Master fraction arithmetic instantly. The “How to Put Fractions into a Calculator” tool is designed to help you quickly add, subtract, multiply, or divide two fractions and see the result in its simplest form.
How to Put Fractions into a Calculator
The Simplified Result is:
Fractions Calculator Formula
The underlying formula depends on the operation selected:
Addition: $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$ Subtraction: $$\frac{a}{b} – \frac{c}{d} = \frac{ad – bc}{bd}$$ Multiplication: $$\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}$$ Division: $$\frac{a}{b} \div \frac{c}{d} = \frac{ad}{bc}$$
Formula Source: Math is Fun – Fraction Operations | Khan Academy – Fraction Arithmetic
Variables Used in the Calculator
To use this calculator effectively, you need to input the following variables:
- Numerator (a, c): The top number of the fraction, representing the number of parts.
- Denominator (b, d): The bottom number of the fraction, representing the total number of parts in the whole. Must be a non-zero integer.
- Operation: The arithmetic function you wish to perform (addition, subtraction, multiplication, or division).
Related Calculators
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- Mixed Number to Improper Fraction Converter
- Decimal to Fraction Converter
- Percentage Change Calculator
- Least Common Multiple (LCM) Finder
What is Fraction Arithmetic?
Fraction arithmetic is the process of performing basic mathematical operations—addition, subtraction, multiplication, and division—on numbers represented as fractions. A fraction is a way to represent a part of a whole, expressed as a ratio of two integers: the numerator (the part) over the denominator (the whole).
Understanding how to manipulate fractions is fundamental to all areas of mathematics and science. When adding or subtracting, finding a common denominator is the most critical step. For multiplication and division, the process is far simpler: multiplication is straight across (numerator times numerator, denominator times denominator), and division involves multiplying the first fraction by the reciprocal (flipped version) of the second.
This calculator handles all the complex steps, including finding the correct common denominator and simplifying the final result by dividing the numerator and denominator by their Greatest Common Divisor (GCD).
How to Calculate $\frac{2}{3} + \frac{1}{4}$ (Example)
Follow these steps to calculate the sum of $\frac{2}{3}$ and $\frac{1}{4}$:
- Identify the Fractions and Operation: The fractions are $\frac{2}{3}$ and $\frac{1}{4}$, and the operation is addition. (a=2, b=3, c=1, d=4).
- Find the Common Denominator: Multiply the two denominators: $3 \times 4 = 12$.
- Adjust the Numerators:
- For $\frac{2}{3}$: $2 \times 4 = 8$. New fraction: $\frac{8}{12}$.
- For $\frac{1}{4}$: $1 \times 3 = 3$. New fraction: $\frac{3}{12}$.
- Perform the Addition: Add the new numerators: $8 + 3 = 11$. The result is $\frac{11}{12}$.
- Simplify the Result: The greatest common divisor (GCD) of 11 and 12 is 1, so the fraction $\frac{11}{12}$ is already in its simplest form.
Frequently Asked Questions (FAQ)
You must first find a common denominator, which is typically the Least Common Multiple (LCM) of the two denominators. Once the denominators are the same, you can simply add or subtract the numerators.
The calculator finds the Greatest Common Divisor (GCD) of the resulting numerator and denominator. Both numbers are then divided by the GCD to produce the equivalent, simplified fraction.
The calculator will prevent division by zero. Entering 0 as a denominator is mathematically undefined and will trigger an error message in the result area, prompting you to enter a positive integer.
Yes, you can input negative integers for the numerators (a and c). The calculator will handle the signs correctly during the operation.