Properties of Numbers in Grade VI

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.

Math Blog on Grade VI

Hello Friends, in today's session we are going to learn about the three most important properties of mathematics. The three properties are Commutative, Associative and Distributive Property which are of great importance to us. They help us in making a very complex problem a simple one.

Let's just take them one by one and see what these properties say:

Distributive property – in a very simple manner the property say that multiplication distributes over addition. Like if we do it in a general manner it will be a ( b + c ) = a b + a c. In numerical form it can be written as 2 ( 3 + 4 ) = 2 x 3 + 2 x 4. If in any question you are asked to used the distributive property then what you have to do is just take something common from the parenthesis or factorize it.

is this true 2 ( x + y ) = 2 x + 2 y.

To check this question we take the Left Hand Side and apply the distributive property, now after applying the property we can see that the LHS becomes 2 x + 2 y, so it is true.

Solve 4 x – 8.

To make this in simpler form, we look at the problem and we see that the term 4 is common from the above the expression, so now by applying distributive property the output is 4 ( x – 2 ), so this is our answer. But whether the property applies over subtraction also or not.

So now in place of x + y we have x – y, then what to do?

So we can write the term x – y as x + (-y), so now you can easily apply the property on it.

Now we can say that the multiplication distributes over subtraction also.

Associative property is usually used to associate or form groups.

For Example a + ( b + c ) = ( a + b ) + c or a ( b x c) = ( a x b ) c.

Numerically it can be written as 2 + (3 + 4) = (2 + 3) + 4 or (3×4) = (2×3)4.

The commutative property is used to commute or move around the numbers in a given expression.

For Example a + b = b + a

and a b = b a.

Restate 3 x 4 x X.

Now in this question what we have to do is shift the numbers and the variables to make different possible combinations. So the different possible combinations could be 4 x 3 x X, 4 x X x 3, 3 x X x 4, X x 3 x 4, and X x 4 × 3.

Now we solve a problem to see what the properties say :

Solve 3 a – 5 b + 7 a.

Commutative property – 3 a + 7 a – 5 b.

Associative property - ( 3 a + 7 a) – 5 b.

Distributive property – a ( 3 +7 ) - 5 b. 

In next post we will talk on Percentage in Grade VI. For more information on class 12 ICSE syllabus, you can visit our website