Calculator with Negative and Positive Fractions

A fraction represents a part of a whole. Fractions can be positive or negative, and they can be added, subtracted, multiplied, and divided. This calculator helps you work with fractions, including negative values.

What are fractions?

A fraction consists of a numerator (top number) and a denominator (bottom number). For example, in 3/4, 3 is the numerator and 4 is the denominator. Fractions can represent parts of a whole, ratios, or operations.

Fractions can be proper (numerator smaller than denominator) or improper (numerator larger than denominator). They can also be mixed numbers (a whole number plus a fraction).

Operations with fractions

Addition and subtraction

To add or subtract fractions, they must have the same denominator. If they don't, find a common denominator by multiplying the denominators.

Addition: a/b + c/d = (ad + bc)/bd

Subtraction: a/b - c/d = (ad - bc)/bd

Multiplication

Multiply the numerators together and the denominators together.

a/b × c/d = (a × c)/(b × d)

Division

To divide fractions, multiply by the reciprocal of the second fraction.

a/b ÷ c/d = a/b × d/c = (a × d)/(b × c)

Negative fractions

Negative fractions have a negative sign before the numerator or denominator. The sign affects the result of operations:

Positive × Positive = Positive
Positive × Negative = Negative
Negative × Negative = Positive

When adding or subtracting fractions with different signs, subtract the smaller absolute value from the larger one and keep the sign of the larger fraction.

Examples

Addition example

Calculate 1/4 + 3/4:

1/4 + 3/4 = (1 + 3)/4 = 4/4 = 1

Subtraction example

Calculate 5/6 - 1/3:

5/6 - 1/3 = 5/6 - 2/6 = 3/6 = 1/2

Multiplication example

Calculate 2/3 × 3/4:

2/3 × 3/4 = (2 × 3)/(3 × 4) = 6/12 = 1/2

Division example

Calculate 3/4 ÷ 2/3:

3/4 ÷ 2/3 = 3/4 × 3/2 = (3 × 3)/(4 × 2) = 9/8

FAQ

How do I add fractions with different denominators?

Find a common denominator by multiplying the denominators, then add the numerators. For example, 1/2 + 1/3 becomes 3/6 + 2/6 = 5/6.

What happens when I multiply a negative fraction by a positive fraction?

The result is negative. For example, -2/3 × 3/4 = -6/12 = -1/2.

How do I simplify a fraction?

Divide both the numerator and denominator by their greatest common divisor. For example, 4/8 simplifies to 1/2.

Can fractions be converted to decimals?

Yes, divide the numerator by the denominator. For example, 3/4 = 0.75.