Fractions Cheat Sheet
Fractions are the building blocks of mathematics, representing parts of a whole in a simple yet powerful way. Our Fractions Cheat Sheet is an essential reference for students, educators, and anyone looking to strengthen their math skills. This printable guide covers fundamental fraction concepts, including the roles of numerators and denominators, converting fractions to decimals and percentages, simplifying fractions, and performing operations such as addition, subtraction, multiplication, and division.
Whether you’re learning how to add 1/4 and 1/8 by finding a common denominator, converting 0.75 to 3/4, or understanding mixed numbers and improper fractions, this cheat sheet provides clear definitions and practical examples. Perfect for classroom learning, homework help, or independent study, this one-page guide is designed to make fractions approachable and fun. Download, print, and keep this indispensable fractions reference handy as you explore the exciting world of numbers!
| Fraction | Decimal | Notes |
|---|---|---|
| 1/2 | 0.5 | Half of a whole |
| 1/3 | 0.333… | One third (repeating) |
| 1/4 | 0.25 | Quarter |
| 1/5 | 0.2 | One fifth |
| 2/3 | 0.666… | Two thirds (repeating) |
| 3/4 | 0.75 | Three quarters |
| 1/6 | 0.1666… | One sixth |
| 1/8 | 0.125 | One eighth |
| 2/5 | 0.4 | Two fifths |
| 3/5 | 0.6 | Three fifths |
| 4/5 | 0.8 | Four fifths |
| 5/6 | 0.8333… | Five sixths |
| 7/8 | 0.875 | Seven eighths |
| 1/10 | 0.1 | One tenth |
| 3/8 | 0.375 | Three eighths |
| 2/7 | 0.2857… | Two sevenths (approx.) |
| 4/7 | 0.5714… | Four sevenths (approx.) |
| 5/7 | 0.7143… | Five sevenths (approx.) |
| 5/8 | 0.625 | Five eighths |
| 3/10 | 0.3 | Three tenths |
| 7/10 | 0.7 | Seven tenths |
| 2/9 | 0.2222… | Two ninths (repeating) |
| 4/9 | 0.4444… | Four ninths (repeating) |
| 7/9 | 0.7777… | Seven ninths (repeating) |
| 8/9 | 0.8888… | Eight ninths (repeating) |
| 3/7 | 0.4286 | Three sevenths (approx.) |
| 6/7 | 0.8571 | Six sevenths (approx.) |
| 2/11 | 0.1818… | Two elevenths (repeating) |
| Term | Explanation |
|---|---|
| Fraction | A fraction represents a part of a whole and is written with two numbers separated by a line. The top number is called the numerator and shows how many parts you have, while the bottom number is the denominator and shows how many equal parts the whole is divided into. For example, if you have a pizza cut into 4 equal slices and you eat 1 slice, you have eaten 1/4 of the pizza. |
| Decimal | A decimal is another way to represent fractions using a decimal point. It is based on the number 10. For example, the fraction 1/2 is equal to 0.5 because when you divide 1 by 2, you get 0.5. Decimals are often used in money and measurements to show parts of a whole. |
| Conversion Method | To convert a fraction to a decimal, divide the numerator by the denominator. For example, for the fraction 1/4, divide 1 by 4 to get 0.25. You can do this using long division or a calculator. This method helps you compare fractions with decimals easily. |
| Repeating Decimals | Some fractions convert to decimals that repeat the same digit or group of digits over and over. For example, 1/3 equals 0.333… because 3 repeats indefinitely. We often show this by putting a bar over the repeating digit, like 0.3̅, to let you know it goes on forever. |
| Simplifying Fractions | Simplifying a fraction means reducing it to its simplest form by dividing the numerator and denominator by their greatest common divisor (GCD). For example, the fraction 4/8 can be simplified by dividing both 4 and 8 by 4, resulting in 1/2. This makes the fraction easier to understand and work with. |
| Operations with Fractions | You can add, subtract, multiply, and divide fractions. When adding or subtracting fractions, you need a common denominator. For example, to add 1/4 and 1/8, change 1/4 to 2/8 so both have the same denominator, then add to get 3/8. When multiplying fractions, multiply the numerators together and the denominators together (e.g., 1/2 × 1/3 = 1/6). For division, multiply by the reciprocal of the second fraction. |
| Mixed Numbers | A mixed number combines a whole number and a fraction, such as 1 1/2. It means you have one whole and an extra half. To make calculations easier, mixed numbers can be converted into improper fractions. For instance, 1 1/2 becomes 3/2 because 1 whole is the same as 2/2, and 2/2 + 1/2 equals 3/2. |
| Improper Fractions | An improper fraction is one where the numerator is equal to or larger than the denominator, like 7/4. This type of fraction represents a number greater than or equal to one. For example, 7/4 can be changed into the mixed number 1 3/4, which means one whole and three quarters. |
| Reciprocals | The reciprocal of a fraction is created by switching its numerator and denominator. For example, the reciprocal of 2/3 is 3/2. When you multiply a fraction by its reciprocal, the product is always 1. This concept is very useful when dividing fractions. |
| Equivalent Fractions | Equivalent fractions are different fractions that represent the same value. For example, 1/2, 2/4, and 3/6 are all equivalent because they all equal the same amount. To find an equivalent fraction, multiply or divide both the numerator and the denominator by the same number. |
| Converting Decimals to Fractions | To convert a decimal to a fraction, write the decimal as a fraction with a denominator that is a power of 10, then simplify. For example, 0.75 can be written as 75/100, which simplifies to 3/4. This process works well with decimals that have a fixed number of digits. |
| Fraction to Percentage Conversion | Converting a fraction to a percentage involves two steps. First, convert the fraction to a decimal by dividing the numerator by the denominator. Then multiply the decimal by 100. For example, 1/2 equals 0.5, and 0.5 × 100 equals 50%. Percentages help you see parts of a whole in everyday situations like grades or discounts. |
| Finding a Common Denominator | When adding or subtracting fractions, it is important that they share the same denominator. The common denominator is usually the least common multiple (LCM) of the denominators. For example, to add 1/3 and 1/4, find the LCM of 3 and 4, which is 12. Then convert 1/3 to 4/12 and 1/4 to 3/12 so you can add them together to get 7/12. |
| Multiplication and Division of Fractions | Multiplying fractions is simple: multiply the numerators together and the denominators together. For instance, 2/3 multiplied by 3/4 gives 6/12, which can be simplified to 1/2. For division, flip the second fraction (find its reciprocal) and multiply. For example, dividing 1/2 by 1/4 means multiplying 1/2 by 4/1, resulting in 4/2, which simplifies to 2. These methods help you solve many different types of fraction problems. |