To determine which of the given rational numbers lie between -3 and -4, we will evaluate each number individually and see where it falls on the number line.
Here are the rational numbers provided:
1. [tex]\( -\frac{8}{2} \)[/tex]
2. [tex]\( -3.75 \)[/tex]
3. [tex]\( -\frac{11}{4} \)[/tex]
4. [tex]\( -2.25 \)[/tex]
Let's evaluate each number:
1. [tex]\( -\frac{8}{2} \)[/tex]:
Simplifying this fraction, we have
[tex]\( -\frac{8}{2} = -4 \)[/tex].
So, [tex]\( -4 \)[/tex] is exactly at -4 and does not lie between -3 and -4.
2. [tex]\( -3.75 \)[/tex]:
This is already in decimal form.
Since [tex]\( -3.75 \)[/tex] is greater than -4 and less than -3, it lies between -3 and -4.
3. [tex]\( -\frac{11}{4} \)[/tex]:
Converting this fraction to a decimal, we have
[tex]\( -\frac{11}{4} = -2.75 \)[/tex].
So, [tex]\( -2.75 \)[/tex] is less than -2.25 and does not lie between -3 and -4.
4. [tex]\( -2.25 \)[/tex]:
This is already in decimal form.
Since [tex]\( -2.25 \)[/tex] is greater than -3, it does not lie between -3 and -4.
Therefore, the rational number that lies between -3 and -4 is:
[tex]\[ -3.75 \][/tex]
