About Fraction Calculator
Fraction calculator to add, subtract, multiply, and divide fractions. Simplify to lowest terms, convert to decimals or mixed numbers. Free with step-by-step solutions.
How to use
- Enter two fractions in the numerator and denominator fields. The calculator accepts proper fractions (1/2), improper fractions (7/4), and mixed numbers (2 3/4). You can also enter whole numbers by leaving the denominator as 1.
- Select the operation: addition, subtraction, multiplication, or division. The calculator performs the operation and shows the result as a fraction in its simplest form, as a mixed number (if improper), and as a decimal equivalent.
- Review the step-by-step solution showing how the answer was calculated. For addition and subtraction, see how the common denominator is found. For multiplication, see how numerators and denominators are multiplied separately. For division, see how the second fraction is inverted and multiplied.
- Use the simplification tool to reduce any fraction to its lowest terms. Enter a fraction like 12/18 and see it simplified to 2/3 with the greatest common factor (GCF) identified. Simplification is essential for final answers in homework, measurements, and recipes.
- Convert between fractions, decimals, and percentages using the conversion display. 3/4 = 0.75 = 75%. This is useful for cooking (converting recipe measurements), construction (converting between fractional inches and decimal inches), and finance (converting percentage rates to fractions).
- Perform comparison operations to determine which of two fractions is larger. The calculator finds a common denominator and shows the equivalent fractions side by side, making the comparison visual and intuitive.
Frequently asked questions
How do I add fractions with different denominators?
Find the least common denominator (LCD), convert both fractions, then add the numerators. For 1/3 + 1/4: the LCD of 3 and 4 is 12. Convert: 1/3 = 4/12, 1/4 = 3/12. Add: 4/12 + 3/12 = 7/12. For 2/5 + 3/7: LCD of 5 and 7 is 35. Convert: 2/5 = 14/35, 3/7 = 15/35. Add: 14/35 + 15/35 = 29/35. The LCD is found by calculating the least common multiple (LCM) of the denominators. This calculator finds the LCD automatically and shows each step of the process.
How do I multiply fractions?
Multiply the numerators together and the denominators together: (a/b) x (c/d) = (a x c) / (b x d). For 2/3 x 4/5: (2 x 4) / (3 x 5) = 8/15. For mixed numbers, first convert to improper fractions: 1 1/2 x 2 1/3 = 3/2 x 7/3 = 21/6 = 3 1/2. You can simplify before multiplying by cross-cancelling common factors: 2/3 x 3/4 — the 3s cancel, giving 2/1 x 1/4 = 2/4 = 1/2.
How do I divide fractions?
Invert the second fraction (flip it) and multiply: (a/b) / (c/d) = (a/b) x (d/c). For 3/4 divided by 2/5: flip 2/5 to get 5/2, then multiply: 3/4 x 5/2 = 15/8 = 1 7/8. The reason this works: dividing by a fraction is the same as asking how many times it fits into the first fraction. 3/4 divided by 1/4 = 3 (three quarters fit into three-quarters three times), which equals 3/4 x 4/1 = 3.
How do I convert a fraction to a decimal?
Divide the numerator by the denominator. 3/4 = 3 divided by 4 = 0.75. 1/3 = 0.3333... (repeating). 5/8 = 0.625. 7/16 = 0.4375. Some fractions produce terminating decimals (the division ends) while others produce repeating decimals (1/3, 1/6, 1/7). Common conversions worth memorizing: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75, 1/8 = 0.125, 1/3 = 0.333, 2/3 = 0.667, 1/5 = 0.2, 1/10 = 0.1. This calculator shows the decimal equivalent for any fraction.
How do I simplify a fraction?
Divide both the numerator and denominator by their greatest common factor (GCF). For 12/18: the GCF of 12 and 18 is 6. Divide both: 12/6 = 2, 18/6 = 3. Simplified: 2/3. To find the GCF, list the factors of each number and find the largest one they share. Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 18: 1, 2, 3, 6, 9, 18. Common factors: 1, 2, 3, 6. GCF = 6. A fraction is fully simplified when the numerator and denominator share no common factors other than 1.
What is an improper fraction vs a mixed number?
An improper fraction has a numerator larger than its denominator: 7/4, 11/3, 9/2. A mixed number combines a whole number and a proper fraction: 1 3/4, 3 2/3, 4 1/2. They represent the same values. To convert improper to mixed: divide numerator by denominator. 7/4 = 1 remainder 3, so 7/4 = 1 3/4. To convert mixed to improper: multiply whole number by denominator, add numerator, place over the original denominator. 2 3/5 = (2x5+3)/5 = 13/5. Improper fractions are easier for calculations; mixed numbers are easier for everyday use.
How are fractions used in cooking and construction?
Cooking frequently uses fractions: doubling a recipe that calls for 3/4 cup requires 3/4 x 2 = 1 1/2 cups. Halving 2/3 cup requires 2/3 x 1/2 = 1/3 cup. Construction in North America uses fractional inches: a 2x4 stud is actually 1 1/2 x 3 1/2 inches, drill bits come in 1/16-inch increments, and tape measures are marked in 1/32-inch gradations. Converting between fractional and decimal inches is essential: 3/8 inch = 0.375 inches. This calculator handles all these real-world fraction operations. When scaling recipes across different measurement systems, use the
Cooking Converter to convert cups to millilitres, ounces to grams, and Fahrenheit to Celsius alongside your fraction calculations.
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