Fraction & Mixed Number Calculator
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Understanding Fractions and Mixed Numbers
Fractions and mixed numbers are fundamental concepts in mathematics, representing parts of a whole. This calculator helps you perform basic arithmetic operations on them, simplifying the process of addition, subtraction, multiplication, and division.
What is a Fraction?
A fraction represents a part of a whole. It consists of two numbers: a numerator and a denominator. The numerator (top number) indicates how many parts you have, and the denominator (bottom number) indicates how many equal parts the whole is divided into. For example, in the fraction 1/2, you have 1 part out of 2 equal parts.
What is a Mixed Number?
A mixed number is a combination of a whole number and a proper fraction. A proper fraction is one where the numerator is smaller than the denominator (e.g., 1/2, 3/4). For instance, 2 1/2 is a mixed number, meaning two whole units and an additional half unit.
Converting Between Mixed Numbers and Improper Fractions
To perform calculations, mixed numbers are often converted into improper fractions. An improper fraction is one where the numerator is greater than or equal to the denominator (e.g., 5/2, 7/4). To convert a mixed number (Whole N/D) to an improper fraction:
(Whole × Denominator + Numerator) / Denominator
For example, 2 1/2 becomes (2 × 2 + 1) / 2 = 5/2.
To convert an improper fraction back to a mixed number, divide the numerator by the denominator. The quotient is the whole number, and the remainder becomes the new numerator over the original denominator. For example, 5/2 is 5 ÷ 2 = 2 with a remainder of 1, so it becomes 2 1/2.
Arithmetic Operations with Fractions
1. Adding and Subtracting Fractions
To add or subtract fractions, they must have a common denominator. If they don't, you need to find the least common multiple (LCM) of the denominators and convert the fractions to equivalent fractions with that common denominator. Once the denominators are the same, you simply add or subtract the numerators and keep the denominator the same.
Example: 1/2 + 1/4
- Find a common denominator for 2 and 4, which is 4.
- Convert 1/2 to 2/4.
- Now, 2/4 + 1/4 = (2+1)/4 = 3/4.
2. Multiplying Fractions
Multiplying fractions is straightforward: multiply the numerators together and multiply the denominators together. Simplify the resulting fraction if possible.
Example: 1/2 × 1/4
- Multiply numerators: 1 × 1 = 1
- Multiply denominators: 2 × 4 = 8
- Result: 1/8
3. Dividing Fractions
To divide fractions, you "keep, change, flip." Keep the first fraction as it is, change the division sign to multiplication, and flip (invert) the second fraction (swap its numerator and denominator). Then, multiply the fractions as usual.
Example: 1/2 ÷ 1/4
- Keep 1/2.
- Change ÷ to ×.
- Flip 1/4 to 4/1.
- Now, 1/2 × 4/1 = (1 × 4) / (2 × 1) = 4/2.
- Simplify: 4/2 = 2.
This calculator automates these steps, allowing you to quickly perform calculations and see the simplified results, including mixed number conversions where applicable.