Convert the Fraction 25/75 to a Percentage

Q: Why do I need to simplify 25/75 before converting?

Simplifying makes the math much easier! Instead of dividing 25 by 75, you divide 1 by 3. Smaller numbers mean fewer calculation errors and cleaner results.

Q: How do I know when to stop the decimal?

For $ \frac{1}{3} $, the decimal repeats forever (0.333...). In percentages, we usually round to two decimal places, so 33.33% is perfect!

Q: Can I just multiply 25/75 by 100 directly?

Yes, but it's harder! You'd calculate $ \frac{25 \times 100}{75} = \frac{2500}{75} $. That's more work than simplifying first to get $ \frac{1}{3} \times 100 $.

Q: What if my calculator shows 33.333333?

That's normal! The 3s repeat forever. For most problems, 33.33% is the correct answer. Some teachers might want 33⅓% (with the fraction symbol).

Q: How can I check if 33.33% is right?

Convert back: 33.33% = 0.3333, and $ \frac{25}{75} = 0.3333 $. They match! Or notice that 25 is exactly one-third of 75, and one-third equals 33.33%.

Fraction to Percentage with Simplification

Calculate 25 over 75 as a percentage:

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate 25 as a percentage of 75

00:03 In order to determine what percentage one number is of another

00:08 Divide the number by the second number, and multiply by 100

00:16 Break down 75 into factors of 25 and 3

00:21 Simplify wherever possible

00:30 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate 25 over 75 as a percentage:

Step-by-step solution

To convert the fraction $\frac{25}{75}$ to a percentage, we follow these steps:

Step 1: Identify the given fraction, which is $\frac{25}{75}$ .
Step 2: Simplify the fraction, if possible. Since both 25 and 75 are divisible by 25, simplify to $\frac{1}{3}$ .
Step 3: Use the percentage conversion formula:
$\frac{\text{Numerator}}{\text{Denominator}} \times 100\%$ .
Step 4: Apply the formula:
$\frac{1}{3} \approx 0.3333$ . Multiply by 100 to convert to a percentage: $0.3333 \times 100 = 33.33\%.$

Therefore, the solution to the problem is 33.33%.

Final Answer

33.33%

Key Points to Remember

Essential concepts to master this topic

Simplification: Reduce fractions first to make calculations easier
Technique: Divide numerator by denominator, then multiply by 100: 25÷75×100
Check: Verify 33.33% equals original fraction: 33.33/100 = 1/3 = 25/75 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to simplify the fraction first
Don't work with 25/75 directly without simplifying = harder calculations and more chance for errors! Working with large numbers increases mistakes. Always simplify to 1/3 first, then convert to get cleaner decimals.

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 need to simplify 25/75 before converting?

Simplifying makes the math much easier! Instead of dividing 25 by 75, you divide 1 by 3. Smaller numbers mean fewer calculation errors and cleaner results.

How do I know when to stop the decimal?

For $\frac{1}{3}$ , the decimal repeats forever (0.333...). In percentages, we usually round to two decimal places, so 33.33% is perfect!

Can I just multiply 25/75 by 100 directly?

Yes, but it's harder! You'd calculate $\frac{25 \times 100}{75} = \frac{2500}{75}$ . That's more work than simplifying first to get $\frac{1}{3} \times 100$ .

What if my calculator shows 33.333333?

That's normal! The 3s repeat forever. For most problems, 33.33% is the correct answer. Some teachers might want 33⅓% (with the fraction symbol).

How can I check if 33.33% is right?

Convert back: 33.33% = 0.3333, and $\frac{25}{75} = 0.3333$ . They match! Or notice that 25 is exactly one-third of 75, and one-third equals 33.33%.

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