vishalranka wrote:If a is equal to one of the numbers 5/11, 7/12,9/13 what is the value of a?
1) 5/11 < a < 3/4
2) 11/13 > a > 1/2
Let's focus on comparing fractions.
You can either compare fractions to each other or you can compare each fraction to a simpler one. 1/4, 1/3 and 1/2 are good fractions for comparison.
For (1), for example, 5/11 is less than 1/2. Since 7/12 and 9/13 are both more than 1/2, they fit into the range from that side.
Now let's compare them to 3/4; well, 9/12=3/4, so 7/12 must be less than 3/4 (since 7 < 9). Further, 9/13 must be less than 3/4 (since in 9/13 vs 9/12, 13 > 12).
Accordingly, based on (1), a could be either 7/12 or 9/13.
For (2), 7/12 and 9/13 are both greater than 1/2, so we don't have to worry about the small end of the range.
11/13 is certainly greater than both 9/13 and 7/12 (since 7/12 is < 3/4 and 11/13 > 3/4), so we don't have to worry about the large end of the range.
Accordingly, based on (2), a could be either 7/12 or 9/13.
* * *
So, here's the general rule for comparing positive fractions:
if two fractions have the
same denominator, the one with the
bigger numerator is
greater; and
if two fractions have the
same numerator, the one with the
bigger denominator is
smaller.
