Calculator with Fractions and Whole Numbers

Fraction & Whole Number Calculator

Perform arithmetic operations with fractions and whole numbers. Enter fractions as "numerator/denominator" (e.g., 1/2) and whole numbers as just the number (e.g., 5).

First Number:

Operation: + – * /

Second Number:

Understanding Fractions and Whole Numbers

Fractions represent parts of a whole, expressed as a ratio of two integers: a numerator (the top number) and a denominator (the bottom number). For example, 1/2 means one part out of two equal parts. Whole numbers are non-negative integers (0, 1, 2, 3, …).

How This Calculator Works

This calculator allows you to perform basic arithmetic operations (addition, subtraction, multiplication, and division) between any combination of fractions and whole numbers. You can enter fractions in the format "numerator/denominator" (e.g., 3/4) and whole numbers as just the number (e.g., 7). The calculator will automatically simplify the result to its lowest terms.

Key Concepts:

Numerator: The top number in a fraction, indicating how many parts of the whole are being considered.
Denominator: The bottom number in a fraction, indicating the total number of equal parts the whole is divided into. It cannot be zero.
Whole Number: An integer that is not negative. In fraction form, a whole number 'N' can be written as 'N/1'.
Simplification: Reducing a fraction to its simplest form by dividing both the numerator and the denominator by their greatest common divisor (GCD). For example, 2/4 simplifies to 1/2.

Arithmetic Operations Explained

1. Addition of Fractions/Whole Numbers

To add fractions, they must have a common denominator. If they don't, you find the least common multiple (LCM) of the denominators and convert the fractions. For example, 1/2 + 1/4. The common denominator is 4. So, 2/4 + 1/4 = 3/4. When adding a whole number, treat it as a fraction with a denominator of 1 (e.g., 3 = 3/1).

2. Subtraction of Fractions/Whole Numbers

Similar to addition, fractions must have a common denominator for subtraction. For example, 3/4 – 1/2. The common denominator is 4. So, 3/4 – 2/4 = 1/4. Again, treat whole numbers as fractions over 1.

3. Multiplication of Fractions/Whole Numbers

Multiplying fractions is straightforward: multiply the numerators together and multiply the denominators together. For example, 1/2 * 3/4 = (1*3)/(2*4) = 3/8. When multiplying by a whole number, convert it to a fraction (e.g., 5 * 1/3 = 5/1 * 1/3 = 5/3).

4. Division of Fractions/Whole Numbers

To divide by a fraction, you "invert and multiply." This means you flip the second fraction (reciprocal) and then multiply. For example, 1/2 / 1/4 = 1/2 * 4/1 = 4/2 = 2. When dividing by a whole number, convert it to a fraction (e.g., 1/2 / 3 = 1/2 / 3/1 = 1/2 * 1/3 = 1/6).

Examples Using the Calculator

Adding a fraction and a whole number: If you enter "1/3" and "2" with the "+" operator, the result will be 2 1/3 (or 7/3).
Subtracting fractions: If you enter "3/4" and "1/2" with the "-" operator, the result will be 1/4.
Multiplying fractions: If you enter "2/3" and "1/5" with the "*" operator, the result will be 2/15.
Dividing a whole number by a fraction: If you enter "5" and "1/2" with the "/" operator, the result will be 10.

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