Could someone explain why is division distributive over addition ?

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SUMMARY

The discussion clarifies that division is distributive over addition through the equation (a + b) / y, which can be rewritten as (a + b) * (1/y). By defining 1/y as x, the equation simplifies to x(a + b) = xa + xb, demonstrating the distributive property. This mathematical principle is confirmed by the participants, particularly Roger and Matt, who engage in a clear explanation of the concept.

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  • Understanding of basic algebraic operations
  • Familiarity with the distributive property
  • Knowledge of fractions and division
  • Ability to manipulate algebraic expressions
NEXT STEPS
  • Study the properties of division and multiplication in algebra
  • Explore the distributive property in more complex equations
  • Learn about the implications of division in different mathematical contexts
  • Practice solving problems that involve distributing division over addition
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Students learning algebra, educators teaching mathematical concepts, and anyone seeking to understand the properties of division and addition in mathematics.

roger
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could someone explain why is division distributive over addition ?

It's not intuitive to me.

Thanks


Roger
 
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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.


:smile:
 

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