SOLUTION: What number is between 6/11 and 0.67? 0.67 is a repeating decimal. A. 11/18 B. 69/99 C. 24/33 D. 26/55

Algebra ->  Rational-functions -> SOLUTION: What number is between 6/11 and 0.67? 0.67 is a repeating decimal. A. 11/18 B. 69/99 C. 24/33 D. 26/55      Log On


   

Question 871085: What number is between 6/11 and 0.67? 0.67 is a repeating decimal.
A. 11/18
B. 69/99
C. 24/33
D. 26/55
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If by 0.67 you mean a repeating decimal, it must be
%220.66666+.+.+.%22=2%2F3

It would be easy to use a calculator to get an approximate decimal value for
all the fractions and compare those approximate decimal values, but I assume calculators are not allowed.

Two of the fractions given can be simplified, and simplifying may help.
69%2F99=3%2A23%2F%283%2A33%29=23%2F33
24%2F33=3%2A8%2F%283%2A11%29=8%2F11

We can easily compare 6%2F11 and 2%2F3 to each other and to
B. 69%2F99=23%2F33 and C. 24%2F33 ,
if we express all four fractions with 33 as a denominator
6%2F11=6%2A3%2F%2811%2A3%29=18%2F33 and 2%2F3=2%2A11%2F%283%2A11%29=22%2F33
6%2F11=18%2F33%3C22%2F33%3C23%2F33%3C24%2F33 shows us that
6%2F11%3C2%2F3 and that
the answer is neither B. nor C.

6%2F11=6%2A5%2F%2811%2A5%29=30%2F55 ,
So 26%2F55%3C30%2F55=6%2F11%3C2%2F3 and D. is not the answer either.

The answer must be highlight%28A%29 because that's all that is left.

Let's verify, anyway.
To compare 11%2F18 to 2%2F3 and 6%2F11 we can use as a common denominator
198=18%2A11=3%2A6%2A11=3%2A66
11%2F18=11%2A11%2F%2818%2A11%29=121%2F198
2%2F3=2%2A66%2F%283%2A66%29=132%2F198
6%2F11=6%2A18%2F%2811%2A18%29=108%2F198
6%2F11=108%2F198%3C121%2F198%3C132%2F98=2%2F3 so 6%2F11%3Chighlight%2811%2F18%29%3C2%2F3