## Properties of Real Numbers

Properties of Real Numbers

Distributive Property

For any real numbers a, b, and c,

a(b + c) = ab + ac and (b + c)a = ba + ca.

Inverse Properties

For any real number a, there is a single real number – a such that

a + (-a) = 0 and –a + a = 0.

The inverse “undoes” addition with the result 0.

For any nonzero real number a , there is a single real number such that

a. = 1 and  .a = 1.

The inverse “undoes” multiplication with the result 1.

Identity Properties

For any real number a , a + 0 = 0 + a = a.

Also, a. 1 = 1. a = a.

Commutative and Associative Properties

For any real numbers a, b, and c,

a + b = b + a

and  ab = ba.

Commutative properties

Interchange the order of the two terms or factors.

Also, a + (b + c) = (a + b) + c

and a(bc) = (ab)c.

Associative properties

Shift parentheses among the three terms or factors; order stays the same.

## Multiply real numbers

Multiply real numbers

The answer to a multiplication problem is called the product. For example, 24 is the product of 8 and 3. The rules for finding signs of products of real numbers are given below.

Multiplying Real Numbers

Like signs:- The product of two numbers with the same sign is positive.

Unlike signs:-  The product of two numbers with different signs is negative.

## Subtract real numbers

Subtract real numbers

Recall that the answer to a subtraction problem is called the difference. Thus, the difference between 6 and 4 is 2. To see how subtraction should be defined, compare the following

two statements.

6 – 4 = 2

6 + (-4) = 2

Subtraction

For all real numbers a and b,

a – b = a + (-b).

In words, change the sign of the second number (subtrahend) and add.

Like signs :- To add two numbers with the same sign, add their absolute

values. The sign of the answer (either + or -) is the same as the sign of

the two numbers.

Unlike signs  :- To add two numbers with different signs, subtract the

smaller absolute value from the larger. The sign of the answer is the

same as the sign of the number with the larger absolute value.