**Commutative and associative properties :**

The order in which you add or multiply numbers does not change their sum or product.

Commutative property of addition is nothing but the rule which says that, when we are doing addition, it doesn't matter, in which order the numbers are.

We can add a and b or b and a ... and we'll get the same answer.

**More clearly, a + b = b + a**

Commutative property of multiplication is nothing but the rule which says that, when we are doing multiplication, it doesn't matter, in which order the numbers are. We can multiply a and b or b and a ... and we'll get the same answer.

**More clearly, a x b = b x a**

The way you group three or more numbers when adding or multiplying does not change their sum or product.

Associative property of addition is nothing but the rule which says that, when we are doing addition, it doesn't matter, in which order the numbers are.

We can add a, b and c or a, b and c ... and we'll get the same answer.

**More clearly, (a + b) + c = a + (b + c)**

For any numbers a, b, and c,

(a + b) + c = a + (b + c)

Example :

(2 + 4) + 6 = 2 + (4 + 6)

Associative property of multiplication is nothing but the rule which says that, when we are doing multiplication, it doesn't matter, in which order the numbers are. We can multiply a, b and c or c, b and a ... and we'll get the same answer.

**More clearly,**(ab) c = a (bc)

Example :

(3 ⋅ 5) 4 = 3 (5 ⋅ 4)

**Example 1 :**

Simplify 3(4x + 2) + 2x

**Solution :**

= 3(4x + 2) + 2x

= 3(4x) + 3(2) + 2x

= 12x + 6 + 2x

= 12x + 2x + 6

= 14x + 6

**Example 2 :**

Simplify 7(ac + 2b) + 2ac

**Solution :**

= 7(ac + 2b) + 2ac

= 7(ac) + 7(2b) + 2ac

= 7ac + 14b + 2ac

= 7ac + 2ac + 14b

= 9ac + 14b

**Example 3 : **

Simplify 3(x + 2y) + 4(3x + y)

**Solution :**

= 3(x + 2y) + 4(3x + y)

= 3 (x) + 3 (2y) + 4 (3x) + 4 (y)

= 3x + 6y + 12x + 4y

= 3x + 12x + 6y + 4y

= 15x + 10y

**Example 4 : **

Write an algebraic expression for half the sum of p and 2q increased by three-fourths q. Then simplify.

**Solution :**

half the sum of p ==> (1/2) p

2q increased by three-fourths q ==> 2q + (3/4) q

= (1/2) p + 2q + (3/4) q

= (p/2) + 2q + (3q/4)

= (p/2) + (2q) x (4/4) + (3q/4)

= (p/2) + (8q/4) + (3q/4)

= (p/2) + (8q + 3q)/4

= (p/2) + 11q/4

**Example 5 : **

Simplify 8 ⋅ 1.6 ⋅ 2.5

**Solution :**

= 8 ⋅ 1.6 ⋅ 2.5

= (8 ⋅ 1.6) ⋅ 2.5

= 12.8 (2.5)

= 32

After having gone through the stuff given above, we hope that the students would have understood "Commutative and associative properties".

Apart from the stuff given above, if you want to know more about "Commutative and associative properties", please click here

Apart from the stuff given on "Using properties of parallel lines", if you need any other stuff in math, please use our google custom search here.

Widget is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**