Associative Property


 
 
Concept Explanation
 

Associative Property

Associative Property:

It states that you can add or multiply numbers regardless of how they are grouped. In both the groups the sum is the same. Addition and multiplication are associative for rational numbers. Subtraction and division are not associative for rational numbers.

Rational numbers follow the associative property for addition and multiplication.

Suppose x, y and z are rational then for addition: x+(y+z)=(x+y)+z

For multiplication: x(yz)=(xy)z.

Some important properties that should be remembered are:

  • 0 is an additive identity and 1 is a multiplicative identity for rational numbers.
  • For a rational number  frac{x}{y} is the additive inverse of-frac{x}{y}.
  • For example, given numbers are 5, -6 and 2/3( 5 – 6 ) + 2/3= -1 + 2/3= – 1/3Now, 5 + ( -6 + 2/3 )=  – 1/3

     

     

     

    Sample Questions
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    Question : 1

    7 + (a + 2) = (7 + a) + 2  ,  is explained by which property?

    Right Option : D
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    Question : 2

    Reciprocal of  3 is  __________________

    Right Option : C
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    Question : 3

    What is the value of x and y? in large frac{2}{3}times frac{-7}{10}+frac{-2}{3}times frac{8}{9}= xtimes [ frac{-7}{10}+ y]

    Right Option : D
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    Explanation
     
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