Calculate addition, subtraction, multiplication, and division of fractions
Solve fraction problems
Calculate ingredient ratios
Ratio and fraction calculations
An improper fraction has a numerator greater than or equal to the denominator (e.g., 7/4). A mixed number consists of an integer part and a proper fraction (e.g., 1 and 3/4). Both forms represent the same value and are mathematically equivalent. Improper fractions are easier for calculations, while mixed numbers can be more intuitive for displaying results.
Finding a common denominator is the process of making the denominators of fractions with different denominators the same. To add or subtract fractions, the denominators must be unified. Using the least common multiple (LCM) of the two denominators as the common denominator is the simplest approach. For example, to calculate 1/2 + 1/3, convert to a common denominator of 6: 3/6 + 2/6 = 5/6.
To multiply fractions, multiply the numerators together and the denominators together (a/b × c/d = ac/bd). To divide fractions, flip the divisor fraction and multiply (a/b ÷ c/d = a/b × d/c = ad/bc). Multiplication and division do not require finding a common denominator, making them simpler than addition and subtraction.
To convert a fraction to a decimal, divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75. Conversely, to convert a decimal to a fraction, use 10, 100, or 1000 as the denominator depending on the number of decimal places. For example, 0.75 is 75/100, which simplifies to 3/4.
Fractions are an important concept widely used in various areas of everyday life and mathematics.
A fraction is a mathematical expression representing a part of a whole divided equally. The numerator indicates how many parts are selected, and the denominator indicates how many equal parts the whole is divided into. The key concept in fraction operations is the simplified fraction (the simplest form obtained by dividing by the greatest common divisor), and it is important to express calculation results as simply as possible. Addition and subtraction require finding a common denominator, but multiplication and division operate directly on the numerators and denominators without needing one.
Fraction calculations are essential when adjusting ingredient ratios in recipes. To scale a recipe for 4 servings up to 6, multiply each ingredient by 3/2. Fractions are also widely used in architecture and engineering for scale calculations in blueprints and dividing member lengths. In finance, interest rates, discount rates, and equity stakes are expressed and calculated as fractions. Probability and statistics also use fractions to express the likelihood of events. The ability to calculate fractions accurately is a very important skill both in academia and in practice.