Fractions and percentages are two ways to represent parts of a whole, commonly used in math and everyday life. Fractions show a part of a whole using two numbers separated by a slash (e.g., 1/2), while percentages express a part out of 100 (e.g., 50%). This article explains how to understand, convert, and use fractions and percentages, with examples to help you apply them confidently.
Fractions
Fractions represent a part of a whole by dividing it into equal parts. The top number is the numerator (the part), and the bottom number is the denominator (the total parts).
How to Read Fractions
- Fractions are read as "numerator over denominator."
- Common fractions have special names (e.g., 1/2 is "one-half," 3/4 is "three-quarters").
- Use ordinal numbers for denominators beyond 10 (e.g., 1/11 is "one-eleventh").
| Fraction | English Example | Usage Example |
|---|---|---|
| /2 | one-half | I ate one-half of the pizza. |
| /3 | one-third | She read one-third of the book. |
| /4 | one-quarter | We waited for one-quarter of an hour. |
| /4 | three-quarters | He drank three-quarters of the juice. |
| /5 | two-fifths | Two-fifths of the students are absent. |
| /8 | five-eighths | The recipe calls for five-eighths cup of sugar. |
| /10 | seven-tenths | Seven-tenths of the road is finished. |
| /100 | one one-hundredth | This is one one-hundredth of a dollar. |
Fractions in Everyday Life
- Cooking and recipes (e.g., 1/2 cup, 3/4 teaspoon)
- Time (e.g., quarter past, half an hour)
- Sharing and dividing items (e.g., half the cake, one-third of the group)
- Measurements (e.g., 5 1/2 feet, 2 3/4 inches)
| Context | Example Sentence |
|---|---|
| Cooking | Add one-half cup of milk. |
| Time | The meeting is in one-quarter hour. |
| Dividing | Share the cake into four parts. |
| Measuring | The table is five and one-half feet long. |
Operations with Fractions
- Addition/Subtraction: Find a common denominator, then add/subtract numerators.
- Multiplication: Multiply numerators and denominators.
- Division: Flip the second fraction (reciprocal) and multiply.
| Operation | Example | Result |
|---|---|---|
| Addition | /4 + 1/4 | /2 |
| Subtraction | /4 - 1/4 | /2 |
| Multiplication | /5 × 3/4 | /20 or 3/10 |
| Division | /2 ÷ 1/4 |
Percentages
Percentages express a number as a part of 100, indicated by the "%" symbol. They are used to show proportions, comparisons, and changes.
How to Understand Percentages
- "20%" means 20 out of 100.
- Percentages can be greater than 100% (e.g., 150%) or less than 1% (e.g., 0.5%).
- Converting: 50% = 50/100 = 1/
| Percentage | English Example | Usage Example |
|---|---|---|
| % | ten percent | Ten percent of the students passed. |
| % | twenty-five percent | Twenty-five percent of the cake is gone. |
| % | fifty percent | Fifty percent is the same as one-half. |
| % | seventy-five percent | Seventy-five percent completed the test. |
| % | one hundred percent | I’m one hundred percent sure. |
| % | one hundred fifty percent | Sales increased by one hundred fifty percent. |
| .5% | zero point five percent | The fee is zero point five percent of the total. |
Percentages in Everyday Life
- Discounts and sales (e.g., 20% off)
- Grades and scores (e.g., 85%)
- Interest rates and finance (e.g., 3% interest)
- Statistics and data (e.g., 40% of people prefer tea)
| Context | Example Sentence |
|---|---|
| Shopping | The jacket is 30% off. |
| School | I got 90% on the test. |
| Banking | The interest rate is 2.5%. |
| Surveys | Forty percent of respondents like coffee. |
Converting Fractions, Decimals, and Percentages
- Fraction → Decimal: Divide numerator by denominator (1/2 = 0.5)
- Decimal → Percentage: Multiply by 100 and add "%" (0.5 × 100 = 50%)
- Percentage → Fraction: Write as fraction over 100 and simplify (75% = 75/100 = 3/4)
| Fraction | Decimal | Percentage |
|---|---|---|
| /2 | .5 | % |
| /4 | .25 | % |
| /4 | .75 | % |
| /5 | .2 | % |
| /5 | .4 | % |
| /10 | .1 | % |
What fraction is equal to 50%?
1/2
50% equals one-half, or 1/2.
Using Fractions and Percentages Together
You can often convert between fractions and percentages to make comparisons easier.
- /2 = 50%
- /4 = 75%
- /5 = 20%
- /5 = 40%
| Fraction | Percentage | Usage Example |
|---|---|---|
| /2 | % | Half of the class (50%) is absent. |
| /4 | % | One-quarter (25%) of the cake is left. |
| /5 | % | Three-fifths (60%) of the project is done. |
| /5 | % | Four-fifths (80%) completed the survey. |
Practice Problems
- What is 1/4 as a percentage?
Answer: 25%
- Convert 0.6 to a fraction.
Answer: 3/5
- If 30% of 50 people like sushi, how many people is that?
Answer: 15 people
- Add 1/3 and 1/6.
Answer: 1/2
- What is 120% as a fraction?
Answer: 120/100 = 6/5
What fraction equals 40%?
2/5
40% = 40/100 = 2/5 after simplifying.
Summary
- Fractions divide a whole into equal parts with numerator/denominator.
- Percentages express parts out of 100 using the "%" symbol.
- Convert between fractions, decimals, and percentages to use them correctly.
- Apply fractions and percentages in cooking, shopping, time, and data interpretation.
Fractions and percentages are powerful tools for describing the world around us. With practice, you can use them confidently in everyday situations.
What do percentages represent?
Parts out of 100
Percentages express a number as a part of 100.
Mix 1/4 cup of milk with 1/4 cup of water. How much liquid do you have?
1/2 cup
1/4 + 1/4 = 2/4 = 1/2 cup.
Flashcards (1 of 15)
- Fraction: 1/2
- Usage Example: I ate one-half of the pizza.
- English Example: one-half
Last updated: Wed Jun 18, 2025
