Question

which inequality correctly orders the numbers $-\frac{5}{4}, -2\frac{1}{2}$, and $-0.1$?
choose 1 answer:
a $-\frac{5}{4} > -2\frac{1}{2} > -0.1$
b $-0.1 > -2\frac{1}{2} > -\frac{5}{4}$
c $-2\frac{1}{2} > -\frac{5}{4} > -0.1$
d $-0.1 > -\frac{5}{4} > -2\frac{1}{2}$

Explanation:

Step1: Convert to decimals

Convert \(-\frac{5}{4}\) to decimal: \(-\frac{5}{4} = -1.25\).
Convert \(-2\frac{1}{2}\) to decimal: \(-2\frac{1}{2} = -2.5\).
The numbers are now \(-1.25\), \(-2.5\), and \(-0.1\).

Step2: Compare negative numbers

For negative numbers, the larger the absolute value, the smaller the number.
Absolute values: \(|-0.1| = 0.1\), \(|-1.25| = 1.25\), \(|-2.5| = 2.5\).
So, \( -0.1 > -1.25 > -2.5 \) (since \(0.1 < 1.25 < 2.5\), their negatives follow the reverse order).
Substituting back, \( -0.1 > -\frac{5}{4} > -2\frac{1}{2} \).

Answer:

D. \( -0.1 > -\frac{5}{4} > -2\frac{1}{2} \)