Calculate Dance Class Attendance: Solve 16% of 9th Graders Problem

Q: Why can't I just find 16% of the 6 students in acting class?

Because the problem states that 16% of ALL 9th grade students attend dance class, not 16% of just the acting students. You need to find the total number of 9th graders first!

Q: What does 'the rest don't participate' mean for my calculation?

This information helps you verify your answer. If 6 attend acting and 4 attend dance, then 25 - 6 - 4 = 15 students don't participate in either activity.

Q: Should I convert percentages to decimals or keep them as percentages?

Either works! 24% = 0.24 and 16% = 0.16. Many students find decimals easier for division and multiplication calculations.

Q: Can students attend both acting and dance classes?

The problem doesn't mention overlap, so we assume separate groups. In real life, always read carefully to see if students can be in multiple categories!

Percentage Problems with Multiple Step Calculations

Six 9th grade students attend acting classes. They make up 24 percent of the class as a whole.

A further 16% of the 9th grade students attend dance class.

The rest of the students do not participate in any extracurricular classes.

How many students attend the dance class?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 How many students are in the dance class?

00:06 Determine the total number of students

00:32 Convert from percentages to fractions

00:37 Multiply the fraction by the original number of students (X)

00:44 This percentage equals the number of students in the games class (6)

00:49 Multiply by the reciprocal fraction to isolate X

01:13 Simplify wherever possible

01:22 This is the total number of students

01:29 Determine the number of students in the dance class (16%)

01:46 Convert from percentages to fractions, and multiply by the total number of students

01:56 Simplify wherever possible

02:03 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Six 9th grade students attend acting classes. They make up 24 percent of the class as a whole.

A further 16% of the 9th grade students attend dance class.

The rest of the students do not participate in any extracurricular classes.

How many students attend the dance class?

Step-by-step solution

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

Step 1: Determine the total number of students in the class.
Step 2: Calculate how many students attend the dance class.

Now, let's work through each step:
Step 1: We know that 6 students are 24% of the class. We use the formula for determining the whole number from a percentage:

\text{Total number of students} = \frac{\text{Number of students attending acting}}{\text{Percentage}} \times 100 = \frac{6}{0.24} = 25

So, the total number of 9th grade students is 25.

Step 2: Now that we have the total number of students, we can find how many attend the dance class (16% of 25):

\text{Number of students in dance classes} = 0.16 \times 25 = 4

Thus, the number of students attending the dance class is 4 students.

Final Answer

4 students

Key Points to Remember

Essential concepts to master this topic

Finding the Whole: Divide known part by its percentage to find total
Calculation Method: 6 ÷ 0.24 = 25 total students, then 16% × 25
Verification Check: 6 acting + 4 dance = 10 students in activities ✓

Common Mistakes

Avoid these frequent errors

Using 16% of 6 students instead of total
Don't calculate 16% of 6 acting students = 0.96 wrong answer! This ignores that 16% applies to ALL 9th graders, not just acting students. Always find the total number of students first, then calculate the percentage of that total.

Practice Quiz

Test your knowledge with interactive questions

Calculate 30 over 100 as a percentage:

FAQ

Everything you need to know about this question

Why can't I just find 16% of the 6 students in acting class?

Because the problem states that 16% of ALL 9th grade students attend dance class, not 16% of just the acting students. You need to find the total number of 9th graders first!

How do I know if 25 total students is correct?

Check your work: if 6 students represent 24% of the class, then 6 ÷ 0.24 = 25. You can verify: 25 × 0.24 = 6 students ✓

What does 'the rest don't participate' mean for my calculation?

This information helps you verify your answer. If 6 attend acting and 4 attend dance, then 25 - 6 - 4 = 15 students don't participate in either activity.

Should I convert percentages to decimals or keep them as percentages?

Either works! 24% = 0.24 and 16% = 0.16. Many students find decimals easier for division and multiplication calculations.

Can students attend both acting and dance classes?

The problem doesn't mention overlap, so we assume separate groups. In real life, always read carefully to see if students can be in multiple categories!

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