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This is the question: Use reasoning other than finding common denominators, cross-multiplying, or converting to decimals to compare each pair of fractions listed below.

Which is greater? Give reasoning.
37/52 or 37/64

7/12 or 5/8

I need help figuring this out without using the ways listed above!

Ben
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2 Answers2

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For the first, the numerators are the same. Check the denominators. Which is larger? What does that imply?

For the second, note that each fraction is one "unit" larger than half. Which of the units is larger?

Matt Samuel
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  • Okay the first one makes a ton of sense, thank you! For the second one, I understand that 5/8 is larger than 7/12 but how could I explain that using the reasoning that each fraction is one "unit" larger than half? – Ben Oct 05 '15 at 04:03
  • The way I see it is that it's saying that $1/8$ is larger than $1/12$., and each is that much larger than half. – Matt Samuel Oct 05 '15 at 04:07
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If a,b,c,d are positive integers and a/b>c/d then a/b>(a+c)/(b+d).In particular 5/8>2/4 so 5/8>(5+2)/(8+4)=7/12. If you are ran in an election and you had a proportion a/b of the votes from one region,but a smaller proportion c/d of the votes from another region, your total proportion (a+c)/(b+d) would be less than a/b.

DanielWainfleet
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