Calculate the Percentage: What is 25 out of 125?

Q: Why do I multiply by 100 at the end?

Multiplying by 100 converts the decimal to a percentage. The decimal 0.2 means "2 out of 10" but 20% means "20 out of 100" - they're the same value, just different ways to express it!

Q: What if I get a decimal that doesn't end cleanly?

That's normal! Just round to a reasonable number of decimal places (usually 1-2 places). For example, 0.333... becomes 33.3%.

Q: Can the percentage be over 100%?

Yes! If the part is larger than the whole, you'll get over 100%. For example, 150 out of 100 = 150%. But in this problem, 25 is smaller than 125, so we expect under 100%.

Q: Is there a shortcut when the numbers divide evenly?

Absolutely! Since 125 = 5 × 25, you can see that 25 is 1/5 of 125. And 1/5 = 0.2 = 20%. This mental math can save time!

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

Think logically: 25 is about 1/4 of 125 (since 125 ÷ 4 ≈ 31). So 25 should be slightly less than 25%, making 20% a reasonable answer.

Percentage Calculations with Simple Division

What is the percentage of 25 over 125?

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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 125

00:05 Apply the formula for calculating percentages

00:10 Divide one number by the other and proceed to multiply by 100

00:15 Break down 125 into factors of 25 and 5

00:25 Break down 100 into factors of 25 and 4

00:35 Reduce wherever possible

00:47 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What is the percentage of 25 over 125?

Step-by-step solution

To solve the problem of finding what percentage 25 is of 125, we will use the following formula:

$\text{Percentage} = \left(\frac{\text{Part}}{\text{Whole}}\right) \times 100$

Let's perform the necessary calculations:

First, divide 25 by 125:

$\frac{25}{125} = 0.2$

Next, convert this fraction to a percentage by multiplying by 100:

$0.2 \times 100 = 20\%$

Therefore, the percentage of 25 over 125 is $20\%$ .

Final Answer

20%

Key Points to Remember

Essential concepts to master this topic

Formula: Percentage = (Part ÷ Whole) × 100
Technique: First divide: 25 ÷ 125 = 0.2, then multiply by 100
Check: Work backwards: 20% of 125 = 0.2 × 125 = 25 ✓

Common Mistakes

Avoid these frequent errors

Dividing whole by part instead of part by whole
Don't calculate 125 ÷ 25 = 5, then 500%! This reverses the relationship and gives an impossibly large percentage. Always divide the smaller number (part) by the larger number (whole) first.

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 multiply by 100 at the end?

Multiplying by 100 converts the decimal to a percentage. The decimal 0.2 means "2 out of 10" but 20% means "20 out of 100" - they're the same value, just different ways to express it!

What if I get a decimal that doesn't end cleanly?

That's normal! Just round to a reasonable number of decimal places (usually 1-2 places). For example, 0.333... becomes 33.3%.

Can the percentage be over 100%?

Yes! If the part is larger than the whole, you'll get over 100%. For example, 150 out of 100 = 150%. But in this problem, 25 is smaller than 125, so we expect under 100%.

Is there a shortcut when the numbers divide evenly?

Absolutely! Since 125 = 5 × 25, you can see that 25 is 1/5 of 125. And 1/5 = 0.2 = 20%. This mental math can save time!

How do I check if my percentage is reasonable?

Think logically: 25 is about 1/4 of 125 (since 125 ÷ 4 ≈ 31). So 25 should be slightly less than 25%, making 20% a reasonable answer.

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