Calculate 50% of 32: Finding Boys in a Classroom Problem

Q: Why do I divide by 100 when calculating percentages?

Percent means 'per hundred'! So 50% means 50 out of 100, which equals $ \frac{50}{100} = 0.5 $. This converts the percentage to a decimal you can multiply with.

Q: Can I solve this problem without converting to decimals?

Yes! You can keep it as a fraction: $ \frac{50}{100} \times 32 = \frac{1600}{100} = 16 $. Both methods give the same answer.

Q: How do I know if 50% means half?

50% always equals half because 50 is half of 100! So 50% of any number is the same as dividing that number by 2: $ 32 ÷ 2 = 16 $.

Q: What if the percentage isn't a nice round number?

The same method works! For example, 25% of 32 would be $ \frac{25}{100} \times 32 = 0.25 \times 32 = 8 $. Just be careful with your decimal calculations.

Q: How can I check my percentage calculations?

Use the reverse calculation! If 16 boys is 50% of the class, then $ \frac{16}{32} \times 100\% = 50\% $ ✓

Percentage Calculations with Real-World Applications

There are 32 children in a class, 50% of whom are boys.

How many boys are there in the class in total?

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

There are 32 children in a class, 50% of whom are boys.

How many boys are there in the class in total?

Step-by-step solution

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

Step 1: Identify the given information.
Step 2: Apply the appropriate percentage calculation.
Step 3: Perform the mathematical operations.

Now, let's work through each step:

Step 1: The total number of children in the class is 32, and 50% of these children are boys.

Step 2: We need to find 50% of 32. This can be calculated by using the formula for percentage:

$\text{Number of boys} = \left(\frac{50}{100}\right) \times 32$

Step 3: Simplify the calculation:

$\frac{50}{100} = 0.5$

Thus, the calculation becomes:

$0.5 \times 32 = 16$

Therefore, the solution to the problem is that there are 16 boys in the class.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Percentage = (percentage rate ÷ 100) × total quantity
Technique: Convert 50% to 0.5, then multiply: 0.5 × 32 = 16
Check: Verify 16 boys + 16 girls = 32 total children ✓

Common Mistakes

Avoid these frequent errors

Confusing percentage with the actual number
Don't think 50% means 50 children = wrong answer of 50! The percentage is the rate, not the quantity. Always convert the percentage to a decimal first, then multiply by the 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 do I divide by 100 when calculating percentages?

Percent means 'per hundred'! So 50% means 50 out of 100, which equals $\frac{50}{100} = 0.5$ . This converts the percentage to a decimal you can multiply with.

Can I solve this problem without converting to decimals?

Yes! You can keep it as a fraction: $\frac{50}{100} \times 32 = \frac{1600}{100} = 16$ . Both methods give the same answer.

How do I know if 50% means half?

50% always equals half because 50 is half of 100! So 50% of any number is the same as dividing that number by 2: $32 ÷ 2 = 16$ .

What if the percentage isn't a nice round number?

The same method works! For example, 25% of 32 would be $\frac{25}{100} \times 32 = 0.25 \times 32 = 8$ . Just be careful with your decimal calculations.

How can I check my percentage calculations?

Use the reverse calculation! If 16 boys is 50% of the class, then $\frac{16}{32} \times 100\% = 50\%$ ✓

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