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Calculate fractions accurately with step-by-step solutions.
Learn everything you need to know about mathematical calculations, formulas, and real-world applications. Find answers to common questions about calculations and using them in everyday situations.
A fraction represents a part of a whole number. It consists of a numerator (top number) and denominator (bottom number). For example, in 3/4, the 3 is the numerator and 4 is the denominator, meaning 3 parts out of 4 total parts.
To add or subtract fractions, you need a common denominator. Find the least common multiple of the denominators, convert both fractions to have this common denominator, then add or subtract the numerators. For example: 1/4 + 1/6 = 3/12 + 2/12 = 5/12.
To multiply fractions, multiply the numerators together and denominators together: (a/b) × (c/d) = (a×c)/(b×d). To divide, multiply by the reciprocal: (a/b) ÷ (c/d) = (a/b) × (d/c) = (a×d)/(b×c).
To simplify a fraction, find the greatest common divisor (GCD) of the numerator and denominator, then divide both by this number. For example, 6/8 can be simplified by dividing both by 2 to get 3/4.
A mixed number combines a whole number with a fraction, like 2 1/3 (two and one-third). Improper fractions (where numerator > denominator) can be converted to mixed numbers by dividing the numerator by the denominator.
An improper fraction has a numerator that is greater than or equal to its denominator, like 7/4 or 5/5. These can be converted to mixed numbers: 7/4 = 1 3/4.
To find a common denominator, find the least common multiple (LCM) of the denominators. For example, for 1/3 and 1/4, the LCM of 3 and 4 is 12, so you convert to 4/12 and 3/12.
To convert a fraction to a decimal, divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75. Some fractions result in repeating decimals, like 1/3 = 0.333...
Fractions are used everywhere: cooking and baking recipes, measurements in construction, time (1/2 hour), money (1/4 = quarter), sports statistics, and sharing items equally among people.
Negative fractions follow the same rules as positive fractions. The negative sign can be placed on the numerator, denominator, or in front of the entire fraction. For example, -1/2 = 1/-2 = -(1/2). When multiplying, two negatives make a positive.
Mathematical FormulaYou ate 1/4 and your friend ate 1/3 of a pizza
Together you ate 7/12 of the pizza!
Recipe calls for 2/3 cup flour, but you need to halve it
You need 1/3 cup of flour!
You have 3/4 inch and need to add 1/8 inch
Total length is 7/8 inch!