Properties of Rational Numbers
Properties of Rational Numbers
Properties of rational numbers are closure property, commutative property and associative property. All these properties have been discussed earlier. Let us briefly describe these properties on the four binary operations (Addition, subtraction, multiplication and division) in mathematics.
Addition
2/9 + (4/9 + 1/9) = 2/9 + 5/9 = 7/9
(2/9 + 4/9) + 1/9 = 6/9 + 1/9 = 7/9
So, 2/9 + (4/9 + 1/9) = (2/9 + 4/9) + 1/9
Subtraction
And, 2/9 - (4/9 - 1/9) ≠ (2/9 - 4/9) - 1/9 . Therefore, Associative property is not true for subtraction.
Multiplication
So, 5/9 x 2/9 = 2/9 x 5/9. Therefore, Commutative property is true for multiplication.
2/9 x (4/9 x 1/9) = 2/9 x 4/81 = 8/729
(2/9 x 4/9) x 1/9 = 8/81 x 1/9 = 8/729
So, 2/9 x (4/9 x 1/9) = (2/9 x 4/9) x 1/9. Therefore, Associative property is true for multiplication.
Division
Distributive Property
1/3 x (2/5 + 1/5) = 1/3 x 3/5 = 1/5 -----(1)
1/3 x 2/5 + 1/3 x 1/5 = 2/15 + 1/15 = (2 + 1)/15 = 3/15 = 1/5 -----(2)
From (1) and (2), 1/3 x (2/5 + 1/5) = 1/3 x 2/5 + 1/3 x 1/5
Therefore, Multiplication is distributive over addition.
1/3 x (2/5 - 1/5) = 1/3 x 1/5 = 1/15 ------- (3)
1/3 x 2/5 - 1/3 x 1/5 = 2/15 - 1/15 = (2 - 1)/15 = 1/15 -----(4)
From (3) and (4),
1/3 x (2/5 - 1/5) = 1/3 x 2/5 - 1/3 x 1/5
Therefore, Multiplication is distributive over subtraction.
7x + 10 = x(7) + 10, is explained by which property? | |||
| Right Option : C | |||
| View Explanation | |||
Which of the following is example of the Associative Property of Multiplication? | |||
| Right Option : C | |||
| View Explanation | |||
5 x (1/5) = 1 is explained by which property? | |||
| Right Option : A | |||
| View Explanation | |||
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