Convert the Fraction 20/40 to a Percentage

Q: Why do I need to simplify the fraction first?

Simplifying makes the math much easier! Working with $ \frac{1}{2} $ instead of $ \frac{20}{40} $ gives you the same answer but with simpler calculations.

Q: How do I find the greatest common divisor quickly?

Look for the largest number that divides both the numerator and denominator. For 20 and 40, think: what's the biggest number that goes into both? That's 20!

Q: Can I just multiply the original fraction by 100?

Yes, you can! $ \frac{20}{40} \times 100 = 50\% $ works perfectly. But simplifying first makes the arithmetic much simpler and reduces chances of calculation errors.

Q: What if I get a decimal when converting?

That's normal! Some fractions like $ \frac{1}{3} $ give 33.33...%. You can round to a reasonable number of decimal places or leave as an exact decimal.

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

Convert your percentage back to a fraction! 50% = $ \frac{50}{100} = \frac{1}{2} $, which should equal your simplified original fraction.

Fraction to Percentage with Simplification

Convert the following fraction into a percentage:

$\frac{20}{40}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert fractions to percentages

00:05 Apply the formula to convert fractions to percentages

00:15 We want the denominator to equal 100

00:27 Divide the desired denominator by our current denominator in order to determine the ratio

00:31 The ratio is the number we multiply both the numerator and denominator by

00:39 This is the final fraction and its corresponding percentage

00:46 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert the following fraction into a percentage:

$\frac{20}{40}=\text{?}$

Step-by-step solution

To convert the fraction $\frac{20}{40}$ into a percentage, we'll follow these steps:

Step 1: Simplify the fraction $\frac{20}{40}$ .
Step 2: Convert the simplified fraction into a percentage.

Step 1: Simplifying the fraction $\frac{20}{40}$ , we divide both the numerator and the denominator by their greatest common divisor, which is 20:

$\frac{20 \div 20}{40 \div 20} = \frac{1}{2}$

Step 2: To convert $\frac{1}{2}$ into a percentage, we multiply by 100:

$\frac{1}{2} \times 100 = 50\%$

Therefore, the fraction $\frac{20}{40}$ is equivalent to 50%.

Final Answer

50%

Key Points to Remember

Essential concepts to master this topic

Rule: Always simplify fractions before converting to percentage
Technique: Divide both 20 and 40 by GCD (20) to get $\frac{1}{2}$
Check: Verify that $\frac{1}{2} \times 100 = 50\%$ equals $\frac{20}{40} \times 100$ ✓

Common Mistakes

Avoid these frequent errors

Converting without simplifying first
Don't calculate $\frac{20}{40} \times 100$ directly = 50% but with harder arithmetic! This makes calculation unnecessarily complex and error-prone. Always simplify $\frac{20}{40}$ to $\frac{1}{2}$ first, then multiply 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 need to simplify the fraction first?

Simplifying makes the math much easier! Working with $\frac{1}{2}$ instead of $\frac{20}{40}$ gives you the same answer but with simpler calculations.

How do I find the greatest common divisor quickly?

Look for the largest number that divides both the numerator and denominator. For 20 and 40, think: what's the biggest number that goes into both? That's 20!

Can I just multiply the original fraction by 100?

Yes, you can! $\frac{20}{40} \times 100 = 50\%$ works perfectly. But simplifying first makes the arithmetic much simpler and reduces chances of calculation errors.

What if I get a decimal when converting?

That's normal! Some fractions like $\frac{1}{3}$ give 33.33...%. You can round to a reasonable number of decimal places or leave as an exact decimal.

How can I check if my percentage is correct?

Convert your percentage back to a fraction! 50% = $\frac{50}{100} = \frac{1}{2}$ , which should equal your simplified original fraction.

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