**Real Numbers Definition**:-

A real number is any positive or negative number. Real numbers is the complete set of rational and irrational numbers. It is represented by **R**. For example 1, 2, -4, ?6 etc all are real numbers. Real numbers also have decimal representation. For example 3 as 3.000 and ?6 as 2.449.

Real Numbers math have the property of ordered set which means for any two different numbers we can always say one is greater or less than other. If a and b are two real numbers than:

i) a is less than b {a<b}

ii) a is greater than b {a>b}

iii) a is equal to b {a=b}

## Real Numbers Properties

Addition | Multiplication | |

Associative law (a, b, c are real) | a + (b + c) = (a + b) + c | a x (b x c) = (a x b) x c |

Commutative law (a, b are real) | a + b = b + a | a x b = b x a |

Identity element ( a is real) | a + 0 = a | a x 1 = a |

Inverse element (a is real) | a – a = 0 | a x 1/a =1 |

Distributive law (a, b, c are real) | a x (b + c) = (a x b) + (a x c) |

In Real Numbers Properties,The commutative and associative laws do not hold for subtraction or division:

a* *– b is not equal to b – a

a ÷ b is not equal to b ÷ a

## Real Numbers Problems

**real numbers problem:** find 8 x (1+4).

**Solution:** According to the BODMAS rule we will first simplify the terms within the bracket and then we perform multiplication

8 x (5) = 40

But according to the distributive law

8 x (1 + 4) = 8 x 1 + 8 x 4 = 8 + 32 = 40