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

$\frac{7}{8} = \frac{3}{8} + \frac{3}{8}$

$\frac{7}{8} = \frac{2}{8} + \frac{5}{8}$

$\frac{7}{8} = \frac{7}{4} + \frac{7}{4}$

$\frac{7}{8} = \frac{1}{8} + \frac{5}{8}$

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

The numerators of the smaller fractions must be the same.

The denominators of the smaller fractions must be the same as the original.

You can only decompose a fraction into two parts.

The original fraction must be a proper fraction.

Decompose Fractions Practice — Grade 4 math

Lesson 2: Decompose Fractions — Practice Questions

1. Decompose the fraction $\frac{4}{5}$ into a sum. What number should be in the blank? $\frac{4}{5} = \frac{1}{5} + \frac{\_\_\_}{5}$
2. 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. $\frac{7}{8} = \frac{1}{8} + \frac{5}{8}$
3. An improper fraction can also be decomposed. Find the missing numerator in the equation: $\frac{9}{7} = \frac{\_\_\_}{7} + \frac{4}{7}$.
4. 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.
5. A fraction can be decomposed into more than two parts. Find the missing numerator in this decomposition: $\frac{10}{12} = \frac{3}{12} + \frac{5}{12} + \frac{\_\_\_}{12}$.
6. A number bond shows a whole connected to three parts. Each part is labeled $\frac{1}{4}$. Which fraction represents the whole in this number bond?
- A. $\frac{1}{4}$
- B. $\frac{3}{4}$
- C. $\frac{4}{3}$
- D. $\frac{1}{3}$
7. A tape diagram shows a rectangle divided into 8 equal parts with 5 parts shaded. The addition sentence for this diagram is $\_\_\_ = \frac{1}{8} + \frac{1}{8} + \frac{1}{8} + \frac{1}{8} + \frac{1}{8}$.
8. Which addition sentence correctly shows the decomposition of the improper fraction $\frac{5}{3}$ into unit fractions?
- A. $\frac{5}{3} = \frac{1}{5} + \frac{1}{5} + \frac{1}{5}$
- B. $\frac{5}{3} = \frac{1}{3} + \frac{1}{3} + \frac{1}{3}$
- C. $\frac{5}{3} = \frac{1}{3} + \frac{1}{3} + \frac{1}{3} + \frac{1}{3} + \frac{1}{3}$
- D. $\frac{5}{3} = \frac{3}{5} + \frac{2}{5}$
9. An addition sentence is given as $\frac{7}{10} = \frac{1}{10} + \frac{1}{10} + \frac{1}{10} + \frac{1}{10} + \frac{1}{10} + \frac{1}{10} + \frac{1}{10}$. A number bond representing this decomposition would have ___ parts.