guys what is the best approach to these kind of questions: they seem to be very time consuming in terms of dividing my their denominator and see what is larger or smaller, but there got to be a fast way to do this, anyone knows?
which is the largest of all?
a. 2/3
b. 8/11
c. 10/17
d. 12/19
13/21
ans. B
I'd use 1/2 as a start point except they're all above 1/2. If some were above and some were below, you could right away eliminate a few. In this particular problem I would eliminate E right away because I know 13/21 is less than 2/3, because 14/21 = 2/3. Now I only have to deal with 4 fractions.
If you have a/b and c/d, take ad and compare it to bc. The key here is to consider the numerators. If ad > bc, then a/b > c/d (since a is a numerator and b is not, you know that ad refers to a/b). If bc > ad, then c/d > a/b.
In this problem start with 2/3 and 8/11. Do what I did above. You get 2*11 = 22 and 3*8 = 24. Obviously the latter is greater. Since that's the one with the numerator from 8/11, that must be the bigger fraction. Now A is gone. Test B with C.
Test 8/11 and 10/17. You get 8*17 = 136 and 11*10 = 110. Obviously the former is greater. Since that's the one with the numerator from 8/11, that must be the bigger fraction. Now C is gone. Test B with D.
Test 8/11 and 12/19. Right away it looks like 8/11 wins but okay we'll go through it anyhow. Do 8*19 = 152 and 11*12 = 132. Yup, 8/11 is the bigger fraction. Since everything is eliminated, that must be the biggest one.
Also it just happens to LOOK like the biggest fraction so I would have leaned towards that anyhow.
the repeating decimal 0.26666... is equal to which of the following?
a. 8/33
b. 26/99
c. 4/15
d. 13/45
e. 9/24
ans. c. what is the fastest way?
First find the repeat. In this case we have "6" as the repeat. If there are any numbers before the start of the repeat, remove them and create a fraction from it. We have 0.2 before the repeat so we remove that and get 1/5 as a fraction. We are left with 0.06666... Multiply by a power of 10 until you get past the repeat. So we multiply by 100 to get past the first "6". So we have 6.66666... Now subtract the original number from it. You get 6.66666 - .066666 = 6.6. Now take the power of 10 that you originally used (in this case 100) and subtract 1. That gives you 99. Your fraction for the repeating decimal is 6.6/99. This is the same as 1/15. You can check that 1/15 = 0.066666...
Now just add 1/15 and 1/5. You get 1/15 + 3/15 = 4/15 (choice C).
