SOLUTION: KUMON MATHEMATICS LEVEL F SOLUTION BOOK - Studypool - Free Printable

The task appears to involve filling in missing values in a table based on some arithmetic or algebraic relationships. Let's analyze the structure and solve it step by step.

Observations:

1. The table is divided into four sections labeled 4 and 5.
2. Each section contains two columns, with one column having fractions and the other having integers or mixed numbers.
3. The left column (labeled 4) seems to follow a pattern involving fractions.
4. The right column (labeled 5) seems to be related to the left column through some operation.

Step-by-Step Solution:

#### Top Section:
- Left Column (4): The fractions are given as \( \frac{1}{4}, \frac{2}{4}, \frac{3}{4}, \frac{4}{4}, \frac{5}{4}, \frac{6}{4} \).
- These can be simplified to \( \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, \frac{5}{4}, \frac{3}{2} \).

- Right Column (5): The values are given as \( 3, \frac{7}{2}, 4, \frac{13}{4}, \frac{17}{4}, 5 \frac{1}{4} \).
- Notice that each value in the right column seems to be derived from the corresponding value in the left column.

#### Relationship Between Columns:
Let's examine the relationship between the left and right columns:
1. For \( \frac{1}{4} \) (left), the corresponding value in the right column is \( 3 \).
2. For \( \frac{1}{2} \) (left), the corresponding value in the right column is \( \frac{7}{2} \).
3. For \( \frac{3}{4} \) (left), the corresponding value in the right column is \( 4 \).
4. For \( 1 \) (left), the corresponding value in the right column is \( \frac{13}{4} \).
5. For \( \frac{5}{4} \) (left), the corresponding value in the right column is \( \frac{17}{4} \).
6. For \( \frac{3}{2} \) (left), the corresponding value in the right column is \( 5 \frac{1}{4} = \frac{21}{4} \).

#### Pattern Identification:
To find the relationship, let's express the right column values in terms of the left column values:
- For \( \frac{1}{4} \): \( 3 = \frac{12}{4} \)
- For \( \frac{1}{2} \): \( \frac{7}{2} = \frac{14}{4} \)
- For \( \frac{3}{4} \): \( 4 = \frac{16}{4} \)
- For \( 1 \): \( \frac{13}{4} \)
- For \( \frac{5}{4} \): \( \frac{17}{4} \)
- For \( \frac{3}{2} \): \( \frac{21}{4} \)

It appears that the right column value is obtained by adding a certain value to the left column value and then converting to a common denominator of 4. Let's verify this:
- For \( \frac{1}{4} \): \( \frac{1}{4} + \frac{11}{4} = \frac{12}{4} = 3 \)
- For \( \frac{1}{2} \): \( \frac{2}{4} + \frac{12}{4} = \frac{14}{4} = \frac{7}{2} \)
- For \( \frac{3}{4} \): \( \frac{3}{4} + \frac{13}{4} = \frac{16}{4} = 4 \)
- For \( 1 \): \( \frac{4}{4} + \frac{9}{4} = \frac{13}{4} \)
- For \( \frac{5}{4} \): \( \frac{5}{4} + \frac{12}{4} = \frac{17}{4} \)
- For \( \frac{3}{2} \): \( \frac{6}{4} + \frac{15}{4} = \frac{21}{4} \)

The pattern suggests that the right column value is obtained by adding a specific fraction to the left column value.

#### Bottom Section:
Now, let's apply the same pattern to the bottom section:
- Left Column (4): The fractions are given as \( \frac{1}{4}, \frac{2}{4}, \frac{3}{4}, \frac{4}{4}, \frac{5}{4}, \frac{6}{4} \).
- These can be simplified to \( \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, \frac{5}{4}, \frac{3}{2} \).

- Right Column (5): We need to fill in the missing values using the same pattern.
- For \( \frac{1}{4} \): \( \frac{1}{4} + \frac{11}{4} = \frac{12}{4} = 3 \)
- For \( \frac{1}{2} \): \( \frac{2}{4} + \frac{12}{4} = \frac{14}{4} = \frac{7}{2} \)
- For \( \frac{3}{4} \): \( \frac{3}{4} + \frac{13}{4} = \frac{16}{4} = 4 \)
- For \( 1 \): \( \frac{4}{4} + \frac{9}{4} = \frac{13}{4} \)
- For \( \frac{5}{4} \): \( \frac{5}{4} + \frac{12}{4} = \frac{17}{4} \)
- For \( \frac{3}{2} \): \( \frac{6}{4} + \frac{15}{4} = \frac{21}{4} \)

Thus, the completed table should look like this:

| Left Column (4) | Right Column (5) |
|------------------|-------------------|
| \( \frac{1}{4} \) | \( 3 \) |
| \( \frac{1}{2} \) | \( \frac{7}{2} \) |
| \( \frac{3}{4} \) | \( 4 \) |
| \( 1 \) | \( \frac{13}{4} \) |
| \( \frac{5}{4} \) | \( \frac{17}{4} \) |
| \( \frac{3}{2} \) | \( \frac{21}{4} \) |

Final Answer:

\[
\boxed{
\begin{array}{c|c}
\text{Left Column (4)} & \text{Right Column (5)} \\
\hline
\frac{1}{4} & 3 \\
\frac{1}{2} & \frac{7}{2} \\
\frac{3}{4} & 4 \\
1 & \frac{13}{4} \\
\frac{5}{4} & \frac{17}{4} \\
\frac{3}{2} & \frac{21}{4} \\
\end{array}
}
\]