Montessori Chart of Equivalent Fractions - Free Printable

Problem Description:

The task is to complete the "Chart of Equivalent Fractions." This involves filling in the missing equivalent fractions in the grid. The chart shows a table with rows labeled by fractions (e.g., \( \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \ldots \)) and columns labeled by denominators (e.g., 2, 3, 4, ..., 24). The goal is to fill in the missing entries with equivalent fractions.

Solution Approach:

1. Understanding Equivalent Fractions:
- Two fractions are equivalent if they represent the same value. For example, \( \frac{1}{2} = \frac{2}{4} = \frac{3}{6} \).
- To find equivalent fractions, multiply both the numerator and the denominator of a fraction by the same non-zero integer.

2. Filling in the Chart:
- For each row labeled by a fraction \( \frac{1}{n} \), we need to find its equivalent fractions with denominators ranging from 2 to 24.
- The equivalent fraction for \( \frac{1}{n} \) with a denominator \( d \) is \( \frac{k}{d} \), where \( k = \frac{d}{n} \) (if \( d \) is a multiple of \( n \)).

3. Step-by-Step Process:
- Row \( \frac{1}{2} \):
- Denominator 2: \( \frac{1}{2} \)
- Denominator 4: \( \frac{2}{4} \)
- Denominator 6: \( \frac{3}{6} \)
- Denominator 8: \( \frac{4}{8} \)
- Continue this pattern up to 24.
- Row \( \frac{1}{3} \):
- Denominator 3: \( \frac{1}{3} \)
- Denominator 6: \( \frac{2}{6} \)
- Denominator 9: \( \frac{3}{9} \)
- Denominator 12: \( \frac{4}{12} \)
- Continue this pattern up to 24.
- Repeat this process for all rows \( \frac{1}{n} \) where \( n \) ranges from 2 to 12.

4. Implementation:
- For each row \( \frac{1}{n} \), check if the column denominator \( d \) is a multiple of \( n \).
- If \( d \) is a multiple of \( n \), the equivalent fraction is \( \frac{k}{d} \), where \( k = \frac{d}{n} \).

Filled Chart:

Below is the completed chart of equivalent fractions:

| | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 |
|---|---|---|---|---|---|---|---|---|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|
| 1/2 | 1/2 | | 2/4 | | 3/6 | | 4/8 | | 5/10 | | 6/12 | | 7/14 | | 8/16 | | 9/18 | | 10/20 | | 11/22 | | 12/24 |
| 1/3 | | 1/3 | | | 2/6 | | | 3/9 | | | 4/12 | | | 5/15 | | | 6/18 | | | 7/21 | | | 8/24 |
| 1/4 | | | 1/4 | | | | 2/8 | | | | 3/12 | | | | 4/16 | | | | | | | | 5/20 |
| 1/5 | | | | 1/5 | | | | | 2/10 | | | | | 3/15 | | | | | | | | | 4/20 |
| 1/6 | | | | | 1/6 | | | | | 2/12 | | | | | | | 3/18 | | | | | | |
| 1/7 | | | | | | 1/7 | | | | | | 2/14 | | | | | | | | | | | |
| 1/8 | | | | | | | 1/8 | | | | | | 2/16 | | | | | | | | | | |
| 1/9 | | | | | | | | 1/9 | | | | | | | | | 2/18 | | | | | | | |
| 1/10 | | | | | | | | | 1/10 | | | | | | | | | | 2/20 | | | | |
| 1/11 | | | | | | | | | | 1/11 | | | | | | | | | | 2/22 | | | |
| 1/12 | | | | | | | | | | | 1/12 | | | | | | | | | | | | |

Final Answer:

\[
\boxed{
\begin{array}{c|ccccccccccccccccccccc}
& 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 & 16 & 17 & 18 & 19 & 20 & 21 & 22 & 23 & 24 \\
\hline
1/2 & 1/2 & & 2/4 & & 3/6 & & 4/8 & & 5/10 & & 6/12 & & 7/14 & & 8/16 & & 9/18 & & 10/20 & & 11/22 & & 12/24 \\
1/3 & & 1/3 & & & 2/6 & & & 3/9 & & & 4/12 & & & 5/15 & & & 6/18 & & & 7/21 & & & 8/24 \\
1/4 & & & 1/4 & & & & 2/8 & & & & 3/12 & & & & 4/16 & & & & & & & & 5/20 \\
1/5 & & & & 1/5 & & & & & 2/10 & & & & & 3/15 & & & & & & & & & 4/20 \\
1/6 & & & & & 1/6 & & & & & 2/12 & & & & & & & 3/18 & & & & & & \\
1/7 & & & & & & 1/7 & & & & & & 2/14 & & & & & & & & & & & \\
1/8 & & & & & & & 1/8 & & & & & & 2/16 & & & & & & & & & & \\
1/9 & & & & & & & & 1/9 & & & & & & & & & 2/18 & & & & & & \\
1/10 & & & & & & & & & 1/10 & & & & & & & & & & 2/20 & & & & \\
1/11 & & & & & & & & & & 1/11 & & & & & & & & & & 2/22 & & & \\
1/12 & & & & & & & & & & & 1/12 & & & & & & & & & & & & \\
\end{array}
}
\]