Master fraction arithmetic quickly and accurately. This calculator helps you add, subtract, multiply, and divide two fractions, simplifying the result to its lowest terms and showing the step-by-step process.
How to Do Fractions on a Calculator
How to Do Fractions on a Calculator Formula
Fractions are calculated based on the chosen operation:
Addition: $A/B + C/D = (AD + BC) / BD$
Subtraction: $A/B – C/D = (AD – BC) / BD$
Multiplication: $A/B \times C/D = (A \times C) / (B \times D)$
Division: $A/B \div C/D = A/B \times D/C = (A \times D) / (B \times C)$
Formula Sources: Math Is Fun: Operations on Fractions, Khan Academy: Fraction Arithmetic.
Variables Explained
- Numerator A (A): The top number of the first fraction.
- Denominator A (B): The bottom number of the first fraction. Must be non-zero.
- Operator: The arithmetic function to perform (+, -, $\times$, $\div$).
- Numerator B (C): The top number of the second fraction.
- Denominator B (D): The bottom number of the second fraction. Must be non-zero.
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What is Fractions Arithmetic?
Fractions arithmetic involves performing the four basic operations (addition, subtraction, multiplication, and division) on fractions. A fraction represents a part of a whole, and arithmetic with them requires understanding how to handle common denominators. The result of a fraction calculation should always be simplified to its lowest terms, meaning the numerator and denominator share no common factors other than 1.
Unlike whole numbers, adding and subtracting fractions requires a common denominator (the Least Common Multiple or LCM). Multiplication and division are generally simpler: multiplication is straight across (numerator times numerator, denominator times denominator), and division is multiplication by the reciprocal of the second fraction.
How to Calculate Fractions (Example: Addition)
Let’s calculate $1/4 + 2/3$.
- Find a Common Denominator: The LCM of 4 and 3 is 12.
- Convert the Fractions: $$1/4 \times 3/3 = 3/12$$ $$2/3 \times 4/4 = 8/12$$
- Add the Numerators: $3/12 + 8/12 = (3+8)/12 = 11/12$.
- Simplify the Result: The fraction $11/12$ cannot be simplified further, so the final answer is $11/12$.
Frequently Asked Questions (FAQ)
How do you divide fractions?
To divide fractions, you “keep” the first fraction, “change” the division sign to multiplication, and “flip” the second fraction (find its reciprocal). Then, multiply the two resulting fractions.
How do I add fractions with different denominators?
First, find the Least Common Multiple (LCM) of the denominators to establish a common denominator. Then, convert both fractions to equivalent fractions using that common denominator. Finally, add the numerators and keep the common denominator.
Can the result of a fraction calculation be a mixed number?
Yes. If the resulting numerator is larger than the denominator (an improper fraction), it can be converted into a mixed number, which consists of a whole number and a proper fraction.
What is the GCD and why is it important for fractions?
GCD stands for Greatest Common Divisor. It is the largest positive integer that divides both the numerator and the denominator. Dividing both by the GCD is the process used to simplify a fraction to its lowest terms.