Practice identifying and placing fractions on a number line with this educational worksheet.

To solve the problem of filling in the missing fractions on each number line, we need to determine the pattern or increment between the given fractions and use it to find the missing values. Let's go through each number line step by step.

---

Number Line 1:

The given fractions are:
- \(0\)
- \(\frac{2}{5}\)
- \(\frac{4}{5}\)

#### Step 1: Determine the increment.
The difference between \(\frac{2}{5}\) and \(0\) is:
\[
\frac{2}{5} - 0 = \frac{2}{5}
\]
The difference between \(\frac{4}{5}\) and \(\frac{2}{5}\) is:
\[
\frac{4}{5} - \frac{2}{5} = \frac{2}{5}
\]
So, the increment is \(\frac{2}{5}\).

#### Step 2: Fill in the missing fractions.
- The fraction before \(\frac{2}{5}\) is:
\[
0 + \frac{2}{5} = \frac{2}{5} - \frac{2}{5} = 0
\]
- The fraction after \(\frac{2}{5}\) and before \(\frac{4}{5}\) is:
\[
\frac{2}{5} + \frac{2}{5} = \frac{4}{5}
\]

Thus, the completed number line is:
\[
0, \frac{1}{5}, \frac{2}{5}, \frac{3}{5}, \frac{4}{5}
\]

The missing fractions are:
\[
\boxed{\frac{1}{5}, \frac{3}{5}}
\]

---

Number Line 2:

The given fractions are:
- \(0\)
- \(\frac{1}{10}\)
- \(\frac{2}{10}\)
- \(\frac{4}{10}\)
- \(\frac{5}{10}\)
- \(\frac{7}{10}\)
- \(\frac{8}{10}\)
- \(\frac{9}{10}\)

#### Step 1: Determine the increment.
The difference between \(\frac{2}{10}\) and \(\frac{1}{10}\) is:
\[
\frac{2}{10} - \frac{1}{10} = \frac{1}{10}
\]
The difference between \(\frac{4}{10}\) and \(\frac{2}{10}\) is:
\[
\frac{4}{10} - \frac{2}{10} = \frac{2}{10}
\]
The difference between \(\frac{5}{10}\) and \(\frac{4}{10}\) is:
\[
\frac{5}{10} - \frac{4}{10} = \frac{1}{10}
\]
The difference between \(\frac{7}{10}\) and \(\frac{5}{10}\) is:
\[
\frac{7}{10} - \frac{5}{10} = \frac{2}{10}
\]
The difference between \(\frac{8}{10}\) and \(\frac{7}{10}\) is:
\[
\frac{8}{10} - \frac{7}{10} = \frac{1}{10}
\]
The difference between \(\frac{9}{10}\) and \(\frac{8}{10}\) is:
\[
\frac{9}{10} - \frac{8}{10} = \frac{1}{10}
\]

The pattern alternates between increments of \(\frac{1}{10}\) and \(\frac{2}{10}\).

#### Step 2: Fill in the missing fractions.
- The fraction after \(\frac{2}{10}\) and before \(\frac{4}{10}\) is:
\[
\frac{2}{10} + \frac{1}{10} = \frac{3}{10}
\]
- The fraction after \(\frac{5}{10}\) and before \(\frac{7}{10}\) is:
\[
\frac{5}{10} + \frac{2}{10} = \frac{7}{10}
\]

Thus, the completed number line is:
\[
0, \frac{1}{10}, \frac{2}{10}, \frac{3}{10}, \frac{4}{10}, \frac{5}{10}, \frac{6}{10}, \frac{7}{10}, \frac{8}{10}, \frac{9}{10}
\]

The missing fractions are:
\[
\boxed{\frac{3}{10}, \frac{6}{10}}
\]

---

Number Line 3:

The given fractions are:
- \(0\)
- \(\frac{2}{7}\)
- \(\frac{3}{7}\)
- \(\frac{4}{7}\)
- \(\frac{6}{7}\)
- \(1\)

#### Step 1: Determine the increment.
The difference between \(\frac{2}{7}\) and \(0\) is:
\[
\frac{2}{7} - 0 = \frac{2}{7}
\]
The difference between \(\frac{3}{7}\) and \(\frac{2}{7}\) is:
\[
\frac{3}{7} - \frac{2}{7} = \frac{1}{7}
\]
The difference between \(\frac{4}{7}\) and \(\frac{3}{7}\) is:
\[
\frac{4}{7} - \frac{3}{7} = \frac{1}{7}
\]
The difference between \(\frac{6}{7}\) and \(\frac{4}{7}\) is:
\[
\frac{6}{7} - \frac{4}{7} = \frac{2}{7}
\]
The difference between \(1\) and \(\frac{6}{7}\) is:
\[
1 - \frac{6}{7} = \frac{1}{7}
\]

The pattern alternates between increments of \(\frac{1}{7}\) and \(\frac{2}{7}\).

#### Step 2: Fill in the missing fractions.
- The fraction before \(\frac{2}{7}\) is:
\[
0 + \frac{1}{7} = \frac{1}{7}
\]
- The fraction after \(\frac{4}{7}\) and before \(\frac{6}{7}\) is:
\[
\frac{4}{7} + \frac{2}{7} = \frac{6}{7}
\]

Thus, the completed number line is:
\[
0, \frac{1}{7}, \frac{2}{7}, \frac{3}{7}, \frac{4}{7}, \frac{5}{7}, \frac{6}{7}, 1
\]

The missing fractions are:
\[
\boxed{\frac{1}{7}, \frac{5}{7}}
\]

---

Number Line 4:

The given fractions are:
- \(\frac{5}{16}\)
- \(\frac{6}{16}\)
- \(\frac{8}{16}\)
- \(\frac{10}{16}\)
- \(\frac{13}{16}\)

#### Step 1: Determine the increment.
The difference between \(\frac{6}{16}\) and \(\frac{5}{16}\) is:
\[
\frac{6}{16} - \frac{5}{16} = \frac{1}{16}
\]
The difference between \(\frac{8}{16}\) and \(\frac{6}{16}\) is:
\[
\frac{8}{16} - \frac{6}{16} = \frac{2}{16}
\]
The difference between \(\frac{10}{16}\) and \(\frac{8}{16}\) is:
\[
\frac{10}{16} - \frac{8}{16} = \frac{2}{16}
\]
The difference between \(\frac{13}{16}\) and \(\frac{10}{16}\) is:
\[
\frac{13}{16} - \frac{10}{16} = \frac{3}{16}
\]

The pattern alternates between increments of \(\frac{1}{16}\), \(\frac{2}{16}\), and \(\frac{3}{16}\).

#### Step 2: Fill in the missing fractions.
- The fraction after \(\frac{6}{16}\) and before \(\frac{8}{16}\) is:
\[
\frac{6}{16} + \frac{2}{16} = \frac{8}{16}
\]
- The fraction after \(\frac{8}{16}\) and before \(\frac{10}{16}\) is:
\[
\frac{8}{16} + \frac{2}{16} = \frac{10}{16}
\]
- The fraction after \(\frac{10}{16}\) and before \(\frac{13}{16}\) is:
\[
\frac{10}{16} + \frac{3}{16} = \frac{13}{16}
\]

Thus, the completed number line is:
\[
\frac{5}{16}, \frac{6}{16}, \frac{7}{16}, \frac{8}{16}, \frac{9}{16}, \frac{10}{16}, \frac{11}{16}, \frac{12}{16}, \frac{13}{16}
\]

The missing fractions are:
\[
\boxed{\frac{7}{16}, \frac{9}{16}, \frac{11}{16}, \frac{12}{16}}
\]

---

Number Line 5:

The given fractions are:
- \(\frac{3}{14}\)
- \(\frac{4}{14}\)
- \(\frac{5}{14}\)
- \(\frac{7}{14}\)
- \(\frac{9}{14}\)

#### Step 1: Determine the increment.
The difference between \(\frac{4}{14}\) and \(\frac{3}{14}\) is:
\[
\frac{4}{14} - \frac{3}{14} = \frac{1}{14}
\]
The difference between \(\frac{5}{14}\) and \(\frac{4}{14}\) is:
\[
\frac{5}{14} - \frac{4}{14} = \frac{1}{14}
\]
The difference between \(\frac{7}{14}\) and \(\frac{5}{14}\) is:
\[
\frac{7}{14} - \frac{5}{14} = \frac{2}{14}
\]
The difference between \(\frac{9}{14}\) and \(\frac{7}{14}\) is:
\[
\frac{9}{14} - \frac{7}{14} = \frac{2}{14}
\]

The pattern alternates between increments of \(\frac{1}{14}\) and \(\frac{2}{14}\).

#### Step 2: Fill in the missing fractions.
- The fraction after \(\frac{5}{14}\) and before \(\frac{7}{14}\) is:
\[
\frac{5}{14} + \frac{2}{14} = \frac{7}{14}
\]
- The fraction after \(\frac{7}{14}\) and before \(\frac{9}{14}\) is:
\[
\frac{7}{14} + \frac{2}{14} = \frac{9}{14}
\]
- The fraction after \(\frac{9}{14}\) is:
\[
\frac{9}{14} + \frac{1}{14} = \frac{10}{14}
\]
- The fraction after \(\frac{10}{14}\) is:
\[
\frac{10}{14} + \frac{1}{14} = \frac{11}{14}
\]

Thus, the completed number line is:
\[
\frac{3}{14}, \frac{4}{14}, \frac{5}{14}, \frac{6}{14}, \frac{7}{14}, \frac{8}{14}, \frac{9}{14}, \frac{10}{14}, \frac{11}{14}
\]

The missing fractions are:
\[
\boxed{\frac{6}{14}, \frac{8}{14}, \frac{10}{14}, \frac{11}{14}}
\]

---

Final Answer:

\[
\boxed{\frac{1}{5}, \frac{3}{5}, \frac{3}{10}, \frac{6}{10}, \frac{1}{7}, \frac{5}{7}, \frac{7}{16}, \frac{9}{16}, \frac{11}{16}, \frac{12}{16}, \frac{6}{14}, \frac{8}{14}, \frac{10}{14}, \frac{11}{14}}
\]