SOLUTION: Which number is between 0.5 and 8/9 ? a. 7/24 b. 22/24 c. 19/24 d. 1/3

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Question 844757: Which number is between 0.5 and 8/9 ?
a. 7/24
b. 22/24
c. 19/24
d. 1/3
Found 2 solutions by rfer, KMST:
Answer by rfer(16322) About Me  (Show Source):
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
0.5=1%2F2 and 8%2F9=1-1%2F9 is greater than 1%2F2.
You should know that 1%2F3%3C1%2F2 and that 7%2F24%3C12%2F24=1%2F2 ,
so 7%2F24 and 1%2F3 are not between 0.5 and 8%2F9 .
The other two fractions are greater than 1%2F2 , because
22%2F24%3E19%2F24%3E12%2F24=1%2F2 .
22%2F24=11%2F12=1-1%2F12 is greater than 8%2F9=1-1%2F9 because 1%2F12%3C1%2F9 ,
and since "non of the above" is not a choice, the answer is highlight%2819%2F24%29 .
For a multiple choice test, the reasoning above gets you to the answer faster.

ANOTHER WAY:
Maybe you were expected to express all those fractions with 72 as a common denominator,
but that as a way to the answer that is neither quick and efficient, nor smart, nor enjoyable:
0.5=1%2F2=1%2A36%2F%282%2A36%29=36%2F72
8%2F9=8%2A8%2F%289%2F8%29=64%2F72
7%2F24=7%2A3%2F%2824%2A3%29=21%2F72%3C36%2F72=0.5
22%2F24=22%2A3%2F%2824%2A3%29=66%2F72%3E64%2F72=8%2F9
1%2F3=1%2A24%2F%283%2A24%29=24%2F72%3C36%2F72=0.5

highlight%2819%2F24%29=19%2A3%2F%2824%2A3%29=57%2F72 and since 0.5=36%2F72%3C57%2F72%3C64%2F72=8%2F9 ,
highlight%2819%2F24%29 is the answer.