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!
On
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.
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?