# Could someone explain why is division distributive over addition ?

• roger
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roger
could someone explain why is division distributive over addition ?

It's not intuitive to me.

Thanks

Roger

as i said in the pm reply, (a+b)/y is the same thing as multiplying (a+b) b y 1/y, call 1/y x then yo'ure happy that x(a+b)=xa+xb.

matt grime said:
as i said in the pm reply, (a+b)/y is the same thing as multiplying (a+b) b y 1/y, call 1/y x then yo'ure happy that x(a+b)=xa+xb.

thanks Matt, I got it.

## 1. What is the definition of the distributive property?

The distributive property states that when multiplying a number by a sum, the result is the same as multiplying each addend by the number and then adding the products together. In other words, a(b + c) = ab + ac.

## 2. How does the distributive property apply to division over addition?

The distributive property can also be applied to division over addition, meaning that when dividing a number by a sum, the result is the same as dividing each addend by the number and then adding the quotients together. In other words, a/(b + c) = a/b + a/c.

## 3. Why is division distributive over addition?

Division is distributive over addition because it follows the same principle as the distributive property for multiplication. When dividing a number by a sum, the division can be distributed to each addend, resulting in the same answer as when dividing by the sum altogether.

## 4. Can you provide an example of division being distributive over addition?

Of course! Let's say we have the expression 12/(4 + 2). Using the distributive property, we can rewrite this as 12/4 + 12/2. Simplifying, we get 3 + 6, which is equal to the original expression of 12/(4 + 2).

## 5. How can understanding the distributive property help with solving mathematical equations?

The distributive property is a fundamental concept in mathematics and is used in various equations and operations. By understanding this property, you can simplify and solve equations more efficiently, leading to a better understanding of mathematical concepts and problem-solving skills.

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