How do I find the fraction of the job done?

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Discussion Overview

The discussion revolves around determining the fraction of a job completed by a worker washing windows, specifically how much of the total job can be accomplished in 6 days if the entire job takes 9 days. The scope includes mathematical reasoning and problem-solving strategies.

Discussion Character

  • Mathematical reasoning
  • Homework-related
  • Exploratory

Main Points Raised

  • One participant suggests that the worker washes 1/9 of the windows in one day, leading to a calculation for 6 days resulting in 6/9 or 2/3 of the job done.
  • Another participant expresses uncertainty and proposes that the answer could be 2/3, indicating a reliance on visual aids to understand the problem.
  • A different participant confirms that 2/3 is indeed correct and provides a method using ratios to explain the solution process.
  • One participant expresses appreciation for the explanations provided and shows interest in different problem-solving approaches, including visual methods.

Areas of Agreement / Disagreement

There is a general agreement among participants that the fraction of the job completed in 6 days is 2/3, although some participants express uncertainty about their understanding and the methods used.

Contextual Notes

Some participants mention the need for visual aids, indicating that different methods of problem-solving may be beneficial. There is also a suggestion to reduce the final answer, which may imply additional steps or considerations not fully explored in the discussion.

Who May Find This Useful

Students seeking assistance with fraction problems, educators looking for diverse problem-solving methods, and individuals interested in mathematical reasoning related to work and time calculations.

jaytheseer
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If a worker can wash all the glass windows of a building in 9 days, what part of the job can
said workers finish in 6 days?1. ¼
2. 1/3
3. 2/3
4. 3/5
5. ¾
 
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Re: Need EXPLANATION on how to solve this one. Thanks!

Here is a hint: If it takes 9 days to wash ALL the windows, what fraction of the total will the worker wash in ONE day? (What number is 1 part of 9 making a whole)?

Multiply your answer to THAT question by six. You may have to "reduce" your final answer.
 
Re: Need EXPLANATION on how to solve this one. Thanks!

Is it 2/3? I tried to draw a figure to be able to visualize it (and it takes much time). I don't know other ways to solve it. :confused:
 
Re: Need EXPLANATION on how to solve this one. Thanks!

jaytheseer said:
Is it 2/3? I tried to draw a figure to be able to visualize it (and it takes much time). I don't know other ways to solve it. :confused:

No drawings are needed. But your answer is correct, in 6 days one person can wash 2/3 of the windows. The easier way is to use ratios.

Set up a ratio "Proportion of the windows washed : Number of days", in this case it will be 1:9. So if you wanted to know how much in one day, you simply have to divide both sides by 9, giving 1/9 : 1 (in other words, 1/9 of the windows in 1 day), then for six days multiply everything by 6, giving 6/9 : 6, or if you like, 2/3 : 6 (2/3 of all the windows will be done in 6 days).

Can you go from here?
 
Got it! Thanks guys! :)
 
Having said that no drawings were necessary, I'd still be very interested in seeing them, as I love seeing different ways to solve problems and will never discourage a student's creativity...
 

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