition brother, like dynamic duo). It is all about taking small number away from big number (sometimes big from small). It is donated with the minus sign (-).
When you are working with subtraction try to keep these key words; subtrahend is the first number, minuend is the second number that result in difference (subtrahend minus minuend equals difference).

The big number can be take away from the small number, do you think am wrong, (4 - 5 = -1).

How larger numbers are subtract

When subtracting larger numbers place then on top of one another, by placing the units digit on top of the units digits and the tens digits on top of the tens digit (in subtraction don`t place more than two number, if you are given a number more than two numbers; first calculate the first and the second and later their result with the third).

Whenever the top digit in a column is smaller than the bottom here is what to do (borrowing process).

•      subtract 1 from the digit at the left of the top digit in the column you are working and write the answer at the top of the digit you are borrowing from.

•     The 1 you borrow is now put in front of the top digit in the column you are working (or you assume the 1 is 10 and add it to the top digit in that column).

 

NOTE: In some cases whereby the digit at the immediate left of the digit in the column you are, is a 0 (the top digit that is less than the bottom digit in the same column), you have to borrow from the next, and if the next digit is also a 0 you have to borrow from the next and so on.
 

 

Addition of number made simple

Addition of number

First among the operation you come across, it`s simple to work with. It is all about putting things in one place. 2 and 5 are two separate numbers which can be bring together by the help of addition and result 7, as the result of getting together (thing of it as a marriage protocol). It is donated with + signs. In the previous example 2 and 5 are called the addends while the 7 is call the sun (number that you add are called addends, the result is called the sum) 2 + 5 = 7.

How larger numbers are add

To add a larger number place then on top of one another, by placing the units digit on top of the units digits and the tens digits on top of the tens digit and so on (even if thousand, million, trillion. place it on top of the value`s holder).






If you follow the step as explain above.
 

In the board above, you should notice that when we add up the tens column it result in two-digit number. For that we just write the two-digit by placing the units’ digit under the tens and the tens (13) at the new column. Which is the hundreds digit.

Place Value

Place Value

When doing a place value it best to understand what numbers and digits are, for shot a number is a string of more digits (345), while a digit is a single numeric (from 0 to 9).

Place value is the system of placing a value in the position corresponding to it place in the string of number, some mathematics teacher says hundred tens unit.

The above table illustrate the million, thousand, and hundred in which digit are place base on their specific state. (Advance place value table is show below at the example 8)

Examples:

    1. Say we want to find the place in which every value in the number 3,001,000. As show below the 3 digit is place under million because it have six zeros next to it, also the digit 1 is place under the thousand under the thousand and note the two zeros in front of the 1.

Because the only number representing thousand is only one, if it place under the hundred thousand or ten thousand it could change the number we are working with (010, 000 means ten thousand while 100,000 means hundred thousand). The hundred has zero due to the number we  were working on (3,001,000).
3,001,000 = 3,000,000 + 1,000.
Three million, one hundred thousand, if says in word.

  2. In the table below the  number 47,040,070 is fill in, At the example 1 above I have state that million always have six number after it, now 4 did not have six number after, it but 47 does, that means the two digit 47 should be place under the million (do we just place all the 47 under the million? No,  the 4 should be place under the ten million and the 7 under the unit million ), you should have know by this time that every number containing only one digit after it is ten and the one that have nun is always unit.
The 40 is place under the hundred because it has three number after it (4 is place under ten, and the zero that is with the 4 is place under the unit thousands). Next is the 70, (7 under tens and 0 under units because it is only one digit as explain above).
47,040,070 = 47,000,000 + 40,000 + 70
 forty seven million, forty thousand, seventy.

    3. To place the number 258,309 in value table, 258 is place under thousand because it has three number next to it , and 309 is place next as show below (read the above example).
258,304 = 258,000 + 304
two hundred  fivety eight thousand, three hundred  nine.

    4. Number 578,387,824 = 578,000,000 + 387, 000 + 823 (as describe below)
five hundred seventy eight million, three hundred eighty seven thousand, eight hundred twenty  three.
 

    5. In the table below, number 78,634,304 is break down to.
78,634,304 = 78,000,000 + 634, 000 + 304
seventy eight million, six hundred  thirty four thousand, three hundred four.

    6. 608,004 = 608, 000 + 004. Which is pronounced sixty hundred eight thousand, four.

 

    7. The number 57,028,003 = 57, 000 000 + 28, 000 + 3. Fivety seven million, twenty eight thousand, three

 

Times are when you have to read number more than million, Below table contain some value with long length of number other than million. The value below is pronounced,
 four hundred ninety two Quintilian, two hundred eighty two quadrillion, three hundred forty six trillion, seven hundred seventy six million, nine hundred six thousand, five hundred thirty one. 

Note: In these examples above I have put some zeros, when zero appear to the right of a digit it sometimes means a placeholder, which help keeping other digit in their proper position. But when it appear to the left of a digit its call the leading zero, it serve n o purpose than to give the space nonempty (you can remove it if you like). Also I have put a comma (,) while writing in word, don`t put and it means a decimal
I plead you to practice as many  questions as you like and free free to share it in the comment section or if you want a question.
 

Understanding Number(s) and its Sequence

Understanding Number(s) and its Sequence

Number Sequence is the arrangement of number according to a rule.

Even number

These are the number that can be divided by 2. (2 4 6 8 10 12 14 ...) are the first even number. even number are easy to get. Start at 2 (I have also start at 2 below) and keep adding 2 to get the next.

  Keep in mind that even number are number that can be divided by 2 without having a remainder.

Odd number

Sequence of odd number are the simplest to generate (simplest or easiest, you may be thinking even number is the quickest number to generate), all you need to do is to start with number 1 and keep adding 2 (whoosh! Am even adding 2, if you think of the calculation Odd number may be the Quickest).

 You just see how I have be adding 2 with number so far (counting by 2), but what if you meet one of your friend and he/she ask you. please, can you count in threes, fours,fives...?(you don`t have to feel dull to answer that question, we will help you out).

Counting number in threes fours fives

After you learn counting in twos (Even and Odd numbers) here is the next step.
 Counting in threes: It follow the parttern of adding 3 with the 3 you started with (I have explain most of it at Even and Odd), and continue adding to the answer you get from your last addition.

 

Counting in fours

 It`s easy, just keep adding 4 after starting with 4(note that, it also follow the same pattern as the threes explain previous)

Counting in fives

Also keep adding 5 after the starting 5.

(Ha! don`t laugh too much we are trying to teach you multiplication, more on that later).
Note: Don`t let adding 2 to both Even and Odd number (positive /negative) confuse you. keep in mind that Even numbers are divisible by 2, while Odd numbers are not divisible by 2 (only if you multiply the Odd by 2. 2×7 = 14, 14/2 = 7).


Integer number (whole number) may be positive or negative, and the are only one number (1, 5, 2, 3, 4,) not twos are more (12, 22, 45, 89, 9000, 92344,) positive integer are called NATURAL NUMBER / POSITIVE NUMBER (+1, +2, +5) while negative integer are called NEGATIVE NUMBER (-2, -3, -4).

Prime numbers are numbers that are only divisible by 1 and itself (2, 3, 5, 11, 13, 17).
composite numbers are the numbers that can be divided by at least one number other than 1 and itself.

Rational numbers are the type of number that are written in the form of m/n, where n is not equal to zero and m/n cannot be reduced further. (1/2, 3/2, 5/6 or 0.6666666).

Real numbers may be rational (integer/fraction) or irrational numbers (-3, -1/4, 5/2).

Irrational number is a number that`s neither a whole number nor a fraction. In fact it can only be approximated as a non-repeating decimal (π = 3.1415926535897932384...).

Whoosh! you have been talking about numbers since, but you have not mention zero, is zero not a number?
Sorry, zero is a number too, I just want to explain numbers that are seriously use in mathematics before explain zero, zero is a number use as a demarcation between the negative -1 and the positive +1, it`s donated by 0.

Note: Natural number or counting number(1, 2, 3, 4, 5), Integer number, Rational number(integer and fraction), Real number(rational and irrational) are the four groups of important number. don`t forget to comment if you have a question.

How Number was invented

How Number was invented

Historian believes that the first number system came into being at the same time as Agriculture and Commerce. However, development in trading later causes the using of stones and order countable materials to track the quantity of their property, which then leads to drawing picture and Numbers that let them count comfortable.
 As the counting by number is widely used among people of different countries and tribes, Some Country invests their own system of writing number (Babylonian, Arabs, Egyptians, Greeks, Romans, Mayans and Chinese ...) little are known nowadays.
 Due to the expanding of the Roman Empire through Europe and parts of Asia and Africa, that allow Roman numeral to gain wide currency. Also, Arabic system of writing is close to being the parent of the Hindu-Arabic Number (Decimal Numbers).
 Prehistorically number are invested for counting commodity, but it`s nowadays widely used in many application (money, Levying tax, and lots more). Numbers are are tools used daily by academic, traders, professionals, administrators to solve problems and transact business.