Convert Fraction to Percentage: Solving 15/20 Step-by-Step

Fraction to Percentage with Equivalent Fractions

Convert the following fraction into a percentage:

1520=? \frac{15}{20}=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:06 Let's turn fractions into percentages.
00:11 To do this, we'll use a formula to convert fractions into percentages. Ready?
00:25 First, we need to make the bottom number, or denominator, equal to one hundred.
00:36 So, we'll multiply both the top number, or numerator, and the bottom by the right number.
00:43 And now, we have our final fraction and its matching percentage!
00:49 Great job! This is how we solve the problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Convert the following fraction into a percentage:

1520=? \frac{15}{20}=\text{?}

2

Step-by-step solution

A percentage is actually a form of fraction, or more precisely, a fraction out of a hundred.

In other words, it is a fraction where the denominator is always 100.

Therefore, in order to convert a fraction into a percentage, we multiply it so that the denominator becomes 100.

20*5=100

15*5=75

Therefore the fraction is 75/100 and the percentage is 75%.

3

Final Answer

75%

Key Points to Remember

Essential concepts to master this topic
  • Concept: A percentage is a fraction with denominator 100
  • Method: Multiply both parts by same number: 15×5 = 75, 20×5 = 100
  • Check: Verify 75100=0.75=75% \frac{75}{100} = 0.75 = 75\%

Common Mistakes

Avoid these frequent errors
  • Multiplying numerator and denominator by different numbers
    Don't multiply 15 by one number and 20 by another = changes the fraction's value! This gives completely wrong percentages like 60% or 80%. Always multiply both numerator and denominator by the exact same number.

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

How do I know what number to multiply by?

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Look at the denominator and ask: "What times 20 equals 100?" Since 20 × 5 = 100, multiply both the numerator (15) and denominator (20) by 5.

What if the denominator doesn't go into 100 evenly?

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No problem! You can still convert by dividing first: 1520=0.75 \frac{15}{20} = 0.75 , then multiply by 100 to get 75%.

Can I simplify the fraction first?

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Yes! 1520=34 \frac{15}{20} = \frac{3}{4} is easier to work with. Since 4 × 25 = 100, we get 3×254×25=75100=75% \frac{3 \times 25}{4 \times 25} = \frac{75}{100} = 75\%

Why do we use 100 for percentages?

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The word "percent" means "per hundred" or "out of 100." So 75% literally means 75 out of every 100 parts.

How can I check if 75% is correct?

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Convert back to a decimal: 75% = 0.75. Now check: 1520=15÷20=0.75 \frac{15}{20} = 15 ÷ 20 = 0.75 ✓ They match!

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