Could someone explain why is division distributive over addition ?

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  • #1
roger
318
0
could someone explain why is division distributive over addition ?

It's not intuitive to me.

Thanks


Roger
 
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  • #2
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.
 
  • #3
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.


:smile:
 

Related to Could someone explain why is division distributive over addition ?

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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