# Distributive Property of Rational Number

Rational numbers are those numbers that can be expressed in the form of p/q, in which 'p' and 'q' both are Integer numbers, where value of 'q' can never be equal to the zero i.e. (q ≠ 0). Do you know distributive property of Rational Numbers? This is an important property for applying any particular operation on the rational numbers. The distributive property of rational number is applied on operations like addition and multiplication of the rational numbers.

To understand the distributive property of the rational number we have go through some of the examples. For instance: San has two rectangles with same height and he wants to calculate total area of the combined Rectangle. He has two choices to calculate the area, one (3, 5) and other (3, 7):

In the first method, he can calculate the areas separately and after that he will add both area, or he can use the distributive property rational numbers.

Area = 3 (5+ 7)

= 3*5 + 3*7 (Distributive property rational numbers)

Area = 36.

This is an example of the distributive property which can be used to find the product of a number, sum or difference.

## Simplify the given equation with the help of distributive property,4/5(6/5 +4/6)?

According to distributive law,

A(B+C)=AB+BC,

So we simplify it as 4/5*6/5 +4/5*4/6,

As we know for multiplication we just need to multiply numerator with numerator and denominator with denominator, so the required result will be,

4*6/5*5 + 4*4/5*6,

24/25 +16/30,

Now, for addition as we are seeing numerator of both the Numbers is not equal so we just need to take the LCM for equalizing the denominator. LCM of 25,30 will be the least number, multiple of both 25 and 30 that number is 150 or we can also apply the method in which we multiply the denominator  of  second number to first one and denominator of 1st to second one.

So required result will be:

24*6+16*5/150,

144+80/150,

224/150,

It can be also simplified as 112/75.

## Simplify the given equation with help of distributive property, {-5/2(6/5 +4/3)}?

Applying distributive law on the given problem,

(-5/2*6/5) +(-5/2*4/3),

As the term contains minus sign so, we need to be careful with sign conventions. If we multiple the above equation we get:
(-30/10 + (-20/6),
We can simplify this equation as,
30 can be written as 10 *3,
And 20 can be written as 10 *2,
-10*3/10 +(-10*2/2*3) so 10 gets cancelled with 10 and 2 gets cancel with 2 so required expression is,
-3 +(-10/3),
Both the quantities are having minus sign so quantities with same sign are always added, with minus sign. Now, for adding them we again need to equalize the denominator and then do the addition this time we will not take LCM we just equalize it by multiplying and divide 1st quantity by 3.
=> (-3*3/3) - (10/3),
=> (-9/3) - (10/3),
=> (-19/3),
This is the required answer.

## Simplify the given equation using Distributive Property, {6/5(44/60 +12/72)}?

Before applying Distributive property we need to simply the quantities for easier calculation.

=> 44 can be factorized as 4*11,
=> 60 can be factorized as 3*5*4,
=> 72 can be factorized as 12*6,
So, above expression can be written as,
=> 6/5(11/15 +1/6),
Now, applying distributive property,
=> 6/5*11/15 +1/6*6/5,
=> 66/75 +6/30,
=> 6/30 also can be written as 1/5,
=> 66/75 +1/5,
Now,for adding them we again need to equalize the denominator and then do the addition this.This time we need to multiply and divide by 5 in second quantity,
=> 66/75 +1*5/5*5,
=> 66/75 +5/25,
= 81/75.
This is the required answer.

## Further Read

Math Topics
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