Converting 30% to Its Mathematical Equivalent: Percentage Practice

Q: Why do I put the percentage over 100?

Because percent means "per hundred"! So 30% literally means 30 out of 100 parts, which is exactly $ \frac{30}{100} $.

Q: How do I find the GCD of 30 and 100?

List the factors: 30 = 2×3×5 and 100 = 2²×5². The common factors are 2 and 5, so GCD = 2×5 = 10.

Q: What if I can't see the GCD right away?

Try dividing by small numbers like 2, 5, or 10 first! For $ \frac{30}{100} $, both numbers end in 0, so they're definitely divisible by 10.

Q: How can I check if my fraction equals the original percentage?

Convert your fraction to a decimal by dividing: $ \frac{3}{10} = 3 ÷ 10 = 0.3 $. Then multiply by 100: 0.3 × 100 = 30% ✓

Q: Are there other ways to simplify fractions?

Yes! You can also use prime factorization or keep dividing by common factors until no more are possible. The key is making sure both numbers can't be divided by anything else.

Percentage to Fraction with Simplification

The percentage 30% is equal to:

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Convert from percentages to fractions

00:05 The percentage equals a fraction where the numerator is the percentage (X) and the denominator is 100

00:10 Apply this formula to our exercise

00:25 Factor 30 into 3 and 10, and 100 into 10 and 10

00:28 Reduce wherever possible

00:33 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The percentage 30% is equal to:

Step-by-step solution

To solve the problem of converting 30% to its equivalent fraction, follow these steps:

Step 1: Convert the percentage to a fraction by placing it over 100:

$30\% = \frac{30}{100}$

Step 2: Simplify the fraction. Find the greatest common divisor (GCD) of 30 and 100.

Both 30 and 100 are divisible by 10. Divide the numerator and denominator by 10:

$\frac{30 \div 10}{100 \div 10} = \frac{3}{10}$

Therefore, the percentage 30% is equivalent to the fraction $\frac{3}{10}$ .

Final Answer

$\frac{3}{10}$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert percentages by placing over 100 as denominator
Technique: Simplify $\frac{30}{100}$ by dividing both by GCD 10
Check: Verify $\frac{3}{10} = 0.3 = 30\%$ ✓

Common Mistakes

Avoid these frequent errors

Not simplifying the fraction to lowest terms
Don't leave your answer as $\frac{30}{100}$ = incorrect form! This isn't in simplest form and doesn't match standard answer choices. Always find the GCD and divide both numerator and denominator to get $\frac{3}{10}$ .

Practice Quiz

Test your knowledge with interactive questions

Convert the fraction into a percentage:

$\frac{24}{100}=\text{?}$

FAQ

Everything you need to know about this question

Why do I put the percentage over 100?

Because percent means "per hundred"! So 30% literally means 30 out of 100 parts, which is exactly $\frac{30}{100}$ .

How do I find the GCD of 30 and 100?

List the factors: 30 = 2×3×5 and 100 = 2²×5². The common factors are 2 and 5, so GCD = 2×5 = 10.

What if I can't see the GCD right away?

Try dividing by small numbers like 2, 5, or 10 first! For $\frac{30}{100}$ , both numbers end in 0, so they're definitely divisible by 10.

How can I check if my fraction equals the original percentage?

Convert your fraction to a decimal by dividing: $\frac{3}{10} = 3 ÷ 10 = 0.3$ . Then multiply by 100: 0.3 × 100 = 30% ✓

Are there other ways to simplify fractions?

Yes! You can also use prime factorization or keep dividing by common factors until no more are possible. The key is making sure both numbers can't be divided by anything else.

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