Calculate 40% of 20: Step-by-Step Percentage Solution

Q: Why do I divide by 100 to convert percentages?

Percent means 'per hundred', so 40% literally means 40 out of 100. When we write $ \frac{40}{100} = 0.4 $, we're showing this relationship as a decimal.

Q: Can I use fractions instead of decimals?

Absolutely! You can calculate $ \frac{40}{100} \times 20 = \frac{800}{100} = 8 $. Both methods give the same answer - use whichever feels easier!

Q: What if the percentage is bigger than 100%?

The same rule applies! For example, 150% of 20 means $ 1.5 \times 20 = 30 $. Your answer will just be larger than the original number.

Q: How can I check if 8 is really 40% of 20?

Work backwards: $ \frac{8}{20} = 0.4 $, and $ 0.4 \times 100 = 40\% $. If you get back to your original percentage, you're correct!

Q: Is there a shortcut for easy percentages?

Yes! For 50%, divide by 2. For 25%, divide by 4. For 10%, divide by 10. But for other percentages like 40%, the decimal method is most reliable.

Percentage Calculations with Decimal Conversion

Calculate 40% of 20:

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:02 Let's find forty percent of twenty.

00:06 First, convert forty percent to a fraction.

00:12 This is the same as saying forty over one hundred.

00:20 Now, multiply this fraction by twenty.

00:31 Simplify by breaking it into factors and reducing.

00:40 And there you have it, that's our solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate 40% of 20:

Step-by-step solution

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

Step 1: Convert the percentage to a decimal.
Step 2: Multiply the decimal by the given whole number.

Let's go through each step with detailed explanation:

Step 1: The percentage given is 40%. To convert this to a decimal, we divide by 100:
$\frac{40}{100} = 0.4$ .

Step 2: Multiply the decimal (0.4) by the whole number (20).
$0.4 \times 20 = 8$ .

Therefore, 40% of 20 is 8.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Convert percentage to decimal by dividing by 100
Technique: Multiply decimal by whole number: 0.4 × 20 = 8
Check: Verify by converting back: 8 ÷ 20 = 0.4 = 40% ✓

Common Mistakes

Avoid these frequent errors

Multiplying by the percentage number directly
Don't multiply 40 × 20 = 800! This skips the crucial conversion step and gives a result that's 100 times too large. Always convert the percentage to a decimal first by dividing by 100.

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 to convert percentages?

Percent means 'per hundred', so 40% literally means 40 out of 100. When we write $\frac{40}{100} = 0.4$ , we're showing this relationship as a decimal.

Can I use fractions instead of decimals?

Absolutely! You can calculate $\frac{40}{100} \times 20 = \frac{800}{100} = 8$ . Both methods give the same answer - use whichever feels easier!

What if the percentage is bigger than 100%?

The same rule applies! For example, 150% of 20 means $1.5 \times 20 = 30$ . Your answer will just be larger than the original number.

How can I check if 8 is really 40% of 20?

Work backwards: $\frac{8}{20} = 0.4$ , and $0.4 \times 100 = 40\%$ . If you get back to your original percentage, you're correct!

Is there a shortcut for easy percentages?

Yes! For 50%, divide by 2. For 25%, divide by 4. For 10%, divide by 10. But for other percentages like 40%, the decimal method is most reliable.

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