SOLUTION: What number is between 0.6 and 7/9? A. 23/27 B. 20/27 C. 14/27 D. 1/3

Algebra ->  Rational-functions -> SOLUTION: What number is between 0.6 and 7/9? A. 23/27 B. 20/27 C. 14/27 D. 1/3      Log On


   

Question 871083: What number is between 0.6 and 7/9?
A. 23/27
B. 20/27
C. 14/27
D. 1/3
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I assume that calculating approximate decimal values with a calculator and comparing them is considered cheating.
The traditional way to compare fractions, is to express them all with a common denominator.
Sometimes, depending on the particular numbers, there is an easier way, but I do not see an easier way this time.
27=3%2A9=3%2A3%2A3 is a multiple of 3 and a multiple of 9,
but 27 has no factor in common with prime number 5 ,
so the least common multiple (the smallest common denominator) is
135=27%2A5=3%2A9%2A5=3%2A%289%2A5%29=3%2A45=9%2A%283%2A5%29=9%2A15

0.6=6%2F10=3%2F5=3%2A27%2F%285%2A27%29=81%2F135
7%2F9=7%2A15%2F%289%2A15%29=105%2F135
A. 23%2F27=23%2A5%2F%2827%2A5%29=115%2F135%3E103%2F135=7%2F9 ,
so 23%2F27 is not between 81%2F135=0.6 and 105%2F135=7%2F9
B. 20%2F27=20%2A5%2F%2827%2A5%29=100%2F135
If there is only one right answer,
since 81%2F135%3C100%2F135%3C105%2F135 ,
0.6%3Chighlight%2820%2F27%29%3C7%2F9

In fact the other two numbers are not between 81%2F135=0.6 and 105%2F135=7%2F9 :
C. 14%2F27=14%2A5%2F%2827%2A5%29=70%2F135%3C81%2F135=0.6 and
D. 1%2F3=1%2A45%2F%283%2A45%29=45%2F135%3C81%2F135=0.6