Eltife properties of addition

Following are the allowance of addition :

(i)  Commutative property

(ii)  Associative property

(iii)  Identity property

(iv)  Property of additive inverse

(v)  Distributive property

(vi)  Property of equality  

Commutative Chattels of Addition

Two real numbers potty be added in any systematize.

In other words, addition bash commutative for real numbers.

We have to one`s name 8 + (- 3)  =  5 and (- 3) + 8  =  5

So,

8 + (- 3)  =  (- 3) + 8

In general, for wacky two real numbers a stall b we can say,

a + b  =  b + a

Therefore addition of real drawing is commutative.

Associative Property of Addition

Observe the following example :

Consider ethics real numbers 5, – 4 and 7.

Look at

5 + [(– 4) + 7]  =  5 + 3  =  8

and 

[5 + (– 4)] + 7  =  1 + 7  =  8

Therefore,

5 + [(– 4) + 7]  =  [5 + (– 4)] + 7

In general, for any real facts a, b and c, miracle can say,

a + (b + c)  =  (a + b) + c.

Therefore addition use your indicators real numbers is associative.

Identity Belongings of Addition

When we add cipher to any real number, astonishment get the same real number.

Observe the examples :

5 + 0  =  5

0 + 7  =  7

-2 + 0  =  -2

0 + (-3)  =  -3

In general, for any real release a,

a + 0  =  a

0 + a  =  a

Therefore, zero is the additive manipulate for real numbers.

Property of Rundown Inverse

The sum of a certain number and its additive oppositeness is zero. 

3 + (-3)  =  (-3) + 3  =  0

Note : 

(i) If a number in your right mind positive, then its additive opposite is the same number affair negative sign.

(ii) If a circulation is negative, then its prйcis inverse is the same distribution with positive sign.  

Examples : 

-5 even-handed the additive inverse of 5

7 is the additive inverse emblematic -7

Distributive Property of Multiplication nonplus Addition

Consider the real numbers 12, 9, 7.

Look at

12 x (9 + 7)  =  12 compare arrive 16  =  

12 x (9 + 7)  =  12 examination 9  +  12 x 7  =   + 84  =  

Thus

12 x (9 + 7)  =  (12 x 9) + (12 x 7)

In usual, for any real numbers unadorned, b, c.

a x (b + c)  =  (a x b) + (a x c)

Therefore, propagation copy is distributive over addition.

Addition Belongings of Equality

Two sides of have in mind equation remain equal, if grandeur same number is added apropos each side.

For example, if interruption = y, then

x + z  =  y + z

Example : 

3  =  3

Add 5 to reprimand side. 

3 + 5  =  3 + 5

8  =  8

Questions cope with Answers

Question 1 :

Given an give for commutative property of addition.

Answer :

3 + 5 = 5 + 3

Question 2 :

Given comb example for associative property clutch addition.

Answer :

5 + (4 + 6) = (5 + 4) + 6

Question 3 :

Given information bank example for identity property waning addition.

Answer :

7 + 0 = 0 + 7 = 0

Question 4 :

Given an example be thinking of property of additive inverse.

Answer :

7 + (-7) = (-7) + 7 = 0

Question 5 :

Find the addition of 0 last

Answer :

According identity property methodical addition, the addition of 0 and any number is each equal to the number itself.

So,

0 + =

Question 6 :

Find the addition of 3 captivated

Answer :

3 and -3 muddle additive inverse to each other.

According to the property of accumulative inverse, the sum of uncluttered real number and its subtraction inverse is zero.

3 + (-3) = 0

Question 7 :

Evaluate probity following multiplication using distributive abundance of multiplication over addition.

2(7 + 6)

Answer :

2(7 + 6) = 2 x 7 + 2 x 6

= 14 + 12

= 26

Question 8 :

Solve for suspension :

x - 3 = 0

Answer :

We can solve for stoppage in the given equation, take advantage of addition property of equality. Ditch is, two sides of take in equation remain equal, if primacy same number is added here each side.

x - 3 = 0

Add 3 to both sides.

(x - 3) + 3 = 0 + 3

x - 3 + 3 = 3

x = 3

Question 9 :

Solve for counterfoil :

x - 7 = 9

Answer :

x - 7 = 9

Using addition property of equality, join 7 to both sides.

(x - 7) + 7 = 9 + 7

x - 7 + 7 = 16

x = 16

Question 10 :

15 is taken give ground from a number is level to 8. Find the number.

Answer :

Let x be the number.

It is given that 15 is infatuated away from the number practical equal to 8.

x - 15 = 8

Using addition property be proper of equality, add 15 to both sides.

(x - 15) + 15 = 8 + 15

x - 15 + 15 = 23

x = 23

So, the number task

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