Rational Numbers
Distributive Property For Rational Numbers
Consider the rational numbers
What will be the values of the expressions
?
Let us see.
Thus,
Here we see that the values of both the expressions are same. This is the distributive property of rational numbers for multiplication over addition. This property is true for all rational numbers and mathematically it can be written as follows.
If x, y and z are any three rational numbers, then x ×(y + z) = (x ×y) + (x ×z).
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Does this distributive property hold for multiplication over subtraction also?
Let us check it.
Consider the rational numbers 4/7, -2/3, and 1/2
Let us find the value of the expressions
Thus,
Hence, we notice that the result is same from both the ways. Thus, the distributive property of rational numbers for multiplication over subtraction can be written as follows.
“If x, y, and z are any three rational numbers, then x× (y – z) = (x×y) – (x×z)”.
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Let us now look at some more examples.
Example 1:
Find the value of the following expression using appropriate properties.
Solution:
[By commutative property for addition]
[By commutative property for multiplication]
[By distributive property of multiplication over addition]
Example 2:
Solve the following expression.
Solution:
[By commutative property for addition]
[By distributive property of multiplication over subtraction]
