Calculate Total Students: Converting 240 Girls at 30% to Full Population

Q: Why do I divide by 0.30 instead of multiplying?

Because 240 girls is already 30% of the total! You're working backwards from a part to find the whole. Think: "240 is 30% of what number?" Use division: $ \frac{240}{0.30} = 800 $

Q: How do I remember to convert the percentage correctly?

Always move the decimal point two places left when converting percentages: 30% becomes 0.30, 15% becomes 0.15. Or divide by 100: $ \frac{30}{100} = 0.30 $

Q: What if I get a decimal answer that doesn't make sense for people?

Round to the nearest whole number since you can't have partial students! However, in this problem, $ \frac{240}{0.30} = 800 $ gives us a perfect whole number.

Q: How can I check if my total of 800 is correct?

Calculate 30% of your answer: $ 800 \times 0.30 = 240 $ girls. This matches the given information, so 800 is correct!

Q: What's the difference between 'what percent' and 'percent of what' problems?

This is a "percent of what" problem because you know the part (240) and the percentage (30%), but need the whole. Use: Part ÷ Percentage = Whole

Percentage Problems with Reverse Calculations

The number of female students participating in the 7th grade camp is 240, and their percentage is 30% of all students participating in the camp. Find the number of students (including girls and boys) participating in the summer camp.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Establish the total number of students

00:05 Convert from a percentage to a fraction

00:11 Use the formula to convert percentages to fractions

00:16 Apply this formula to our exercise

00:26 Construct the appropriate equation according to the given data

00:46 Isolate the total number of students

01:26 Break down 240 into factors of 30 and 8

01:36 Reduce wherever possible

01:41 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given information
Step 2: Convert the percentage to a decimal
Step 3: Use the percentage formula
Step 4: Calculate the total number of students

Now, let's work through each step:
Step 1: The problem gives us the number of female students participating in the camp, which is 240.
Step 2: Convert the percentage of females into a decimal: $30\% = \frac{30}{100} = 0.30$ .
Step 3: Apply the formula for total students:
$\text{Total number of students} = \frac{240}{0.30}$
Step 4: Perform the calculation:
$\frac{240}{0.30} = 800$
Thus, the total number of students participating in the summer camp is 800.

Therefore, the solution to the problem is 800.

Final Answer

800

Key Points to Remember

Essential concepts to master this topic

Formula: Total = Part ÷ Percentage (as decimal)
Technique: Convert 30% to 0.30, then divide 240 ÷ 0.30
Check: Multiply back: 800 × 0.30 = 240 girls ✓

Common Mistakes

Avoid these frequent errors

Multiplying instead of dividing by the percentage
Don't multiply 240 × 0.30 = 72 total students! This gives you 30% of 240, not the whole population. The 240 girls already represent 30%, so you need to find what number has 240 as its 30%. Always divide the part by the percentage: 240 ÷ 0.30 = 800.

Practice Quiz

Test your knowledge with interactive questions

Convert the fraction into a percentage:

$\frac{2}{100}=\text{?}$

FAQ

Everything you need to know about this question

Why do I divide by 0.30 instead of multiplying?

Because 240 girls is already 30% of the total! You're working backwards from a part to find the whole. Think: "240 is 30% of what number?" Use division: $\frac{240}{0.30} = 800$

How do I remember to convert the percentage correctly?

Always move the decimal point two places left when converting percentages: 30% becomes 0.30, 15% becomes 0.15. Or divide by 100: $\frac{30}{100} = 0.30$

What if I get a decimal answer that doesn't make sense for people?

Round to the nearest whole number since you can't have partial students! However, in this problem, $\frac{240}{0.30} = 800$ gives us a perfect whole number.

How can I check if my total of 800 is correct?

Calculate 30% of your answer: $800 \times 0.30 = 240$ girls. This matches the given information, so 800 is correct!

What's the difference between 'what percent' and 'percent of what' problems?

This is a "percent of what" problem because you know the part (240) and the percentage (30%), but need the whole. Use: Part ÷ Percentage = Whole

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