Add, subtract, multiply, and divide fractions with step-by-step solutions and simplification
Fractions represent parts of a whole, written as a/b where 'a' is the numerator (parts taken) and 'b' is the denominator (total parts). They express division, ratios, and proportions in mathematics.
Fraction calculations are essential in cooking, construction, science, and finance. They help solve real-world problems involving parts, measurements, and proportions with mathematical precision.
Proper fractions (numerator < denominator), improper fractions (numerator ≥ denominator), and mixed numbers (whole number + fraction) each serve different mathematical purposes and applications.
Division by zero is undefined. Very large numbers may cause precision issues. Some decimal representations are infinite (like 1/3 = 0.333...). Always verify critical calculations.
Fractions are fundamental in K-12 mathematics education, forming the basis for algebra, ratios, and proportional reasoning. This calculator supports homework, test preparation, and concept understanding.
Used in engineering measurements, recipe scaling, financial calculations, probability, statistics, and scientific notation. Essential for STEM fields and everyday problem-solving.
Understanding fractions is a critical predictor of success in algebra and higher mathematics
Visual representations and step-by-step solutions improve fraction comprehension by 40%
Ancient Egyptians used unit fractions (1/n) in their mathematical calculations over 4000 years ago
To simplify a fraction, find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both by the GCD. For example, 6/8 simplifies to 3/4 because GCD(6,8) = 2.
An improper fraction has a numerator greater than or equal to its denominator (like 7/4). A mixed number combines a whole number with a proper fraction (like 1¾). They represent the same value in different forms.
Divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75. Some fractions produce repeating decimals (1/3 = 0.333...), which can be rounded or expressed with a bar notation.
Find the Least Common Multiple (LCM) of the denominators. List multiples of each denominator and find the smallest common one, or use prime factorization. For 1/4 and 1/6, LCD = 12.
Cross multiplication is a method to compare fractions or solve proportions. For a/b = c/d, cross multiply to get a×d = b×c. It's useful for checking fraction equality and solving equations.
Common denominators ensure we're adding or subtracting the same-sized parts. You can't directly add 1/2 + 1/3 because halves and thirds are different sizes. Converting to 3/6 + 2/6 allows addition.
Multiply numerators together and denominators together: (a/b) × (c/d) = (a×c)/(b×d). For example, 2/3 × 3/4 = 6/12 = 1/2. Simplify the result when possible.
Multiply by the reciprocal (flip the second fraction): (a/b) ÷ (c/d) = (a/b) × (d/c). For example, 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3 = 2⅔.
"This calculator saved my homework! The step-by-step solutions help me understand HOW to solve fractions, not just get the answer. My grades improved from C to A!"
"I recommend this to all my students. The visual representation and clear steps make teaching fractions so much easier. It's become an essential classroom tool."
"Finally, a tool that helps me help my kids with math homework! The explanations are clear enough that I can relearn and teach them properly. Absolutely brilliant!"
"I use this with all my tutoring students. The step-by-step breakdown is perfect for teaching concepts. Mixed numbers feature is especially helpful for advanced problems."
"Essential for our homeschool curriculum! My three kids (grades 4-7) all use it. The different modes and detailed solutions adapt perfectly to each learning level."
"Still using this in college for quick fraction checks in chemistry and physics problems. The decimal conversion is super helpful for lab calculations. Wish I had this in high school!"