Fractions Transitional Reasoning Download PDF

Questions

1. 1.

   An artisan calibrates an electronic meter that displays values along a line from 0 to 1, marked with equal intervals of eighths. A container of resin has a volume of $\frac{3}{4}$ liter, while a container of hardener has a volume of $\frac{3}{8}$ liter. A test mixture is prepared whose volume is greater than the hardener but less than the resin, and its volume corresponds to a unit fraction. Which statement correctly identifies the equivalent position of the resin on the meter and the unit fraction representing the test mixture?

   • A) The resin is located at $\frac{4}{8}$, and the unit fraction is $\frac{1}{3}$.
   • B) The resin is located at $\frac{6}{8}$, and the unit fraction is $\frac{1}{2}$.
   • C) The resin is located at $\frac{6}{8}$, and the unit fraction is $\frac{1}{4}$.
   • D) The resin is located at $\frac{5}{8}$, and the unit fraction is $\frac{1}{2}$.
2. 2.

   A laboratory technician fills three identical 1-liter glass cylinders, labeled X, Y, and Z, with different test solutions. Cylinder X is filled to a level represented by 3 unit fractions of size $\frac{1}{4}$ liter, and Cylinder Y is filled to $\frac{5}{8}$ liter. Cylinder Z has a fill level equivalent to $\frac{1}{2}$ liter, but it is measured using an eighths scale. Which statement correctly gives the fill level of Cylinder Z in eighths and identifies the cylinder whose liquid level lies strictly between the levels of the other two cylinders on a number line from 0 to 1?

   • A) Cylinder Z has a fill level of $\frac{2}{8}$ liter, and Cylinder Y lies strictly between Cylinders X and Z.
   • B) Cylinder Z has a fill level of $\frac{4}{8}$ liter, and Cylinder Y lies strictly between Cylinders X and Z.
   • C) Cylinder Z has a fill level of $\frac{4}{8}$ liter, and Cylinder X lies strictly between Cylinders Y and Z.
   • D) Cylinder Z has a fill level of $\frac{6}{8}$ liter, and Cylinder Z lies strictly between Cylinders X and Y.
3. 3.

   Three student teams test robotic carts along a straight 1-meter track marked from 0 to 1. Team Alpha's cart stops at a distance formed by 3 unit fractions of size $\frac{1}{6}$ meter from 0, while Team Beta's cart stops at an equivalent position measured in twelfths. Team Gamma's cart stops at $\frac{2}{3}$ meter from 0. Which statement correctly identifies the stopping position of Team Beta's cart and compares the locations of all three carts?

   • A) Team Beta stopped at $\frac{4}{12}$ meter, and Team Gamma stopped closer to the starting line than Team Alpha.
   • B) Team Beta stopped at $\frac{5}{12}$ meter, and Team Alpha stopped further from the starting line than Team Gamma.
   • C) Team Beta stopped at $\frac{6}{12}$ meter, and Team Gamma stopped closer to the starting line than Team Alpha and Team Beta.
   • D) Team Beta stopped at $\frac{6}{12}$ meter, and Team Gamma stopped further from the starting line than Team Alpha and Team Beta.
4. 4.

   An engineer tests four identical storage batteries labeled W, X, Y, and Z. Battery W is charged to $\frac{2}{3}$ of its total capacity, and Battery X has an equivalent charge measured in sixths. Battery Y has a charge formed by combining 3 unit fractions of size $\frac{1}{4}$, while Battery Z has a charge of $\frac{5}{12}$. Which statement correctly identifies the charge of Battery X and orders Batteries W, Y, and Z from least to greatest charge?

   • A) Battery X has a charge of $\frac{3}{6}$, and the correct order from least to greatest is Battery Z, Battery Y, Battery W.
   • B) Battery X has a charge of $\frac{4}{6}$, and the correct order from least to greatest is Battery Z, Battery W, Battery Y.
   • C) Battery X has a charge of $\frac{4}{6}$, and the correct order from least to greatest is Battery W, Battery Z, Battery Y.
   • D) Battery X has a charge of $\frac{5}{6}$, and the correct order from least to greatest is Battery Y, Battery W, Battery Z.
5. 5.

   A landscape designer marks a straight walking path between a garden gate at 0 and a greenhouse at 1 on a planning line. She installs a water fountain at a point located $\frac{3}{4}$ of the total distance from the gate and plans to place a resting bench at an equivalent location using an eighths grid. A stone marker is also set at a location that is closer to the gate than the fountain, specifically at a unit fraction with a denominator greater than 3. Which statement correctly identifies the equivalent position for the bench and a possible location for the stone marker?

   • A) The bench is located at $\frac{5}{8}$, and the stone marker can be located at $\frac{1}{2}$.
   • B) The bench is located at $\frac{6}{8}$, and the stone marker can be located at $\frac{1}{3}$.
   • C) The bench is located at $\frac{7}{8}$, and the stone marker can be located at $\frac{1}{5}$.
   • D) The bench is located at $\frac{6}{8}$, and the stone marker can be located at $\frac{1}{5}$.