Fractions on a Number Line - Worksheet 14 Answer Key

It looks like you've uploaded a completed worksheet titled *"Fractions on a Number Line: Plotting Fractions – Worksheet 14"*, which includes an answer key. This worksheet helps students practice identifying fractions from shaded shapes and plotting them on a number line.

Let me walk you through the solution and explanation for each problem:

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🔷 Objective of the Worksheet

- Students are given circular figures (circles) divided into equal parts, with some parts shaded.
- They must:
1. Identify the fraction represented by the shaded portion.
2. Plot that fraction on a number line from 0 to 1.

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✔ How to Solve Each Problem

#### Step-by-step Instructions (as shown in the worksheet):
1. Determine the denominator: Count how many equal parts the circle is divided into.
2. Determine the numerator: Count how many parts are shaded.
3. Write the fraction.
4. Plot on the number line:
- Divide the segment from 0 to 1 into equal parts based on the denominator.
- Mark the point corresponding to the numerator.

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📌 Now, let's go through each row:

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#### 1. First Row (Example Given)
- Circle: Divided into 6 equal parts; 1 part shaded → Fraction = 1/6
- Number line: Split into 6 parts; mark at the first tick after 0 → ✔ Correct

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#### 2. Second Row
- Circle: Divided into 3 equal parts; 1 part shaded → Fraction = 1/3
- Number line: Split into 3 parts; mark at the first tick after 0 → ✔ Correct

> ✔️ The dot is placed at 1/3.

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#### 3. Third Row
- Circle: Divided into 5 equal parts; 4 parts shaded → Fraction = 4/5
- Number line: Split into 5 parts; mark at the fourth tick → ✔ Correct

> ✔️ The dot is placed at 4/5.

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#### 4. Fourth Row
- Circle: Divided into 8 equal parts; 5 parts shaded → Fraction = 5/8
- Number line: Split into 8 parts; mark at the fifth tick → ✔ Correct

> ✔️ The dot is placed at 5/8.

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#### 5. Fifth Row
- Circle: Divided into 4 equal parts; 3 parts shaded → Fraction = 3/4
- Number line: Split into 4 parts; mark at the third tick → ✔ Correct

> ✔️ The dot is placed at 3/4.

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#### 6. Sixth Row
- Circle: Divided into 4 equal parts; 6 parts shaded? Wait — this seems problematic.

Wait! Let’s examine closely.

The circle is divided into 4 equal parts, but all 4 parts are shaded (yellow), and the answer says 6/4?

That’s not possible — you can't shade more parts than exist in the circle!

But here’s what’s likely happening:

👉 The figure shows a circle split into 4 parts, all shaded → That would be 4/4 = 1, not 6/4.

However, the answer key says 6/4, and the number line has a dot at the 6th tick out of 4 divisions? That doesn’t make sense.

Let’s double-check the number line:
- It’s labeled from 0 to 1, divided into 4 segments → So it should have 4 ticks between 0 and 1 (at 1/4, 2/4, 3/4, 1).
- But the dot is placed at the 6th tick — which implies the number line has 6 divisions?

Wait — actually, looking at the number line in the last row:
- There are 7 marks (including 0 and 1), so 6 intervals → meaning it’s split into 6 equal parts.

So the number line is split into 6 parts, not 4.

But the circle is split into 4 parts, all shaded → 4/4 = 1

Yet the answer says 6/4, and the dot is at the 6th tick on a 6-part number line → that would be 6/6 = 1

So there’s a mismatch.

Let’s analyze carefully.

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❗ Critical Observation:

The last circle shows 4 equal parts, all shaded → that means the fraction is 4/4 = 1

But the answer key says 6/4, and plots it at 6/6 on a number line split into 6 parts.

This is incorrect unless there’s a typo or misunderstanding.

But wait — perhaps the circle is meant to represent 6/4? But 6/4 > 1, and the circle only has 4 parts.

You can’t shade 6 parts if only 4 exist.

So either:
- The figure is wrong, or
- The label is wrong, or
- There’s a misunderstanding.

But look at the number line: it has 6 ticks between 0 and 1 → 6 equal parts → so it's measuring sixths.

And the dot is at the 6th tick, so it represents 6/6 = 1

So the fraction being plotted is 1, not 6/4.

But 6/4 = 1.5, which is greater than 1, and cannot be plotted on a number line from 0 to 1.

Therefore, 6/4 is incorrect.

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✔ Correct Interpretation:

The circle is divided into 4 parts, all shaded → 4/4 = 1

So the correct fraction is 1, and it should be plotted at 1 on the number line.

But the answer key says 6/4, which is wrong.

Also, the number line has 6 divisions, so the 6th tick is 6/6 = 1, which is correct.

So even though the label says 6/4, the plot is correct — it's at 1.

But 6/4 ≠ 1, so this is an error in labeling.

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🛠️ Conclusion: Error in Answer Key

There is a mistake in the last row:

| Circle | Fraction | Number Line |
|-------|----------|-------------|
| 4 parts, all shaded | Should be 4/4 = 1 | Dot at 1 → Correct |

But the answer key says 6/4, which is impossible because:
- You can’t have 6 shaded parts in a 4-part circle.
- 6/4 = 1.5 > 1, can’t be plotted on [0,1].

So the correct fraction should be 4/4, and the label is wrong.

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✔ Final Answer Summary:

| Row | Figure | Correct Fraction | Plot Location | Comment |
|-----|--------|------------------|----------------|---------|
| 1 | 1/6 | ✔ | ✔ | Correct |
| 2 | 1/3 | ✔ | ✔ | Correct |
| 3 | 4/5 | ✔ | ✔ | Correct |
| 4 | 5/8 | ✔ | ✔ | Correct |
| 5 | 3/4 | ✔ | ✔ | Correct |
| 6 | 4/4 = 1 | ✘ Labeled as 6/4 | ✔ Plotted at 1 | Error in labeling |

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✔ Corrected Answer for Last Row:

- Fraction: $ \frac{4}{4} $
- Number line: Plot at 1 (which is correct)
- Answer key error: Should say $ \frac{4}{4} $, not $ \frac{6}{4} $

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💡 Teaching Tip:

When a circle is fully shaded, the fraction is always 1, regardless of how many parts it’s divided into (as long as all parts are shaded).

So even if it's divided into 4 parts, all shaded → $ \frac{4}{4} = 1 $

Similarly, 5/5 = 1, 8/8 = 1, etc.

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✔ Final Note:

The worksheet is mostly correct, but the last row has a labeling error. The plot is correct, but the fraction written is wrong.

✔ Corrected Answer Key (Last Row):
- Fraction: $ \frac{4}{4} $
- Plot: At 1 on the number line.

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