How to do this without a calculator?

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westin

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The ratio 3,579,545.45454545..... : 5,000,000 can be expressed as a common fraction m/n . What is the value of m + n? (attached is the question screenshot)

Solution is 151.

I think we can do it with calculator in a very slow way by simplifying (3579545 + 45/99) / (5000,000).

However, this is from Mathcount and calculator should be used. Can anyone help?

Thanks!
 

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Why not just double the numerator and denominator and then just move the decimal?
 
the numerator is a repeating decimal 0.45454545454545........ i am not sure if this works
 
westin said:
I think we can do it with calculator in a very slow way by simplifying (3579545 + 45/99) / (5000,000).
Click to expand...
Why is that slow, and why does it require a calculator?

I'd start by observing that 3,579,545.4545... = 3,579.5454... * 1000, and that 0.5454... = 54/99 can be simplified. Then start working with the fractions.

The main thing is, don't say "I am not sure if this works"; try it and find out! And while you're at it, be looking for ways to speed the work.
 
sorry, i still don't get it.

3,579,545.45454545..... : 5,000,000 multiply numerator and denominator by 2. become 7159090.90909090.... /10000000 = 0.715909090.....

then how do i convert this number into m and n in order to find m+n.
 
Let x = .7159090....
100000x = 71590.90....
1000x = 715.90...
99,000x = 70875

Continue....
 
Last edited:
cool. then X will become 63/88. I never thought of that. do you just think of it on top of your head or is there something I can read more deeply from the internet? is there a name for this kind of method that convert decimal into fraction, that I can googled? or do you have a recommendation where I can learn more about this method?

thanks!
 
How did you know that .454545.... = 45/99?

Let x = .4545....
Then 100x = 45.454545...
So 99x=45 and x= 45/99.

Again, how did you conclude that .45... = 45/99

The method I used to get 99,000x = 70875 is exactly the same.

Yes, I did this on the spot. That does not say too much about my ability.
 
I just searched .454545.... = 45/99 from the internet. then used the calculator to keep simplifying the fractions. lol

thank you for your explanation. it makes more sense now. thanks!
 
westin said:
I just searched .454545.... = 45/99 from the internet. then used the calculator to keep simplifying the fractions. lol

thank you for your explanation. it makes more sense now. thanks!
Click to expand...
Maybe if you stop searching the internet for answers and spend time thinking about how to solve problems you would be able to figure out how to write .454545... as a fraction on your own. Didn't you wonder why .454545... = 45/99? The more things you blindly accept in math the harder math will be for you.
 
westin said:
cool. then X will become 63/88. I never thought of that. do you just think of it on top of your head or is there something I can read more deeply from the internet? is there a name for this kind of method that convert decimal into fraction, that I can googled? or do you have a recommendation where I can learn more about this method?

thanks!
Click to expand...
My 1st recommendation for you is to stop using google to replace thinking. It will not benefit you in the end.
 
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