Simplify fractions using the highest common factor with this educational worksheet.

To solve this task, we need to simplify each fraction by finding the Highest Common Factor (HCF) of the numerator and denominator, then dividing both by that factor.

Let’s go step by step for a few examples:

---

Example 1: Fraction 4/20

- Numerator = 4, Denominator = 20
- Factors of 4: 1, 2, 4
- Factors of 20: 1, 2, 4, 5, 10, 20
- HCF = 4
- Divide numerator and denominator by 4 → 4÷4 = 1, 20÷4 = 5 → Simplified fraction = 1/5

✔ This matches the example given in the table.

---

Example 2: Fraction 3/9

- Numerator = 3, Denominator = 9
- Factors of 3: 1, 3
- Factors of 9: 1, 3, 9
- HCF = 3
- 3÷3 = 1, 9÷3 = 3 → Simplified fraction = 1/3

---

Example 3: Fraction 6/8

- Numerator = 6, Denominator = 8
- Factors of 6: 1, 2, 3, 6
- Factors of 8: 1, 2, 4, 8
- HCF = 2
- 6÷2 = 3, 8÷2 = 4 → Simplified fraction = 3/4

---

Example 4: Fraction 10/15

- Numerator = 10, Denominator = 15
- Factors of 10: 1, 2, 5, 10
- Factors of 15: 1, 3, 5, 15
- HCF = 5
- 10÷5 = 2, 15÷5 = 3 → Simplified fraction = 2/3

---

Example 5: Fraction 8/16

- Numerator = 8, Denominator = 16
- Factors of 8: 1, 2, 4, 8
- Factors of 16: 1, 2, 4, 8, 16
- HCF = 8
- 8÷8 = 1, 16÷8 = 2 → Simplified fraction = 1/2

---

Example 6: Fraction 10/20

- Numerator = 10, Denominator = 20
- Factors of 10: 1, 2, 5, 10
- Factors of 20: 1, 2, 4, 5, 10, 20
- HCF = 10
- 10÷10 = 1, 20÷10 = 2 → Simplified fraction = 1/2

---

Example 7: Fraction 3/18

- Numerator = 3, Denominator = 18
- Factors of 3: 1, 3
- Factors of 18: 1, 2, 3, 6, 9, 18
- HCF = 3
- 3÷3 = 1, 18÷3 = 6 → Simplified fraction = 1/6

---

Example 8: Fraction 9/12

- Numerator = 9, Denominator = 12
- Factors of 9: 1, 3, 9
- Factors of 12: 1, 2, 3, 4, 6, 12
- HCF = 3
- 9÷3 = 3, 12÷3 = 4 → Simplified fraction = 3/4

---

Example 9: Fraction 12/15

- Numerator = 12, Denominator = 15
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 15: 1, 3, 5, 15
- HCF = 3
- 12÷3 = 4, 15÷3 = 5 → Simplified fraction = 4/5

---

Example 10: Fraction 6/15

- Numerator = 6, Denominator = 15
- Factors of 6: 1, 2, 3, 6
- Factors of 15: 1, 3, 5, 15
- HCF = 3
- 6÷3 = 2, 15÷3 = 5 → Simplified fraction = 2/5

---

Now let’s do the right column:

Example 11: Fraction 15/20

- Numerator = 15, Denominator = 20
- Factors of 15: 1, 3, 5, 15
- Factors of 20: 1, 2, 4, 5, 10, 20
- HCF = 5
- 15÷5 = 3, 20÷5 = 4 → Simplified fraction = 3/4

---

Example 12: Fraction 18/24

- Numerator = 18, Denominator = 24
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- HCF = 6
- 18÷6 = 3, 24÷6 = 4 → Simplified fraction = 3/4

---

Example 13: Fraction 25/30

- Numerator = 25, Denominator = 30
- Factors of 25: 1, 5, 25
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- HCF = 5
- 25÷5 = 5, 30÷5 = 6 → Simplified fraction = 5/6

---

Example 14: Fraction 12/20

- Numerator = 12, Denominator = 20
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 20: 1, 2, 4, 5, 10, 20
- HCF = 4
- 12÷4 = 3, 20÷4 = 5 → Simplified fraction = 3/5

---

Example 15: Fraction 22/33

- Numerator = 22, Denominator = 33
- Factors of 22: 1, 2, 11, 22
- Factors of 33: 1, 3, 11, 33
- HCF = 11
- 22÷11 = 2, 33÷11 = 3 → Simplified fraction = 2/3

---

Example 16: Fraction 27/36

- Numerator = 27, Denominator = 36
- Factors of 27: 1, 3, 9, 27
- Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- HCF = 9
- 27÷9 = 3, 36÷9 = 4 → Simplified fraction = 3/4

---

Example 17: Fraction 45/50

- Numerator = 45, Denominator = 50
- Factors of 45: 1, 3, 5, 9, 15, 45
- Factors of 50: 1, 2, 5, 10, 25, 50
- HCF = 5
- 45÷5 = 9, 50÷5 = 10 → Simplified fraction = 9/10

---

Example 18: Fraction 15/25

- Numerator = 15, Denominator = 25
- Factors of 15: 1, 3, 5, 15
- Factors of 25: 1, 5, 25
- HCF = 5
- 15÷5 = 3, 25÷5 = 5 → Simplified fraction = 3/5

---

Example 19: Fraction 48/60

- Numerator = 48, Denominator = 60
- Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
- Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
- HCF = 12
- 48÷12 = 4, 60÷12 = 5 → Simplified fraction = 4/5

---

Example 20: Fraction 10/15

We already did this one above — it’s 2/3

Wait — actually, looking back at the image, the last fraction is 10/15, which we solved as 2/3. But note: there are two columns. The left has 10 fractions, the right has 10 more? Let me recount from the image description.

Actually, based on standard layout and your upload, here's the full list you likely need to fill:

Left Column Fractions:
1. 4/20 → done (example)
2. 3/9
3. 6/8
4. 10/15
5. 8/16
6. 10/20
7. 3/18
8. 9/12
9. 12/15
10. 6/15

Right Column Fractions:
11. 15/20
12. 18/24
13. 25/30
14. 12/20
15. 22/33
16. 27/36
17. 45/50
18. 15/25
19. 48/60
20. 10/15 ← Wait, duplicate? Probably typo — maybe 10/25 or something else? But since image shows “10/15” again, perhaps it’s intentional. We’ll keep it as 2/3.

But wait — looking at original user image description, the last fraction in right column is written as “10/15”, but that’s same as #4. Maybe it’s meant to be different? Since I can’t see the actual image clearly beyond text, I’ll assume all listed are correct as per common worksheets.

Alternatively, perhaps the last one is “10/25”? Let me check typical patterns.

Actually, re-examining the initial prompt’s image transcription:

In the right column, after 48/60, it says “10/15” — but that might be a misread. In many such sheets, the last one is often 10/25 or similar. However, since the instruction says “do not describe the image”, and we must rely on what was transcribed, I will proceed with the values provided.

But to avoid duplication error, let me double-check the original problem statement.

Looking back: the user wrote:

> ...and so on... until 10/15 at the end.

Actually, no — in the initial message, the fractions listed are:

From top to bottom, left column:

4/20 (done), 3/9, 6/8, 10/15, 8/16, 10/20, 3/18, 9/12, 12/15, 6/15

Right column:

15/20, 18/24, 25/30, 12/20, 22/33, 27/36, 45/50, 15/25, 48/60, 10/15

Yes, 10/15 appears twice — once in left (#4) and once in right (#20). That’s unusual but possible. Perhaps it’s intentional for repetition practice.

So we’ll compute both as 2/3.

---

Final compiled answers:

Left Column:

| Fraction | HCF | Simplified |
|----------|-----|------------|
| 4/20 | 4 | 1/5 |
| 3/9 | 3 | 1/3 |
| 6/8 | 2 | 3/4 |
| 10/15 | 5 | 2/3 |
| 8/16 | 8 | 1/2 |
| 10/20 | 10 | 1/2 |
| 3/18 | 3 | 1/6 |
| 9/12 | 3 | 3/4 |
| 12/15 | 3 | 4/5 |
| 6/15 | 3 | 2/5 |

Right Column:

| Fraction | HCF | Simplified |
|----------|-----|------------|
| 15/20 | 5 | 3/4 |
| 18/24 | 6 | 3/4 |
| 25/30 | 5 | 5/6 |
| 12/20 | 4 | 3/5 |
| 22/33 | 11 | 2/3 |
| 27/36 | 9 | 3/4 |
| 45/50 | 5 | 9/10 |
| 15/25 | 5 | 3/5 |
| 48/60 | 12 | 4/5 |
| 10/15 | 5 | 2/3 |

All calculations verified.

Final Answer:
The completed table with Highest Common Factors and Simplified Fractions is as calculated above. For brevity and clarity, here is the final answer formatted as requested:

Since the question asks to "solve the problem" and the problem is to fill the table, and we’ve done so accurately, the final output should reflect the key results.

But per instructions: “Provide only the final correct answer — this should come AFTER all explanations and reasoning.”

However, since the answer is a filled table, and we cannot display tables easily in plain text without formatting, and the instruction says “only the final correct answer”, I will summarize the simplified fractions in order as they appear in the worksheet, assuming the student needs to write them in the blank cells.

Thus, listing the simplified fractions in sequence (left column first, then right):

Left Column Simplified Fractions (after first row):
1/3, 3/4, 2/3, 1/2, 1/2, 1/6, 3/4, 4/5, 2/5

Right Column Simplified Fractions:
3/4, 3/4, 5/6, 3/5, 2/3, 3/4, 9/10, 3/5, 4/5, 2/3

But to match exact expectation, perhaps just state the method and confirm correctness.

Given constraints, and since the user didn't specify how to present the answer, I'll provide the final simplified fractions in order as blanks to fill.

Final Answer:
For the left column (excluding first row): 1/3, 3/4, 2/3, 1/2, 1/2, 1/6, 3/4, 4/5, 2/5
For the right column: 3/4, 3/4, 5/6, 3/5, 2/3, 3/4, 9/10, 3/5, 4/5, 2/3

But to make it clean and direct:

Final Answer:
[1/3, 3/4, 2/3, 1/2, 1/2, 1/6, 3/4, 4/5, 2/5] for left; [3/4, 3/4, 5/6, 3/5, 2/3, 3/4, 9/10, 3/5, 4/5, 2/3] for right

However, since the system expects a single boxed answer, and this is a multi-part task, I think the best approach is to recognize that the core task is understanding the process, and the final answer is the set of simplified fractions.

But per strict instruction: “ONLY THEN provide the final answer” — and if multiple parts, still give concise version.

I will now box the entire solution as a summary.

Actually, reconsidering: the problem is to simplify fractions using HCF, and we've shown the work. The final answer expected is likely the completed table entries. Since we can't render table, I'll list them plainly.

Final Answer:
Left Column (rows 2–10): \frac{1}{3}, \frac{3}{4}, \frac{2}{3}, \frac{1}{2}, \frac{1}{2}, \frac{1}{6}, \frac{3}{4}, \frac{4}{5}, \frac{2}{5}
Right Column (all 10 rows): \frac{3}{4}, \frac{3}{4}, \frac{5}{6}, \frac{3}{5}, \frac{2}{3}, \frac{3}{4}, \frac{9}{10}, \frac{3}{5}, \frac{4}{5}, \frac{2}{3}

But to fit in one line as final answer:

Final Answer:
\boxed{\text{See detailed simplifications above}}

No — that violates "only final correct answer".

Perhaps the simplest is to say the process is correct and the answers are as computed.

Given the ambiguity, I'll provide the most critical part: the method is sound, and each fraction is correctly simplified.

But to comply strictly, here is the final answer as a list of simplified fractions in order of appearance in the worksheet (first column down, then second column down), excluding the pre-filled example:

Final Answer:
1/3, 3/4, 2/3, 1/2, 1/2, 1/6, 3/4, 4/5, 2/5, 3/4, 3/4, 5/6, 3/5, 2/3, 3/4, 9/10, 3/5, 4/5, 2/3

This covers 19 entries (since first row is given).

Count: Left has 9 additional, Right has 10, total 19.

Yes.

So:

Final Answer:
\boxed{\dfrac{1}{3},\ \dfrac{3}{4},\ \dfrac{2}{3},\ \dfrac{1}{2},\ \dfrac{1}{2},\ \dfrac{1}{6},\ \dfrac{3}{4},\ \dfrac{4}{5},\ \dfrac{2}{5},\ \dfrac{3}{4},\ \dfrac{3}{4},\ \dfrac{5}{6},\ \dfrac{3}{5},\ \dfrac{2}{3},\ \dfrac{3}{4},\ \dfrac{9}{10},\ \dfrac{3}{5},\ \dfrac{4}{5},\ \dfrac{2}{3}}