Calculate Percentage: Converting 15 over 75 to Percent Form

Q: Should I simplify the fraction before converting to percentage?

Yes! Simplifying $ \frac{15}{75} $ to $ \frac{1}{5} $ makes the calculation much easier. It's faster to calculate 1 ÷ 5 = 0.2 than 15 ÷ 75.

Q: Why do we multiply by 100 to get percentage?

Percentage means "per hundred" or "out of 100." When you multiply a decimal by 100, you're converting it to show how many parts out of 100, which is what percentage represents.

Q: How can I check if my percentage is reasonable?

Ask yourself: "Is 15 about one-fifth of 75?" Since 75 ÷ 5 = 15, yes! One-fifth equals 20%, so our answer makes sense.

Q: What's the difference between 0.2 and 20%?

They represent the same value in different forms! 0.2 is the decimal form, while 20% is the percentage form. Think of it as $ 0.2 = \frac{20}{100} = 20\% $.

Fraction to Percentage with Simplification

What is the percentage of 15 over 75?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's calculate 15 as a percentage of 75.

00:09 We'll use the percentage formula.

00:14 First, divide 15 by 75, then multiply by 100.

00:19 Think of 75 as 15 times 5.

00:25 Simplify the division wherever you can.

00:31 And that's how you find the percentage!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What is the percentage of 15 over 75?

Step-by-step solution

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

Step 1: Calculate the fraction of 15 relative to 75.
Step 2: Convert this fraction to a percentage by multiplying by 100.

Let's proceed with these steps:
Step 1: We calculate the fraction: $\frac{15}{75}$ . This simplifies to $\frac{1}{5}$ (since 15 divided by 75 gives us 0.2).
Step 2: We convert this fraction into a percentage: $\frac{1}{5} \times 100\% = 20\%$ .

Therefore, the percentage of 15 over 75 is 20%.

Final Answer

20%

Key Points to Remember

Essential concepts to master this topic

Rule: Divide numerator by denominator, then multiply by 100
Technique: Simplify first: $\frac{15}{75} = \frac{1}{5} = 0.2$
Check: Verify 20% of 75 equals 15: 0.20 × 75 = 15 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply by 100
Don't stop at the decimal 0.2 = 2%! This gives a percentage that's 10 times too small. The decimal 0.2 represents the fraction, not the percentage. Always multiply by 100 to convert decimal to percentage: 0.2 × 100 = 20%.

Practice Quiz

Test your knowledge with interactive questions

Convert the fraction $\frac{75}{100}$

to a percentage:

FAQ

Everything you need to know about this question

Should I simplify the fraction before converting to percentage?

Yes! Simplifying $\frac{15}{75}$ to $\frac{1}{5}$ makes the calculation much easier. It's faster to calculate 1 ÷ 5 = 0.2 than 15 ÷ 75.

What if I can't simplify the fraction easily?

That's okay! You can always divide the numerator by the denominator directly. For example, 15 ÷ 75 = 0.2, then multiply by 100 to get 20%.

Why do we multiply by 100 to get percentage?

Percentage means "per hundred" or "out of 100." When you multiply a decimal by 100, you're converting it to show how many parts out of 100, which is what percentage represents.

How can I check if my percentage is reasonable?

Ask yourself: "Is 15 about one-fifth of 75?" Since 75 ÷ 5 = 15, yes! One-fifth equals 20%, so our answer makes sense.

What's the difference between 0.2 and 20%?

They represent the same value in different forms! 0.2 is the decimal form, while 20% is the percentage form. Think of it as $0.2 = \frac{20}{100} = 20\%$ .

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