Mastering Fractions in 2026
Fractions are the building blocks of advanced mathematics, engineering, and everyday calculations. Whether you are a student tackling algebra, a carpenter measuring materials, or a chef adjusting recipes, accuracy is paramount.
Common Fraction Operations Examples
The table below shows examples of common fraction operations with step-by-step results. These examples demonstrate addition, subtraction, multiplication, and division of fractions, including mixed numbers.
| Operation | Fraction 1 | Fraction 2 | Result | Simplified |
|---|---|---|---|---|
| Addition | 1/4 | 1/3 | 7/12 | 7/12 |
| Addition | 2/5 | 3/10 | 7/10 | 7/10 |
| Subtraction | 3/4 | 1/2 | 1/4 | 1/4 |
| Subtraction | 5/6 | 1/3 | 1/2 | 1/2 |
| Multiplication | 2/3 | 3/4 | 6/12 | 1/2 |
| Multiplication | 1/2 | 2/5 | 2/10 | 1/5 |
| Division | 3/4 | 1/2 | 6/4 | 3/2 or 1 1/2 |
| Division | 2/3 | 4/5 | 10/12 | 5/6 |
| Mixed Addition | 1 1/2 | 2 1/4 | 3 3/4 | 3 3/4 |
| Mixed Multiplication | 2 1/3 | 1 1/2 | 3 1/2 | 3 1/2 |
Related Math Calculators
Working with fractions often requires understanding related mathematical concepts:
- GCD & LCM Calculator: Find the Greatest Common Divisor (GCD) to simplify fractions and the Least Common Multiple (LCM) to find common denominators when adding or subtracting fractions.
- Proportion Calculator: Solve ratio and proportion problems, which often involve working with fractions and equivalent ratios.
- Percentage Calculator: Convert between fractions, decimals, and percentages. Understanding fractions is essential for percentage calculations.
Frequently Asked Questions
Q:How do I add fractions with different denominators?
To add fractions with different denominators: 1) Find the Least Common Multiple (LCM) of the denominators. 2) Convert each fraction to an equivalent fraction with the LCM as the denominator. 3) Add the numerators and keep the common denominator. 4) Simplify the result if possible.
Q:How do I simplify a fraction?
To simplify a fraction, divide both the numerator and denominator by their Greatest Common Divisor (GCD). For example, to simplify 8/12, find GCD(8,12) = 4, then divide: 8÷4 / 12÷4 = 2/3.
Q:What is the difference between a proper fraction and an improper fraction?
A proper fraction has a numerator smaller than the denominator (e.g., 3/4). An improper fraction has a numerator equal to or larger than the denominator (e.g., 5/4 or 4/4). Improper fractions can be converted to mixed numbers.
Q:How do I convert a mixed number to an improper fraction?
Multiply the whole number by the denominator, then add the numerator. Place this sum over the original denominator. Example: 2 3/4 = (2×4 + 3)/4 = 11/4.