Calculate Survey Completion: Finding Percentage of 35 out of 49 Responses

Q: Why do I multiply by 100 at the end?

Multiplying by 100 converts your decimal to a percentage. The decimal 0.714 means the same thing as 71.4%, but percentages are easier to understand and compare!

Q: Should I round 71.43% to 71% or 72%?

Since the question asks for an approximate percentage, 71% is the correct answer. The decimal 0.7143 is closer to 0.71 than 0.72.

Q: Can I use cross-multiplication for percentage problems?

Yes! Set up the proportion: $\frac{35}{49} = \frac{x}{100}$. Cross-multiply to get 35 × 100 = 49 × x, so x = 71.43%.

Q: How do I check if 71% is reasonable?

Think logically: 35 out of 49 is more than half but not close to all 49, so the percentage should be between 50% and 100%. 71% fits perfectly!

Q: What's the difference between 35/49 and 49/35?

35/49 = What fraction Dan completed (0.714 or 71%)49/35 = How many times bigger the total is than completed (1.4 times)For percentages, always use part/whole!

Percentage Calculations with Survey Data

Dan is doing a project in which he must conduct a survey among 49 people.

So far, 35 people have responded to the survey.

Approximately what percentage of the project has Dan completed?

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Dan is doing a project in which he must conduct a survey among 49 people.

So far, 35 people have responded to the survey.

Approximately what percentage of the project has Dan completed?

Step-by-step solution

To determine the percentage of the project that Dan has completed, we'll perform the following steps:

Step 1: Recognize the total number of survey responses that Dan has received: 35 out of 49.
Step 2: Apply the percentage formula: $\text{Percentage Completed} = \left(\frac{35}{49}\right) \times 100\%$ .
Step 3: Calculate the fraction: $\frac{35}{49} = 0.7142857$ (approximate).
Step 4: Convert this decimal to a percentage: $0.7142857 \times 100 \approx 71.42857\%$ .
Step 5: Round the result if necessary to obtain a whole number percentage. In this case, $71.42857\%$ rounds to $71\%$ .

Therefore, the approximate percentage of the project that Dan has completed is $\textbf{71\%}$ .

Final Answer

71%

Key Points to Remember

Essential concepts to master this topic

Formula: Percentage = (Part/Whole) × 100%
Technique: Calculate 35/49 = 0.714, then multiply by 100
Check: 71% of 49 should equal approximately 35 people ✓

Common Mistakes

Avoid these frequent errors

Dividing whole by part instead of part by whole
Don't calculate 49/35 = 1.4 × 100 = 140%! This gives an impossible percentage over 100% because you're finding how many times the part fits into the whole. Always divide part by whole: 35/49 for correct percentage.

Practice Quiz

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Approximately what is $\frac{6}{25}$ as a percentage?

FAQ

Everything you need to know about this question

Why do I multiply by 100 at the end?

Multiplying by 100 converts your decimal to a percentage. The decimal 0.714 means the same thing as 71.4%, but percentages are easier to understand and compare!

Should I round 71.43% to 71% or 72%?

Since the question asks for an approximate percentage, 71% is the correct answer. The decimal 0.7143 is closer to 0.71 than 0.72.

What if the numbers don't divide evenly?

That's totally normal! Most real-world percentages result in decimals. Use your calculator to get the decimal, then round appropriately based on what the question asks for.

Can I use cross-multiplication for percentage problems?

Yes! Set up the proportion: $\frac{35}{49} = \frac{x}{100}$ . Cross-multiply to get 35 × 100 = 49 × x, so x = 71.43%.

How do I check if 71% is reasonable?

Think logically: 35 out of 49 is more than half but not close to all 49, so the percentage should be between 50% and 100%. 71% fits perfectly!

What's the difference between 35/49 and 49/35?

35/49 = What fraction Dan completed (0.714 or 71%)
49/35 = How many times bigger the total is than completed (1.4 times)

For percentages, always use part/whole!

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