Ratios

We often compare two things and this comparison is called 'Ratio' in mathematics. A ratio compares two different quantities. So, it also a relation between two quantities. 

For example, there are 10 instructors and 30 girls in a hall room. So the ration between instructor and girl is 10 to 30 and in simplification it is 1 to 3 which means for every 3 girls there is one instructor.

Here are a few different ways we can describe the ratio of instructors to girls:

• There is 1 instructor for every 3 girls.
• The ratio of instructor to girls 1 to 3.
• The ratio of instructor to girls 1/3
• The ratio of instructor to girls 1:3

Ways to write ratios:

Here are several ways to describe the same ratio:

-  6 to 11

-  6:11

-  6/11

Fraction

A fraction is part of a whole. If we divide a whole thing, it will be divided into several pieces. Each piece can be seen as fractional part of the original whole thing.

In the above picture a circle is cut into 2 pieces and another circle is cut into 8 pieces. Each part can be said as fraction of the original circle and it can be represented as 1/2 and 1/8. Here 1 is called numerator and 2 and 8 is called denominator.

The numerator represents a number of equal parts while the denominator indicates how many of those parts make up a unit or a whole. For example, in the fraction 4/8, the numerator, 4, tells us that the fraction represents 4 equal parts, and the denominator, 8, tells us that 8 parts make up a whole. The denominator cannot be zero here. So, relation between can represented as :

Numerator

-------------------

Denominator

Proper Fraction and Improper Fraction:

A proper fraction is a fraction where the numerator is smaller than denominator.

Below are examples of improper fractions:
2/4, 3/5, 3/7

An improper fraction is a fraction where the numerator is greater than or equal to the denominator. Below are examples of improper fractions:
9/4, 5/5, 7/3

Mixed number:
A mixed number sometimes also called mixed fraction has a whole number and proper fraction. It is actually sum of a  whole number(not zero) and a proper fraction. This sum (+) symbol is never expressed.
3 4⁄5
It is actually  3 + 4⁄5 and is equivalent to 19/5.

Prime Number and Composite Number

What are prime numbers?
It is a whole number which has exactly two factors. The factors are 1 and the number itself. So, a prime number can be divided evenly by 1 and the number itself.

Example:
2,3,5,7 etc.
Pick a number 3 or 7. 3 can be divided by 1 and 3 itself. It is not evenly divisible by any other whole numbers.

What are composite numbers?
Composite numbers have more than two factors. A composite number has factors in addition to 1 and the itself.

Example:
4,9,18,77 etc.
Pick a number 18. it can be divided by 1,3,6,9 and 18 itself. So, it has more factors.

What is Multiple?

Multiples are numbers that result when we multiply one whole number by another whole number. The first four multiples of 3 are 3,6,9,12
3 × 1 = 3
3 × 2= 6
3 × 3= 9
3 × 4 = 12

We can write multiples of 5 as below:
5 × 1 = 5
5 × 2 = 10
5 × 3 = 15
5 × 8 = 40 

 We can never list all of the multiples of a number. In our example, 3 could be multiplied by an infinite number of numbers to find new multiples.

What is Factor in mathematics?

Factors are whole numbers that can evenly divide another number. Factors give us a way to break down a number into smaller pieces.
Example:
1×12=12
2× 6 =12
3×4 = 12
So, we see that the number 12 can be formed by multiplying these number. All these number(1,12,2,6,3,4) are factor of 12.
A number can have MANY factors!
Finding Factors
We can find the factors for 16 by thinking about numbers that will divide into 16 evenly.
1 is a factor of 16 because 1 can be divided into 16 with no remainder.
16÷1=16
The quotient 16 is also a factor of 16.
2 is a factor of 16 because 2 can be divided into 16 with no remainder.
16÷2=8
The quotient 8 is also a factor of 16.
4 is a factor of 16 because 4 can be divided into 16 with no remainder.
16÷4=4
The quotient 4 is also a factor of 16.
So, the 'Factor' of 16 are 1,16,2,8 and 4.

Googol Number

Hey, it's not Google, it is Googol.

In mathematics, some large number has naming and googol is such one. You may be confused with the word 'Google' - the giant search engine name but Googol, not Google is a number that describe a huge number.

A googol is the large number that equals 1 followed by 100 zeros. In exponent form it written as 10¹⁰⁰.

The term was used in 1920 by a 9 years old boy Milton Sirotta (1911–1981), nephew of American mathematician Edward Kasner. May be it was silly when he named it as googol.

Googol, a quantity that surpasses even the number of hydrogen atoms in the observable universe.

It is a belief that Larry Page and Sergey Brin, the founders of Google, named their search engine after the term googol.