PROBLEMS ON PROPERTIES OF REAL NUMBERS

Write the name of the property they use here.

Problem 1 :

11 + 0 = 11

Solution :

The sum of any real number and zero is the real number itself .If '11' is real number, then

11 + 0 = 0 + 11 = 11

Zero is the additive identity for real numbers.

Problem 2 :

x × (y × z) = (x × y) × z

Solution :

Multiplication of real numbers is associative.

If x, y and z are any three real numbers, then 

x × (y × z) = (x × y) × z

Problem 3 :

8 + (-8) = 0

Solution :

Additive inverse of 8 is (-8)

Additive inverse of (-8) is 8

Additive inverse of 0 is 0 itself

Problem 4 :

14 + 20 = 20 + 14

Solution :

Addition of two real numbers is commutative.

If 14 and 20 are any two real numbers,

Then, 

14 + 20 = 34

20 + 14 = 34

Hence, 14 + 20 = 20 + 14.

Problem 5 :

2 × 1/2 = 1

Solution :

If a real number 1/2 such that 2 × 1/2 = 1. Then 1/2 is the multiplicative inverse of a.

Problem 6 :

22 × 1 = 22

Solution :

The product of any real number and 1 is rational number itself. 'One' is the multiplicative identity for real numbers..

If 22 is real number, then

22 × 1 = 1 × 22 

Problem 7 :

(19 + 12) + 8 = 19 + (12 + 8)

Solution :

Addition of real numbers is associative.

If 19, 12 and 8 are real numbers.

then, 

(19 + 12) + 8 = (31) + 8 = 39

19 + (12 + 8) = 19 + (20) = 39

Hence, (19 + 12) + 8 = 19 + (12 + 8)

Problem 8 :

a × 9 = 9 × a

Solution :

a × 9 = 9 × a

Multiplication of real numbers is commutative.

If a and 9 are any two real numbers, then

a × 9 = 9a

9 × a = 9a

Hence, a × 9 = 9 × a

Therefore, Commutative Property is true for multiplication of real numbers.

Problem 9 :

7(4 + 11) = 7(4) + 7(11)

Solution ;

Multiplication of real numbers is distributive over addition.

If 7, 4 and 11 are three real numbers, then

7(4 + 11) = 7(15) = 105

7(4 + 11) = 7(4) + 7(11)

= 28 + 77

= 105

Hence, 7(4 + 11) = 7(4) + 7(11)