Real numbers include all numbers that can be used in everyday life and represented on the number line. They comprise integers, rational numbers like fractions, irrational numbers with non-repeating decimals, natural numbers starting at 1, and whole numbers including 0. Integers include natural numbers and their negatives. Rational numbers can be written as fractions, while irrational numbers have non-repeating decimals. Order of operations and properties like commutativity, associativity, and distributivity govern mathematical operations on real numbers.

1. REAL NUMBERS

2. WHAT IS REAL NUMBER?
Real number comprises of any number
you can think or use in everyday life.
Each real number represents a unique
number of the number line.
Real number are the compilation of all
types of number.

3. WHAT COMPRISES OF REAL NUMBERS?
Whole numbers
Natural numbers
Rational numbers
Irrational numbers
Integers

4. INTEGERS
 Integers are natural
numbers with zero and
their negative integers.
 They have a natural
number zero, the
positive number with
their negative
counterparts.

5. NATURAL NUMBERS
 All counting numbers
start from 1 are natural
numbers.
 They have only positive
value numbers.

6. WHOLE NUMBERS
 Whole numbers are
natural numbers with 0
added with them.
 They have one number
0 neither negative nor
positive but all other
numbers are positive.

7. RATIONAL NUMBERS
 Rational number are those numbers
which cannot be written as integers.
 They have written as the integer
divided by an another integer and
denominator is not be zero and both
numbers don’t have common factors.
 Rational number have either ending
or non terminating repeating decimal
expansion.
 Between every 2 rational number you
will find 2 more rational numbers.
 Rational numbers can be called
fractions

8. IRRATIONAL NUMBERS
 All numbers which can’t be
written as an integer upon
integer where the
denominator is zero and
both integers are co-prime
and irrational numbers.
 They are non- terminating
and non repeating decimal
expansions.
 The root of prime numbers
are irrational.

9. ORDER OF OPERATION
 When there is more than one symbol of operation in
an expression, it is agreed to complete the
operations in a certain order. A mnemonic to help
you remember this order is below
B I M D A S
Do any simplifying possible inside of brackets starting with
innermost brackets and working out
Apply Indices
Complete addition and subtraction from left to right
Complete multiplication and division from left to right

10. COMMUTATIVE PROPERTY
The operations of both addition and multiplication are commutative
abba  3223 
When adding, you can “commute” or trade the terms places
abba  3223 
When multiplying, you can “commute” or trade the factors places

11. ASSOCIATIVE PROPERTY
   cbacba 
   321321 
When adding, you can “associate” and add any terms first and then add the
other term.
   cbacba 
   432432 
When multiplying, you can “associate” and multiply any factors first and then
multiply the other factor.
The operations of both addition and multiplication are associative

12. DISTRIBUTIVE PROPERTY
The operation of multiplication distributes over addition
  acabcba 
  4323423 
The distributive property also holds for a factor that is multiplied on the left.
  acabacb 
  2423243 