Convert Fraction to Percentage: Calculate 40/80 as a Percentage

Q: Do I always need to simplify the fraction first?

While not required, simplifying first makes the conversion much easier! $ \frac{40}{80} = \frac{1}{2} $ is easier to work with than dealing with larger numbers.

Q: What if the fraction doesn't simplify nicely?

That's okay! Some fractions like $ \frac{1}{3} $ give repeating decimals (33.33...%). You can round to a reasonable number of decimal places.

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

Percentage means "per hundred" or "out of 100". So $ \frac{1}{2} $ becomes $ \frac{50}{100} $ which is 50%.

Fraction to Percentage with Simplification

Calculate 40 over 80 as a percentage:

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate 40 as a percentage of 80

00:04 Apply the formula to calculate percentages

00:10 Divide the first number by the second number and proceed to multiply by 100

00:20 Break down into factors and simplify wherever possible

00:29 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate 40 over 80 as a percentage:

Step-by-step solution

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

Step 1: Calculate the ratio of 40 to 80.
Step 2: Convert the ratio into a percentage.

Now, let's work through each step:
Step 1: Calculate the ratio of 40 to 80:
$\frac{40}{80} = \frac{1}{2}$

Step 2: Convert the ratio into a percentage by multiplying by 100:
$\left(\frac{1}{2}\right) \times 100 = 50\%$

Therefore, the solution to the problem is 50%.

Final Answer

50%

Key Points to Remember

Essential concepts to master this topic

Conversion Rule: Multiply fraction by 100 to get percentage
Technique: Simplify first: $\frac{40}{80} = \frac{1}{2} = 50\%$
Check: Verify 50% of 80 equals 40: 0.5 × 80 = 40 ✓

Common Mistakes

Avoid these frequent errors

Converting without simplifying first
Don't calculate 40 ÷ 80 = 0.5 × 100 = 50% the long way every time! This creates unnecessary decimal work and more chance for errors. Always simplify the fraction first: 40/80 = 1/2, then convert 1/2 to 50%.

Practice Quiz

Test your knowledge with interactive questions

Calculate 15% of 100:

FAQ

Everything you need to know about this question

Do I always need to simplify the fraction first?

While not required, simplifying first makes the conversion much easier! $\frac{40}{80} = \frac{1}{2}$ is easier to work with than dealing with larger numbers.

Can I just divide 40 by 80 on a calculator?

Yes! 40 ÷ 80 = 0.5, then multiply by 100 to get 50%. Both methods work, but understanding the fraction simplification helps with mental math.

What if the fraction doesn't simplify nicely?

That's okay! Some fractions like $\frac{1}{3}$ give repeating decimals (33.33...%). You can round to a reasonable number of decimal places.

How do I check if my percentage is correct?

Convert your percentage back to a decimal and multiply by the denominator. For 50% of 80: 0.5 × 80 = 40 ✓ This matches our numerator!

Why do we multiply by 100 to get a percentage?

Percentage means "per hundred" or "out of 100". So $\frac{1}{2}$ becomes $\frac{50}{100}$ which is 50%.

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