Ordering Rational Numbers - Pre Algebra

1. On a number line, point P is located at $\frac{5}{6}$ and point Q is located at $0.83$. Point R is positioned exactly halfway between points P and Q. Which of the following is closest to the location of point R?
   Answer: $0.831$ First convert ⁵⁄₆ to decimal: ⁵⁄₆ = 0.8333... Point R is halfway between 0.8333... and 0.83, so R = (0.8333... + 0.83)/2 = 1.6633.../2 ≈ 0.8317. Checking each choice: A) 0.825 is too far from 0.8317, B) ⁵⁄₇ ≈ 0.714 is much too small, C) 0.831 is very close to 0.8317, D) ⁴⁄₅ = 0.8 is too small.
2. Marcus is comparing temperatures recorded at different weather stations. Station A recorded $-8.5°F$, Station B recorded $-7\frac{3}{4}°F$, Station C recorded $-8\frac{1}{8}°F$, and Station D recorded $-8.05°F$. Which list shows these temperatures ordered from coldest to warmest?
   Answer: $-8.5, -8\frac{1}{8}, -8.05, -7\frac{3}{4}$ First, convert all temperatures to decimals: -8.5, -7¾ = -7.75, -8⅛ = -8.125, and -8.05. For negative numbers, the number with the greatest absolute value is the smallest (coldest). Ordering by absolute value: 8.5 > 8.125 > 8.05 > 7.75, so the temperatures from coldest to warmest are: -8.5, -8⅛, -8.05, -7¾. Choice B incorrectly orders -8⅛ and -8.5. Choice C reverses the entire order. Choice D incorrectly places -8.05 before -8⅛.
3. On a coordinate plane, point A is located at $(-\frac{3}{2}, 0)$ and point B is located at $(0.75, 0)$. Point C is positioned on the x-axis such that it is equidistant from both A and B. What is the x-coordinate of point C?
   Answer: $-\frac{3}{8}$ Point C is equidistant from A and B, so it's the midpoint of segment AB. The x-coordinate of the midpoint is: (x₁ + x₂)/2 = (-3/2 + 0.75)/2 = (-1.5 + 0.75)/2 = (-0.75)/2 = -0.375 = -3/8. Choice B (-1/4 = -0.25) is incorrect. Choice C gives 1/8 = 0.125, and choice D also gives 0.125, both resulting from sign or calculation errors.

Start this quiz