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