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Which inequality correctly orders the numbers 
-(5)/(4),-2(1)/(2), and -0.1 ?
Choose 1 answer:
(A) 
-0.1 > -(5)/(4) > -2(1)/(2)
(B) 
-2(1)/(2) > -(5)/(4) > -0.1
(C) 
-(5)/(4) > -2(1)/(2) > -0.1
(D) 
-0.1 > -2(1)/(2) > -(5)/(4)

Which inequality correctly orders the numbers 54,212 -\frac{5}{4},-2 \frac{1}{2} , and 0-0.11 ?\newlineChoose 11 answer:\newline(A) -0.1>-\frac{5}{4}>-2 \frac{1}{2} \newline(B) -2 \frac{1}{2}>-\frac{5}{4}>-0.1 \newline(C) -\frac{5}{4}>-2 \frac{1}{2}>-0.1 \newline(D) -0.1>-2 \frac{1}{2}>-\frac{5}{4}

Full solution

Q. Which inequality correctly orders the numbers 54,212 -\frac{5}{4},-2 \frac{1}{2} , and 0-0.11 ?\newlineChoose 11 answer:\newline(A) 0.1>54>212 -0.1>-\frac{5}{4}>-2 \frac{1}{2} \newline(B) 212>54>0.1 -2 \frac{1}{2}>-\frac{5}{4}>-0.1 \newline(C) 54>212>0.1 -\frac{5}{4}>-2 \frac{1}{2}>-0.1 \newline(D) 0.1>212>54 -0.1>-2 \frac{1}{2}>-\frac{5}{4}
  1. Convert to decimals: Convert all numbers to decimals to make comparison easier. The number 54-\frac{5}{4} is equivalent to 1.25-1.25, and 212-2\frac{1}{2} is equivalent to 2.5-2.5.
  2. Compare decimal values: Compare the decimal values. We have 1.25-1.25, 2.5-2.5, and 0.1-0.1. Since we are dealing with negative numbers, the number with the smallest absolute value is the greatest. Therefore, 0.1-0.1 is greater than 1.25-1.25, and 1.25-1.25 is greater than 2.5-2.5.
  3. Translate comparison: Translate the comparison back into the original fractions and mixed number. The inequality -0.1 > -\frac{5}{4} > -2\frac{1}{2} represents the comparison we made in Step 22.

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