What is 75% as a Fraction?

S1-SA2-0862

Grade Level:

Class 5

Maths, Finance, Data Science, AI

Definition

What is it?

To express 75% as a fraction means to write it as a part of a whole, where the whole is 100. A percentage literally means 'per hundred'. So, 75% means 75 out of 100.

Simple Example

Quick Example

Imagine your school has a cricket team, and out of 100 matches played, they won 75 matches. We can say they won 75% of their matches. To write this as a fraction, it would be 75/100, which can then be simplified.

Worked Example

Step-by-Step

Let's convert 75% into a fraction.
1. Understand that 'percent' means 'out of 100'. So, 75% is the same as 75 out of 100.
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2. Write this as a fraction: 75/100.
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3. Now, we need to simplify this fraction. Find the largest number that can divide both 75 and 100 without leaving a remainder. Both numbers end in 5 or 0, so they are divisible by 5.
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4. Divide both numerator and denominator by 5: 75 ÷ 5 = 15 and 100 ÷ 5 = 20. So the fraction becomes 15/20.
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5. Can we simplify 15/20 further? Yes, both 15 and 20 are divisible by 5 again.
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6. Divide both by 5: 15 ÷ 5 = 3 and 20 ÷ 5 = 4. So the fraction becomes 3/4.
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7. We cannot simplify 3/4 further because 3 and 4 have no common factors other than 1.
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ANSWER: 75% as a fraction is 3/4.

Why It Matters

Understanding percentages and fractions is super important in many fields! In Finance, it helps calculate interest on your savings or loans. Data Scientists use it to show parts of a whole dataset, and in AI, it's used to express probabilities or model accuracy. These skills can lead to exciting careers in banking, data analysis, or even developing new technologies.

Common Mistakes

MISTAKE: Forgetting to simplify the fraction to its lowest terms (e.g., leaving 75/100 instead of 3/4). | CORRECTION: Always divide both the numerator and denominator by their greatest common factor until they cannot be divided further.

MISTAKE: Writing 75% as 0.75 and stopping there, instead of converting to a fraction. | CORRECTION: Remember that 0.75 is a decimal. To make it a fraction, think of it as 75/100 and then simplify.

MISTAKE: Dividing only the numerator or only the denominator when simplifying. | CORRECTION: Whatever you do to the numerator (top number), you must also do to the denominator (bottom number) to keep the fraction equivalent.

Practice Questions

Try It Yourself

QUESTION: Convert 25% into a simplified fraction. | ANSWER: 1/4

QUESTION: A mobile phone battery is charged to 50%. Express this as a fraction in its simplest form. | ANSWER: 1/2

QUESTION: In a class of 40 students, 30 students passed an exam. What percentage of students passed, and what is this percentage as a simplified fraction? | ANSWER: 75%, which is 3/4

MCQ

Quick Quiz

Which of the following fractions is equivalent to 75%?

1/4

3/4

75/1

1/75

The Correct Answer Is:

75% means 75 out of 100, which is written as 75/100. When simplified by dividing both by 25, it becomes 3/4. Options A, C, and D are incorrect representations.

Real World Connection

In the Real World

When you see 'Up to 75% off!' during a sale at a shop like Reliance Digital or Big Bazaar, it means you pay only 1/4th of the original price, saving 3/4th! Similarly, when a news report says '75% of Indian households now have access to clean water,' it means 3 out of every 4 homes have it.

Key Vocabulary

Key Terms

PERCENTAGE: A way to express a number as a fraction of 100 | FRACTION: A number that represents a part of a whole | NUMERATOR: The top number in a fraction, showing how many parts are being considered | DENOMINATOR: The bottom number in a fraction, showing the total number of equal parts | SIMPLIFY: To reduce a fraction to its lowest terms by dividing the numerator and denominator by their greatest common factor.

What's Next

What to Learn Next

Great job learning about converting percentages to fractions! Next, you can explore 'Converting Fractions to Decimals' and 'Converting Decimals to Percentages'. This will help you understand how all these different ways of showing parts of a whole are connected and how to switch between them easily.