Lesson 4: Find common units or number of units to compare two fractions. — Practice Questions

1. 1. Decompose the improper fraction $\frac{13}{4}$ into a whole number and a proper fraction: $\frac{13}{4} = 3 + \frac{\_\_\_}{4}$.

2. 2. Which of the following statements is true?

   • A. $\frac{13}{6} > \frac{15}{7}$
   • B. $\frac{13}{6} < \frac{15}{7}$
   • C. $\frac{13}{6} = \frac{15}{7}$
   • D. The fractions cannot be compared

3. 3. Fill in the blank with the correct symbol: $>, <,$ or $=$. $\frac{8}{3}$ ___ $\frac{11}{4}$

4. 4. When comparing $\frac{9}{2}$ and $\frac{13}{4}$, what is the correct first step using the number bond method?

   • A. Find a common denominator for both fractions.
   • B. Decompose each fraction into a whole number and a proper fraction.
   • C. Multiply the numerators.
   • D. Convert the fractions to decimals.

5. 5. When $\frac{23}{5}$ is decomposed into a whole number and a proper fraction, the whole number part is ___.

6. 6. Which fraction is greater, $\frac{11}{3}$ or $\frac{17}{5}$?

   • A. $\frac{11}{3}$
   • B. $\frac{17}{5}$
   • C. They are equal
   • D. It cannot be determined

7. 7. Fill in the blank with the correct symbol: $>, <,$ or $=$. $\frac{17}{3}$ ___ $\frac{19}{4}$

8. 8. If $\frac{7}{3} = 2 + \frac{1}{3}$ and $\frac{9}{4} = 2 + \frac{1}{4}$, why must you compare $\frac{1}{3}$ and $\frac{1}{4}$ to find the greater fraction?

   • A. Because the whole number parts are equal.
   • B. Because the denominators are different.
   • C. Because the original fractions are improper.
   • D. Because finding a common denominator is required.

9. 9. To compare the fractions $\frac{2}{5}$ and $\frac{3}{7}$ using area models, what common denominator would be created by partitioning both models?

   • A. 14
   • B. 21
   • C. 35
   • D. 42