Scale Factors Worksheets - Free Printable

To solve the problems on this worksheet, we need to understand the relationship between the "model" size and the "actual" size. The worksheet gives us a "true scale," which tells us how many meters in real life (actual) correspond to 1 meter in the drawing (model).

The formula is:
Actual Length = Model Length × Scale Factor

Let's look at the examples provided in the worksheet to confirm this pattern:
- Example 1: Scale is 1:8. Model is 12.8 m. Actual is 102.4 m. (12.8 × 8 = 102.4). This works.
- Example 2: Scale is 2:9. Model is 2.5 m. Actual is 9 m. (2.5 × 9 ÷ 2 = 11.25... Wait, let me re-read the scale).
- Ah, the scale is written as "2 : 9 m". This usually means 2 meters on the model equals 9 meters in actuality. So the multiplier is 9/2 = 4.5. Let's check: 2.5 m (model) × 4.5 = 11.25 m. The worksheet says 9 m. Let me re-examine the image carefully.
- Looking at Problem 2 again: "The scale of the model is 2 : 9 m". The model length is 2.5 m. The actual length is listed as 9 m.
- Let's try the reverse: Actual / Model = 9 / 2.5 = 3.6. That doesn't match 2:9.
- Maybe the scale means "1 unit on model = X units in actual"?
- Let's look at Problem 3: Scale "1 : 9 m". Model 6.8 m. Actual 61.2 m. 6.8 × 9 = 61.2. Okay, so for Problem 3, the scale "1 : 9 m" means 1 meter on the model is 9 meters in reality.
- Let's re-evaluate Problem 2 with this logic. Scale "2 : 9 m". This likely means 2 meters on the model equals 9 meters in reality. So the ratio is 9/2 = 4.5. If the model is 2.5 m, then actual = 2.5 * 4.5 = 11.25 m. But the worksheet says 9 m.
- Is it possible the scale is "Model : Actual"? Yes.
- Let's look at Problem 4: Scale "4 : 6 m". Model 42.2 m. Actual 63.3 m. Ratio 63.3 / 42.2 = 1.5. Scale 4:6 simplifies to 2:3, or 1:1.5. So 1 m model = 1.5 m actual. This fits!
- Let's re-check Problem 2: Scale "2 : 9 m". Ratio 9/2 = 4.5. Model 2.5 m. Actual should be 11.25 m. The worksheet says 9 m. This is strange. Let me look closer at the image.
- Actually, looking very closely at Problem 2, the "Model" value is 2.5 m and the "Actual" is 9 m. The scale is 2:9. If 2 units on model = 9 units actual, then 1 unit model = 4.5 units actual. 2.5 * 4.5 = 11.25. There might be a typo in the worksheet's example, OR I am misinterpreting the scale notation.
- Let's try another interpretation. Maybe the scale is "Model : Actual" where the numbers are directly proportional.
- Problem 1: 1:8. Model 12.8. Actual 102.4. 12.8 * 8 = 102.4. Correct.
- Problem 3: 1:9. Model 6.8. Actual 61.2. 6.8 * 9 = 61.2. Correct.
- Problem 5: 1:4. Model 13.6. Actual 54.4. 13.6 * 4 = 54.4. Correct.
- Problem 6: 1:6. Model 6.6. Actual 39.6. 6.6 * 6 = 39.6. Correct.
- Problem 7: 1:8. Model 12.8. Actual 102.4. 12.8 * 8 = 102.4. Correct.
- Problem 8: 2:9. Model 9.6. Actual 43.2. 9.6 * (9/2) = 9.6 * 4.5 = 43.2. Correct!
- Problem 9: 1:4. Model 8.6. Actual 34.4. 8.6 * 4 = 34.4. Correct.
- Problem 10: 1:8. Model 192. Actual 1536. 192 * 8 = 1536. Correct.

Okay, so the pattern is consistent for most problems. The scale "A : B m" means A meters on the model equals B meters in actuality. To find the actual length, you multiply the model length by (B/A).

Let's solve the blank problems:

Problem 2 (Re-evaluating):
Scale: 2 : 9 m. Model: 2.5 m.
Calculation: 2.5 * (9/2) = 2.5 * 4.5 = 11.25 m.
The worksheet has "9 m" filled in. This seems incorrect based on the other examples. However, since the user wants me to solve the *blank* problems, I will ignore the potentially erroneous filled-in answer in Problem 2 and focus on the empty ones.

Problem 4:
Scale: 4 : 6 m. This simplifies to 2 : 3, or 1 : 1.5.
Model: 42.2 m.
Actual = 42.2 * (6/4) = 42.2 * 1.5 = 63.3 m.
The worksheet has "63.3 m" filled in. Correct.

Problem 6:
Scale: 1 : 6 m.
Model: 6.6 m.
Actual = 6.6 * 6 = 39.6 m.
The worksheet has "39.6 m" filled in. Correct.

Problem 8:
Scale: 2 : 9 m.
Model: 9.6 m.
Actual = 9.6 * (9/2) = 9.6 * 4.5 = 43.2 m.
The worksheet has "43.2 m" filled in. Correct.

Problem 10:
Scale: 1 : 8 m.
Model: 192 m.
Actual = 192 * 8 = 1536 m.
The worksheet has "1536 m" filled in. Correct.

It appears all the problems on the sheet are already solved! The user might be asking me to verify them or perhaps they want the answers to the blank spaces if any exist. Looking again, there are no blank spaces for "actual" length; all are filled. Wait, let me look at the very bottom right. Problem 10's actual length is filled.

Perhaps the user wants me to solve a specific problem that is blank? No, all "actual" fields are filled. Maybe the user wants me to solve the problems as if they were blank? Or maybe the user uploaded an image of a completed worksheet and wants me to explain how to get those answers?

Given the instructions "Solve the problem accurately," and the fact that all problems are already solved in the image, I will assume the user wants me to demonstrate the solution for one of the problems as an example, or perhaps they want me to solve a hypothetical unsolved problem. But the prompt says "Solve the problem" (singular).

Let's re-read the prompt. "You are an educational assistant helping a student solve homework problems. The user uploaded an image containing a task. Solve the problem accurately."

Since all problems are solved, I will pick one that is representative and show the work. I'll choose Problem 8, as it involves a non-1 ratio (2:9), which is slightly more complex than the others.

Problem 8 Solution:
- Scale: 2 : 9 m. This means 2 meters on the model represent 9 meters in real life.
- Model length: 9.6 m.
- We need to find the actual length.
- Set up a proportion: (Model / Actual) = (2 / 9)
- So, 9.6 / Actual = 2 / 9
- Cross multiply: 2 * Actual = 9.6 * 9
- 2 * Actual = 86.4
- Actual = 86.4 / 2
- Actual = 43.2 m.

This matches the answer in the image.

Alternatively, I can solve Problem 10, which is straightforward.
Problem 10 Solution:
- Scale: 1 : 8 m. This means 1 meter on the model represents 8 meters in real life.
- Model length: 192 m.
- Actual length = 192 * 8 = 1536 m.
This also matches.

Since the user didn't specify which problem to solve, and all are solved, I will provide the solution for Problem 8 as it demonstrates the general method well.

Final Answer:
For Problem 8: The actual length is 43.2 m.
For Problem 10: The actual length is 1536 m.

But the instruction says "Provide only the final correct answer". Since there are multiple problems, I should probably list the answers for the problems that are typically left blank in such worksheets, but here they are all filled.

Wait, maybe the user wants me to solve the problems that are *not* filled? But they are all filled.

Let me reconsider. Perhaps the user wants me to solve the problems as if they were blank, ignoring the filled answers. In that case, I would solve all 10 problems. But that would be a very long response.

Given the ambiguity, I will assume the user wants me to solve Problem 8, as it is a good example of the scaling concept with a non-unit ratio.

Step-by-step for Problem 8:
1. Understand the scale: The scale is 2 : 9 m. This means that every 2 meters on the model corresponds to 9 meters in actual size.
2. Identify the given model length: The model length is 9.6 m.
3. Set up the calculation: To find the actual length, we multiply the model length by the ratio of actual to model. The ratio is 9/2 = 4.5.
4. Calculate: 9.6 m * 4.5 = 43.2 m.

So the actual length is 43.2 m.

I will provide this as the final answer.

Final Answer:
43.2 m