Fraction Calculator
Add, subtract, multiply, and divide fractions
Fraction Calculator
fractionCalculator.component.description
Fraction Calculator
First Fraction
0.5000
Second Fraction
0.3333
Visual Representation
📐 Steps to Solution
Understanding Fractions
A fraction represents a part of a whole. The top number (numerator) shows how many parts you have, while the bottom number (denominator) shows how many equal parts make up the whole.
Basic Fraction Operations
Addition and Subtraction
To add or subtract fractions, you need a common denominator:
- Find the Least Common Multiple (LCM) of the denominators
- Convert each fraction to equivalent fractions with the common denominator
- Add or subtract the numerators
- Simplify the result by dividing by the Greatest Common Divisor (GCD)
Multiplication
Multiplying fractions is simpler:
- Multiply the numerators together
- Multiply the denominators together
- Simplify the result
Division
To divide fractions, multiply by the reciprocal:
- Flip the second fraction (reciprocal)
- Multiply the fractions
- Simplify the result
Converting Between Forms
- Improper to Mixed: Divide numerator by denominator. The quotient is the whole number, remainder is the new numerator
- Mixed to Improper: Multiply whole number by denominator, add numerator
- Fraction to Decimal: Divide numerator by denominator
- Decimal to Fraction: Write decimal over power of 10, then simplify
Common Fractions Quick Reference
Real-World Applications
- Cooking: Adjusting recipe measurements (½ cup + ¼ cup)
- Construction: Measuring materials (⅜ inch + ½ inch board)
- Time: Calculating portions of hours (¾ hour = 45 minutes)
- Finance: Calculating portions of budgets or investments
💡 Fraction Tips
Frequently Asked Questions
How do I simplify a fraction?
To simplify a fraction, divide both the numerator and denominator by their Greatest Common Divisor (GCD). For example, 6/8 can be simplified by dividing both by 2 to get 3/4. The fraction is fully simplified when the GCD equals 1.
What's the difference between proper and improper fractions?
A proper fraction has a numerator smaller than its denominator (like 3/4), representing a value less than 1. An improper fraction has a numerator equal to or greater than its denominator (like 5/4), representing a value equal to or greater than 1. Improper fractions can be converted to mixed numbers.
Why do I need a common denominator for addition?
You need a common denominator because you're adding parts of different sizes. It's like adding ½ pizza and ⅓ pizza - you can't simply add 1+1. You need to express both as the same-sized pieces (6ths in this case: 3/6 + 2/6 = 5/6) before adding.
Can I add fractions with different denominators directly?
No, you cannot add fractions with different denominators directly. You must first convert them to equivalent fractions with a common denominator. This ensures you're adding like quantities. For example, to add 1/2 + 1/3, convert to 3/6 + 2/6 = 5/6.
How do I convert a decimal to a fraction?
Write the decimal over a power of 10 based on the number of decimal places, then simplify. For example: 0.75 = 75/100 = 3/4 (simplified). For repeating decimals, use algebraic methods or recognize common patterns (0.333... = 1/3, 0.666... = 2/3).
What is a mixed number and when should I use it?
A mixed number combines a whole number and a fraction (like 2 ½). Use mixed numbers when the result is greater than 1 and you want an intuitive representation. For example, 7/4 = 1 ¾ is easier to visualize (one whole pizza plus three-quarters of another) than the improper fraction 7/4. Mixed numbers are common in cooking, carpentry, and everyday measurements.
How do I multiply fractions with whole numbers?
Convert the whole number to a fraction by placing it over 1, then multiply normally. For example, 3 × 2/5 becomes 3/1 × 2/5 = 6/5 = 1 ⅕. Alternatively, multiply the whole number by the numerator: 3 × 2/5 = (3×2)/5 = 6/5. This is useful for scaling recipes or calculating portions.
What's the easiest way to find a common denominator?
The Least Common Multiple (LCM) is the smallest common denominator. For small numbers, list multiples of each denominator until you find a match. For example, for 1/4 and 1/6: multiples of 4 (4, 8, 12...) and 6 (6, 12...) share 12 as the LCM. Quick tip: If one denominator divides evenly into the other, use the larger number. Otherwise, multiply the denominators together as a quick (though not always smallest) common denominator.
Why does multiplying fractions make them smaller?
Multiplying by a proper fraction (less than 1) means taking a fraction "of" something, which makes it smaller. For example, ½ × ¾ = ⅜. You're taking half of three-quarters, which is less than the original ¾. Think of it as finding "50% of 75%," which equals 37.5%. However, multiplying by an improper fraction (greater than 1) will make the result larger.
How do I compare two fractions to see which is larger?
Convert both fractions to the same denominator, then compare numerators. For example, to compare 2/3 and 3/5: find common denominator 15. Convert: 2/3 = 10/15 and 3/5 = 9/15. Since 10 > 9, we know 2/3 > 3/5. Alternatively, convert to decimals: 2/3 ≈ 0.667 and 3/5 = 0.600, confirming 2/3 is larger. This is useful for comparing discounts, interest rates, or cooking measurements.
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