Breaking Down Division when divisor is <1

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Discussion Overview

The discussion revolves around understanding division when the divisor is less than 1, specifically how to conceptualize and break down such division problems. Participants explore various methods and explanations related to this arithmetic concept.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • One participant expresses confusion about dividing by numbers less than 1 and seeks a breakdown of the process.
  • Another participant states that division by a number less than 1 can be understood as finding a quantity such that the product of the divisor and that quantity equals the dividend.
  • A different participant suggests adjusting both the numerator and denominator to make the divisor a whole number, using the example of multiplying by 10 to simplify the division.
  • Repeated subtraction is proposed as a method to understand division, specifically asking how many times 0.5 can be subtracted from 5, leading to the conclusion that the answer is 10.
  • One participant expresses gratitude for the explanations and confirms that the repeated subtraction method was particularly helpful.

Areas of Agreement / Disagreement

The discussion does not reach a consensus, as participants provide different methods and perspectives on understanding division by numbers less than 1, indicating multiple competing views on the best approach.

Contextual Notes

Some participants rely on specific arithmetic manipulations, such as adjusting the divisor, while others focus on conceptual interpretations like repeated subtraction. The effectiveness of these methods may depend on individual understanding and preferences.

ISX
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I haven't been able to figure this out but I am sure it's very simple but I can't understand how to do it.

If you take 5 x 0.5, that is the same as 0.5 + 0.5 +...

Alright so how do you break a division problem down? I realize how dividing by a number greater than 1 works, but under 1 I don't get it and if there was a way it broke down I think I would understand it. If you have 5/0.5 you get 10 obviously but how would that break down into simple terms?
 
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It works exactly the same way: It returns q such that 5 = 0.5q.
 
This works as you already learned combined maybe with a fancy way of multiplying by or dividing by 1. So, in your concept, you want to know how to handle divisor less than 1. You want to adjust the dividend AND the divisor so that the divisor is a whole number.

In your example, [itex]\frac{5}{0.5}[/itex], try multiplying both numerator and denominator by 10.

[itex]\frac{5}{0.5} \frac{10}{10}=\frac{50}{5}[/itex].

Now, you can handle the process more easily.
 
ISX said:
I haven't been able to figure this out but I am sure it's very simple but I can't understand how to do it.

If you take 5 x 0.5, that is the same as 0.5 + 0.5 +...

Alright so how do you break a division problem down? I realize how dividing by a number greater than 1 works, but under 1 I don't get it and if there was a way it broke down I think I would understand it. If you have 5/0.5 you get 10 obviously but how would that break down into simple terms?
For simple arithmetic problems such as this, you can think of division as repeated subtraction. In other wods, how many times can you subtract 0.5 from 5? Pretty obviously, the answer is 10.
 
Mark44 said:
For simple arithmetic problems such as this, you can think of division as repeated subtraction. In other wods, how many times can you subtract 0.5 from 5? Pretty obviously, the answer is 10.

That's exactly what I was looking for! Thanks for the help. Thanks to the others who expanded on this as well.
 

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