Calculate Failed Students: 50% of 48 Eighth Graders in Math Test

Q: Why can't I just calculate 50% of 48 for the failed students?

Because the problem says 50% passed, not failed! You need to calculate the passed students first: $ 48 \times 0.50 = 24 $ passed, then subtract to find failed.

Q: What if the passing percentage wasn't 50%?

Same method! If 60% passed, calculate $ 48 \times 0.60 = 28.8 $ passed, then $ 48 - 28.8 = 19.2 $ failed. Always subtract from the total.

Q: How do I convert percentages to decimals?

Divide by 100! Move the decimal point two places left: 50% = 0.50, 25% = 0.25, 75% = 0.75. Then multiply by your total.

Q: What if my answer isn't a whole number?

That's fine for most problems! But if counting people, check your work - you usually can't have partial students. Round appropriately or re-check your calculations.

Percentage Problems with Complementary Groups

50% of the 48 students in an eighth grade class passed their math test. How many students failed?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine the number students who failed the test

00:05 The total number of students according to the data

00:12 The percentage of students who passed according to the data

00:24 Subtract this percentage from 100% in order to determine the percentage of students who failed the test

00:29 This is the percentage of students who failed the test

00:49 The number of students who failed is equal to the number of students who passed

00:59 Therefore divide the total number of students by 2 in order to determine the number of students who failed

01:04 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

50% of the 48 students in an eighth grade class passed their math test. How many students failed?

Step-by-step solution

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

Step 1: Identify the percentage of students who passed the test and calculate their number.
Step 2: Find the number of students who failed by subtracting the number of students who passed from the total number of students.

Now, let's work through each step:
Step 1: We know 50% of the 48 students passed. To calculate this, convert 50% to a decimal by dividing by 100, giving us 0.50.
Multiply by the total number of students: $48 \times 0.50 = 24$
This means 24 students passed the test.

Step 2: To find how many students failed, subtract the number of students who passed from the total number of students:
$48 - 24 = 24$

Therefore, the number of students who failed the test is $24$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Find one group first, then subtract from total
Technique: Calculate $48 \times 0.50 = 24$ passed, then subtract
Check: Verify passed + failed equals total: 24 + 24 = 48 ✓

Common Mistakes

Avoid these frequent errors

Calculating the failed percentage directly instead of finding passed first
Don't try to find 50% who failed directly = wrong group! The problem states 50% passed, not failed. Always identify which group the percentage describes first, then find the complementary group by subtraction.

Practice Quiz

Test your knowledge with interactive questions

Convert the fraction into a percentage:

$\frac{24}{100}=\text{?}$

FAQ

Everything you need to know about this question

Why can't I just calculate 50% of 48 for the failed students?

Because the problem says 50% passed, not failed! You need to calculate the passed students first: $48 \times 0.50 = 24$ passed, then subtract to find failed.

Is there a faster way to solve this?

Yes! Since 50% passed and 50% failed (they add to 100%), you can calculate either group directly. But always read carefully to see which percentage the problem gives you.

What if the passing percentage wasn't 50%?

Same method! If 60% passed, calculate $48 \times 0.60 = 28.8$ passed, then $48 - 28.8 = 19.2$ failed. Always subtract from the total.

How do I convert percentages to decimals?

Divide by 100! Move the decimal point two places left: 50% = 0.50, 25% = 0.25, 75% = 0.75. Then multiply by your total.

What if my answer isn't a whole number?

That's fine for most problems! But if counting people, check your work - you usually can't have partial students. Round appropriately or re-check your calculations.

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