Fraction Calculator
Perform fraction calculations with ease: add, subtract, multiply, and divide fractions. Convert between mixed numbers and improper fractions, and simplify to lowest terms.
Fraction Calculator
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Fraction Facts
- • The sum of fractions with different denominators requires a common denominator
- • An improper fraction has a numerator greater than or equal to its denominator
- • A proper fraction has a numerator less than its denominator
- • A mixed number combines a whole number and a proper fraction
- • When multiplying fractions, you multiply the numerators and denominators separately
Working with Fractions
Adding and Subtracting Fractions
To add or subtract fractions with the same denominator, combine the numerators while keeping the denominator the same. For different denominators, find a common denominator first, then add or subtract the numerators.
Multiplying Fractions
Multiply the numerators together and the denominators together. Simplify the result by finding the greatest common divisor (GCD) of the numerator and denominator.
Dividing Fractions
To divide by a fraction, multiply by its reciprocal (flip the numerator and denominator). For example, to calculate a ÷ b, compute a × (1/b).
Simplifying Fractions
Divide both the numerator and denominator by their greatest common divisor (GCD) to simplify a fraction to its lowest terms.
Teaching Tip:
Fractions are easier to understand when visualized as parts of a whole. Consider using visual aids like pie charts or grids to help understand fraction concepts.
Understanding Fractions
A fraction represents a part of a whole or, more generally, any number of equal parts. It consists of a numerator (the number above the line) and a denominator (the number below the line). The denominator cannot be zero.
Types of Fractions
Proper Fractions
A proper fraction has a numerator that is less than its denominator. The value of a proper fraction is always less than 1.
Examples: 1/2, 3/4, 5/8
Improper Fractions
An improper fraction has a numerator that is greater than or equal to its denominator. The value of an improper fraction is always greater than or equal to 1.
Examples: 5/3, 7/4, 11/10
Mixed Numbers
A mixed number consists of a whole number and a proper fraction. It represents the sum of the whole number and the fraction.
Examples: 1 1/2, 2 3/4, 5 2/3
Equivalent Fractions
Equivalent fractions are fractions that represent the same value but have different numerators and denominators.
Examples: 1/2 = 2/4 = 3/6 = 4/8
Common Fraction Operations
| Operation | Method | Example |
|---|---|---|
| Addition | Find common denominator, add numerators | 1/4 + 3/4 = 4/4 = 1 |
| Subtraction | Find common denominator, subtract numerators | 3/4 - 1/4 = 2/4 = 1/2 |
| Multiplication | Multiply numerators, multiply denominators | 2/3 × 3/4 = 6/12 = 1/2 |
| Division | Multiply by the reciprocal of the divisor | 2/3 ÷ 3/4 = 2/3 × 4/3 = 8/9 |
| Simplification | Divide numerator and denominator by their GCD | 8/12 = (8÷4)/(12÷4) = 2/3 |
Real-World Applications
Cooking & Baking
Recipes often use fractions for ingredient measurements (1/2 cup, 3/4 teaspoon, etc.)
Construction & DIY
Measurements in construction often involve fractions of inches or feet
Finance
Interest rates, discounts, and tax rates are often expressed as fractions
Educational Note:
Understanding fractions is fundamental to advancing in mathematics. Fractions form the basis for understanding algebraic expressions, ratios, proportions, and many other mathematical concepts.