Lesson 56: Using Models and Pictures to Compare Fractions, Activity Comparing Fractions — Practice Questions

1. 1. Four swimmers recorded their lap times in seconds. The times were 25.6, 25.07, 25.59, and 25.7. Which time is the fastest (least)?

   • A. 25.6
   • B. 25.07
   • C. 25.59
   • D. 25.7

2. 2. Arrange the following decimals in order from greatest to least: $4.8, 4.75, 4.81$. Use commas to separate the numbers. ___

3. 3. Simplify the expression $(15m^3n^2)^0$, assuming $m$ and $n$ are non-zero numbers. The result is ___.

4. 4. Which of the following numbers is greater than 0.4 but less than 0.45?

   • A. 0.5
   • B. 0.46
   • C. 0.39
   • D. 0.42

5. 5. Solve the equation for the variable $x$: $4(x + 5) = 36$. The value of $x$ is ___.

6. 6. To accurately compare the fractions $\frac{2}{5}$ and $\frac{3}{5}$ by drawing, what must be true about the two shapes you use?

   • A. The shapes must have different sizes.
   • B. One shape must be a circle and the other a square.
   • C. The shapes must be congruent.
   • D. The shapes must be divided into a different number of parts.

7. 7. A recipe uses $\frac{1}{2}$ of a large block of cheese. Another recipe uses $\frac{3}{4}$ of a small block of cheese. Can you conclude that $\frac{3}{4}$ is the larger amount of cheese used?

   • A. Yes, because $\frac{3}{4}$ is a larger fraction than $\frac{1}{2}$.
   • B. Yes, because three pieces are more than one piece.
   • C. No, because the blocks of cheese (the 'wholes') are not congruent.
   • D. No, because fractions cannot be used for recipes.

8. 8. Solve for the value of $x$ in the equation $9x - 4 = 5x + 16$. The value of $x$ is ___.

9. 9. When comparing two fractions with a numerator of 1, like $\frac{1}{9}$ and $\frac{1}{7}$, which statement is true?

   • A. The fraction with the larger denominator is larger.
   • B. The fraction with the smaller denominator is larger.
   • C. The fractions are always equal.
   • D. You cannot compare them without drawing a picture.

10. 10. Find the value of $p$ that makes the equation true: $3p + 12 = 8p + 2$. The value of $p$ is ___.