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Which inequality correctly orders the numbers 
-(9)/(3),-(3)/(9), and -1 ?
Choose 1 answer:
(A) 
-1 > -(9)/(3) > -(3)/(9)
(B) 
-(9)/(3) > -1 > -(3)/(9)
(C) 
-1 > -(3)/(9) > -(9)/(3)
(D) 
-(3)/(9) > -1 > -(9)/(3)

Which inequality correctly orders the numbers 93,39 -\frac{9}{3},-\frac{3}{9} , and 1-1 ?\newlineChoose 11 answer:\newline(A) -1>-\frac{9}{3}>-\frac{3}{9} \newline(B) -\frac{9}{3}>-1>-\frac{3}{9} \newline(C) -1>-\frac{3}{9}>-\frac{9}{3} \newline(D) -\frac{3}{9}>-1>-\frac{9}{3}

Full solution

Q. Which inequality correctly orders the numbers 93,39 -\frac{9}{3},-\frac{3}{9} , and 1-1 ?\newlineChoose 11 answer:\newline(A) 1>93>39 -1>-\frac{9}{3}>-\frac{3}{9} \newline(B) 93>1>39 -\frac{9}{3}>-1>-\frac{3}{9} \newline(C) 1>39>93 -1>-\frac{3}{9}>-\frac{9}{3} \newline(D) 39>1>93 -\frac{3}{9}>-1>-\frac{9}{3}
  1. Simplify fractions: Simplify each of the given fractions to understand their values.\newlineThe fraction 93-\frac{9}{3} simplifies to 3-3 because 99 divided by 33 is 33, and the negative sign makes it 3-3.\newlineThe fraction 39-\frac{3}{9} simplifies to 13-\frac{1}{3} because 33 divided by 99 is 3-300, and the negative sign makes it 13-\frac{1}{3}.
  2. Compare simplified values: Compare the simplified values with 1-1. We know that 3-3 is less than 1-1 because the more negative a number, the smaller it is. We also know that 13-\frac{1}{3} is greater than 3-3 because 13-\frac{1}{3} is closer to zero than 3-3 is. Finally, we know that 13-\frac{1}{3} is less than 1-1 because 13-\frac{1}{3} is a fraction of 1-1 and therefore not as negative.
  3. Order numbers from greatest to least: Order the numbers from greatest to least based on the comparisons.\newlineFrom the comparisons, we can see that 13-\frac{1}{3} is the greatest, followed by 1-1, and then 3-3 is the least.\newlineSo the correct order is: -\frac{3}{9} > -1 > -\frac{9}{3}
  4. Match correct order to given choices: Match the correct order to the given choices.\newlineThe correct order we found is represented by option (D): -\frac{3}{9} > -1 > -\frac{9}{3}

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