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Associative Distributive Properties

Associative And Distributive Property Of Multiplication Game

Associative Property

The word Associative itself gives an idea of grouping the terms or associating the terms with each other. In Mathematics, Associative Property allows us to group or join the different terms using addition or multiplication.

To create an associative property, the usage of Parentheses is very important as it groups and distinguishes the terms that are being joined. Hence the parentheses also establish the order of operations where the terms within the parentheses are solved first. An Example of the associative property of addition: (a + b) +c = a + (b + c)

The Basic concept of an associative property explains that solving either of the terms first won’t affect the results i.e. no matter if the first two terms or last two terms are solved first, the answer would be the same in both cases.

Implementation:  2 + (6+3) = (2+6) + 3.

The first thing to be solved is what’s within the parentheses.

  • 6+3=9 and 2+6=8
  • 2+9 = 8+3
  • 2+9=11 and 8+3=11
  • 11=11

So, 11=11 indicates that both sides of the equations are equal and the results won’t get affected by the order of operations.

An example of the associative property of multiplication: (a x b) x c = a x (b x c)

Implementation: (2 x 6) x 3 = 2 x (6 x 3)

Solving the parentheses first, (12) x 3 = 2 x (18) . 36 = 36 . So 36 = 36 indicates that both sides of the equations are equal and the results would be the same regardless of the order of operations.

Distributive Property

This property applies to the multiplication and addition operations. As the word Distributive indicates, this mathematical property implies that if a term is being multiplied by an expression in parentheses, then the multiplication is performed on each of the terms.

An example of distributive property:  a x (b + c) = a x b + a x c

Implementation:

3(6+9) = 3 x 6 + 3 x 9 Solving the parentheses first by adding 6 + 9

  • 3 (15) = 18 + 27
  • 45 = 45

45 = 45 indicates that the sum of the products on the right side of the equation gives the same result as multiplying on the left. Please credit this website by linking back to it. Also feel free to check other relevant educational content for your young ones Here.

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