Hello friends, in this session we are going to learn about the Commutative, associative, Distributive Property for grade VI of west bengal board of primary education. These properties are formally introduced in the section algebraic expressions of algebra classes but they are taught in many elementary schools. We probably already know many of these properties. For example the associative property basically states that we can arrange in any order: (3 + 7) +1 is the same as 3+ (1+ 7). Now we will discuss each property one by one.
In associative property the indication of the grouping of numbers does not matter. Grouping means where the parentheses are placed. In associative property, it involves 3 or more numbers. The terms which are in parenthesis indicates one unit group. That means numbers are 'associated' together. On other hand in multiplication, the product is always the same as the addition grouping. Remember one thing, the groupings in the brackets are always solved first. Now I am taking examples for both that is addition and multiplication.
Associative property of addition states that when we change the grouping of the number the sum does not change. For example (3 + 6) + 4 = 13 or 3 + (6 + 4) = 13, (8 + 3) + 4 = 15 or 8 + (3 + 4) = 15. So the sum remains the same. Associative property of Multiplication is same as addition when we change the groupings of numbers, the product remains the same. For example (4 x 2) x 6 = 24 or 3 x (2 x 4) = 24.
Now I am going to the next property that is commutative property. Basically Commutative property is the basic property of numbers. The meaning of word commute is exchanged or swapped over. It states that the numbers can be added or multiplied in any order that is when we add any two numbers by changing the order of addends does not change the sum. That is x + y = y + x. Similarly commutative property of multiplication states that when we change the order of factors that will not affect the product. That is, x × y = y × x. for example 3 + 4 = 4 + 3. Whether we add 3 to 4 or 4 to 3 we get same result that is 7. This is for addition and same for multiplication that is 3 x 4=4 x 3=12 the product is the same.
Lastly the distributive property in which we can multiply the number by each of the values separately and then add all together. So the distributive property states that the product and sum of a number is equal to the sum of the individual products of addends and the number. This property allows us to remove the brackets in the expression and multiply the value outside the brackets with each of the terms which are in the brackets. For example x(y + z) = xy + xz.4 (2 + 1) = 4 × 2 + 4 × 1
LHS: 4(2 + 1) = 4(3) = 12
Consider RHS: 4 × 2 + 4 × 1 = 8 + 4 = 12, LHS = RHS and to know more about it click here.
From the above discussion I hope that it would be helpful to you to understand commutative, associative and distributive property and to get information about other Grade VI topics like Algebraic Expressions and grade VII topic like Properties of lines you can refer text books and Internet.
In associative property the indication of the grouping of numbers does not matter. Grouping means where the parentheses are placed. In associative property, it involves 3 or more numbers. The terms which are in parenthesis indicates one unit group. That means numbers are 'associated' together. On other hand in multiplication, the product is always the same as the addition grouping. Remember one thing, the groupings in the brackets are always solved first. Now I am taking examples for both that is addition and multiplication.
Associative property of addition states that when we change the grouping of the number the sum does not change. For example (3 + 6) + 4 = 13 or 3 + (6 + 4) = 13, (8 + 3) + 4 = 15 or 8 + (3 + 4) = 15. So the sum remains the same. Associative property of Multiplication is same as addition when we change the groupings of numbers, the product remains the same. For example (4 x 2) x 6 = 24 or 3 x (2 x 4) = 24.
Now I am going to the next property that is commutative property. Basically Commutative property is the basic property of numbers. The meaning of word commute is exchanged or swapped over. It states that the numbers can be added or multiplied in any order that is when we add any two numbers by changing the order of addends does not change the sum. That is x + y = y + x. Similarly commutative property of multiplication states that when we change the order of factors that will not affect the product. That is, x × y = y × x. for example 3 + 4 = 4 + 3. Whether we add 3 to 4 or 4 to 3 we get same result that is 7. This is for addition and same for multiplication that is 3 x 4=4 x 3=12 the product is the same.
Lastly the distributive property in which we can multiply the number by each of the values separately and then add all together. So the distributive property states that the product and sum of a number is equal to the sum of the individual products of addends and the number. This property allows us to remove the brackets in the expression and multiply the value outside the brackets with each of the terms which are in the brackets. For example x(y + z) = xy + xz.4 (2 + 1) = 4 × 2 + 4 × 1
LHS: 4(2 + 1) = 4(3) = 12
Consider RHS: 4 × 2 + 4 × 1 = 8 + 4 = 12, LHS = RHS and to know more about it click here.
From the above discussion I hope that it would be helpful to you to understand commutative, associative and distributive property and to get information about other Grade VI topics like Algebraic Expressions and grade VII topic like Properties of lines you can refer text books and Internet.
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