Calculate 50% of 48: Finding Successful Students in Math Test

Q: Why do I convert 50% to 0.5 instead of just using 50?

Percent means 'per hundred' - so 50% = 50 out of 100 = $\frac{50}{100}$ = 0.5. Using 50 directly would give you 50 × 48 = 2,400 students, which is impossible!

Q: Is there a faster way to find 50% of any number?

Yes! Since 50% = $\frac{1}{2}$, you can simply divide by 2. So 50% of 48 = 48 ÷ 2 = 24. This works because half of anything is that number divided by 2.

Q: How can I check if 24 students is the right answer?

Several ways to verify: (1) 24 + 24 = 48 (half + half = whole), (2) 24 ÷ 48 = 0.5 = 50%, or (3) Think logically: if half the class passed, that should be about half of 48, which is 24!

Q: Can the number of successful students be a fraction?

In real-life problems about people, we usually round to whole numbers since you can't have half a student! But in math problems, fractional answers are possible depending on the context.

Percentage Calculations with Practical Applications

50% of the 48 students in an eighth grade class were successful on their math test. How many students were successful?

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Step-by-step video solution

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00:00 Determine the number of students who passed their maths test

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

00:15 The percentage of students who passed according to the data

00:25 Convert from a percentage to a fraction

00:29 We'll use the formula to convert the given data from a percentage to a fraction

00:35 Apply the formula to our exercise

00:45 Break down 100 into factors of 2 and 50

00:50 Reduce wherever possible

00:53 This is the percentage now represented in fraction form

00:58 Multiply the fraction by the total number of students in order to determine the total number of students who passed

01:12 This is the solution

Step-by-step written solution

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Understand the problem

50% of the 48 students in an eighth grade class were successful on their math test. How many students were successful?

Step-by-step solution

To solve the problem of finding the number of successful students, we need to follow these steps:

Step 1: Understand that 50% of 48 students were successful.
Step 2: Convert the percentage into a decimal or fraction. Since 50% is equivalent to $\frac{50}{100}$ , we simplify it to $\frac{1}{2}$ .
Step 3: Apply the percentage formula by calculating $\frac{1}{2} \times 48$ .

Now, let's calculate:

$\frac{1}{2} \times 48 = 24$

This calculation shows that 24 students were successful in the math test.

Therefore, the solution to the problem is $24$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Conversion: Change 50% to decimal 0.5 or fraction $\frac{1}{2}$
Technique: Multiply: $\frac{1}{2} \times 48 = 24$ successful students
Check: Verify 24 is half of 48 since 24 + 24 = 48 ✓

Common Mistakes

Avoid these frequent errors

Adding percentage to the original number
Don't add 50 + 48 = 98! This treats percentage as a regular number instead of a portion. Percentage means 'out of 100', so 50% = 50/100 = 0.5. Always multiply the percentage (as decimal) by the total number.

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 convert 50% to 0.5 instead of just using 50?

Percent means 'per hundred' - so 50% = 50 out of 100 = $\frac{50}{100}$ = 0.5. Using 50 directly would give you 50 × 48 = 2,400 students, which is impossible!

Is there a faster way to find 50% of any number?

Yes! Since 50% = $\frac{1}{2}$ , you can simply divide by 2. So 50% of 48 = 48 ÷ 2 = 24. This works because half of anything is that number divided by 2.

What if the percentage isn't 50%? Like 25% or 75%?

Same process! Convert to decimal first: 25% = 0.25, so 25% of 48 = 0.25 × 48 = 12. For 75% = 0.75, so 75% of 48 = 0.75 × 48 = 36. Always convert percentage to decimal first!

How can I check if 24 students is the right answer?

Several ways to verify: (1) 24 + 24 = 48 (half + half = whole), (2) 24 ÷ 48 = 0.5 = 50%, or (3) Think logically: if half the class passed, that should be about half of 48, which is 24!

Can the number of successful students be a fraction?

In real-life problems about people, we usually round to whole numbers since you can't have half a student! But in math problems, fractional answers are possible depending on the context.

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