Lesson 4: Decomposition, Mixed Numbers, and Improper Fractions — Practice Questions

1. 1. Decompose the improper fraction $\frac{9}{7}$ by separating out one whole. The resulting expression is $1 +$ ___.

2. 2. Which expression correctly shows the decomposition of the improper fraction $\frac{11}{8}$ by separating one whole?

   • A. $1 + \frac{3}{11}$
   • B. $1 + \frac{3}{8}$
   • C. $\frac{8}{11} + \frac{3}{11}$
   • D. $1 + \frac{8}{3}$

3. 3. When the improper fraction $\frac{12}{5}$ is decomposed as $1 + \frac{x}{5}$, what is the value of the numerator $x$? The value of $x$ is ___.

4. 4. To decompose the fraction $\frac{15}{11}$ by separating one whole, what fraction equivalent to 1 should be used?

   • A. $\frac{1}{11}$
   • B. $\frac{15}{15}$
   • C. $\frac{4}{11}$
   • D. $\frac{11}{11}$

5. 5. An improper fraction was decomposed into the expression $1 + \frac{4}{9}$. What was the original improper fraction? The fraction is ___.

6. 6. Decompose the fraction $\frac{4}{5}$ into a sum. What number should be in the blank? $\frac{4}{5} = \frac{1}{5} + \frac{\_\_\_}{5}$

7. 7. Which of the following correctly shows a way to decompose the fraction $\frac{7}{8}$?

   • A. $\frac{7}{8} = \frac{3}{8} + \frac{3}{8}$
   • B. $\frac{7}{8} = \frac{2}{8} + \frac{5}{8}$
   • C. $\frac{7}{8} = \frac{7}{4} + \frac{7}{4}$
   • D. $\frac{7}{8} = \frac{1}{8} + \frac{5}{8}$

8. 8. An improper fraction can also be decomposed. Find the missing numerator in the equation: $\frac{9}{7} = \frac{\_\_\_}{7} + \frac{4}{7}$.

9. 9. When decomposing a fraction like $\frac{a}{b}$ into a sum of smaller fractions, which statement is always true?

   • A. The numerators of the smaller fractions must be the same.
   • B. The denominators of the smaller fractions must be the same as the original.
   • C. You can only decompose a fraction into two parts.
   • D. The original fraction must be a proper fraction.

10. 10. A fraction can be decomposed into more than two parts. Find the missing numerator in this decomposition: $\frac{10}{12} = \frac{3}{12} + \frac{5}{12} + \frac{\_\_\_}{12}$.