equivalent fractions chart in mathematics Stock-Vektorgrafik ... - Free Printable

The image shows a visual representation of fractions that add up to 1, arranged in a stacked bar format. Each row corresponds to a different denominator, and the number of blocks in each row is equal to the denominator. Each block represents a fraction with that denominator, and all blocks in a row sum to 1.

Let’s analyze this step by step:

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🔍 Understanding the Pattern

Each row is divided into equal parts, where:
- The denominator increases from row to row (from 2 to 15).
- The number of blocks in each row equals the denominator.
- Each block has value $ \frac{1}{n} $, where $ n $ is the denominator for that row.
- So, in row $ n $, there are $ n $ blocks, each of size $ \frac{1}{n} $, and their total sum is:
$$
n \times \frac{1}{n} = 1
$$

Thus, each row sums to 1, and the entire figure is built from rows representing unit fractions.

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🧮 What is the total area?

Since every row sums to 1, and we have rows from $ \frac{1}{2} $ up to $ \frac{1}{15} $, we can count how many rows there are:

- Rows: $ \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \dots, \frac{1}{15} $
- This is from $ n = 2 $ to $ n = 15 $

So, the number of rows = $ 15 - 2 + 1 = 14 $

Each row contributes 1 to the total sum.

✔ Therefore, the total sum of all the fractions shown is:
$$
14 \times 1 = 14
$$

But wait — the topmost green bar labeled "1" is not part of the fractional rows. Let's clarify:

- The very top bar is labeled "1", and it's separate.
- Then below it, we have rows starting from $ \frac{1}{2} $ down to $ \frac{1}{15} $.

So, the structure seems to be:
- One bar of size 1 (top)
- Then 14 rows, each summing to 1

So total = $ 1 + 14 = 15 $

Wait — but let's double-check whether the top "1" is meant to represent the whole or just a label.

Actually, looking at the layout:
- The top green bar says "1", and it spans the full width.
- Then the next row is split into two $ \frac{1}{2} $ blocks → sum = 1
- Next row: three $ \frac{1}{3} $ blocks → sum = 1
- And so on...

So each row below the top one is a decomposition of 1.

Therefore, the entire figure consists of:
- A single bar of height 1 (top)
- Plus 14 more rows, each of height 1 (since they represent full units)

But actually, the top bar might just be a title or label. It's not subdivided, and it's colored differently.

Alternatively, perhaps the entire figure is meant to show that:
> $ \sum_{n=2}^{15} 1 = 14 $, because each row sums to 1.

But that would mean the total is 14.

However, if we consider the top bar as an additional unit, then total is 15.

But let's look again: the top bar is only one bar, labeled "1", and then beneath it, we have 14 rows (from $ \frac{1}{2} $ to $ \frac{1}{15} $), each summing to 1.

So the total value represented is:
$$
1\ (\text{top}) + 14 \times 1 = 15
$$

But here's the key insight: is the top bar meant to be part of the sum, or just a header?

Looking at the design:
- The top bar is green, and it's above all others.
- The rest are color-coded per row.
- It appears to be a title or legend, not a data row.

Alternatively, maybe the entire rectangle is supposed to represent one unit, and the subdivisions show how to break it into fractions?

But that doesn’t make sense, because:
- The first row after the top bar is $ \frac{1}{2} + \frac{1}{2} = 1 $
- Then $ \frac{1}{3} + \frac{1}{3} + \frac{1}{3} = 1 $
- etc.

So each row is a complete unit.

Thus, the entire figure represents 14 units (from $ n=2 $ to $ n=15 $), each made of $ n $ pieces of $ \frac{1}{n} $.

And the top bar labeled "1" may just be indicating that each row is a unit.

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✔ Final Interpretation

The figure shows 14 rows, each representing a unit (value 1), decomposed into $ n $ equal parts of $ \frac{1}{n} $, for $ n = 2 $ to $ 15 $.

So:
$$
\text{Total sum} = 14 \times 1 = 14
$$

But the question is: what is the task?

Since no explicit question was asked in your message, I assume the task is likely one of the following common problems associated with such diagrams:

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💡 Likely Task: What is the total number of fractional pieces shown?

Let’s compute that.

For each row $ n $ from 2 to 15:
- Number of blocks = $ n $
- So total number of blocks = $ \sum_{n=2}^{15} n $

Compute:
$$
\sum_{n=2}^{15} n = \sum_{n=1}^{15} n - 1 = \frac{15 \cdot 16}{2} - 1 = 120 - 1 = 119
$$

✔ So there are 119 fractional pieces in total.

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🧩 Alternative Task: What is the total sum of all the fractions shown?

As established, each row sums to 1, and there are 14 rows:
$$
\text{Total sum} = 14 \times 1 = 14
$$

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📌 Conclusion

Without an explicit question, the most probable tasks based on such diagrams are:

#### 🔹 Task 1: How many fractional pieces are there?
→ Answer: $ \sum_{n=2}^{15} n = 119 $

#### 🔹 Task 2: What is the total sum of all the fractions?
→ Answer: $ 14 $

#### 🔹 Task 3: What does each row represent?
→ Each row represents 1, broken into $ n $ equal parts of $ \frac{1}{n} $

#### 🔹 Task 4: Why are there 14 rows?
→ Because denominators go from 2 to 15 inclusive → $ 15 - 2 + 1 = 14 $ rows

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✔ Final Answer (Most Likely):

> The diagram shows 14 rows, each summing to 1, using unit fractions from $ \frac{1}{2} $ to $ \frac{1}{15} $.
>
> - Total number of fractional pieces: 119
> - Total sum of all fractions: 14

If you have a specific question about the image (e.g., “How many $ \frac{1}{7} $ pieces are there?” or “What is the sum of the red blocks?”), please specify, and I’ll tailor the answer.

But based on the image alone, the most meaningful solution is:

> There are 119 fractional pieces, and their total sum is 14.