Subtracting Fractions Calculator - Fraction Subtraction Online

What is Subtracting Fractions?

Subtracting fractions is a fundamental mathematical operation that involves finding the difference between two fractions. It's essential in algebra, geometry, and many real-world applications. The process requires finding a common denominator, converting both fractions to equivalent fractions with the same denominator, and then subtracting the numerators.

a/b - c/d = (a×d - c×b) / (b×d)

Definition of Fraction Subtraction

Fraction subtraction is the process of finding the difference between two fractions. The result is another fraction that represents how much the first fraction is greater than the second fraction. When the first fraction is smaller than the second, the result is negative.

Key Concepts

Minuend: The first fraction (the one being subtracted from)
Subtrahend: The second fraction (the one being subtracted)
Common Denominator: A shared denominator for both fractions
Least Common Multiple (LCM): The smallest common multiple of two denominators
Equivalent Fractions: Fractions that represent the same value
Simplified Form: A fraction reduced to its lowest terms

Frequently Asked Questions

How do I subtract fractions with different denominators?

To subtract fractions with different denominators: 1) Find the Least Common Multiple (LCM) of the denominators, 2) Convert both fractions to equivalent fractions with the common denominator, 3) Subtract the numerators while keeping the common denominator, 4) Simplify the result if possible. For example, 3/4 - 1/2 = 3/4 - 2/4 = 1/4.

What if the result is negative when subtracting fractions?

A negative result occurs when the first fraction (minuend) is smaller than the second fraction (subtrahend). This is perfectly normal and mathematically correct. For example, 1/4 - 3/4 = -2/4 = -1/2. The negative sign indicates that the second fraction is larger than the first.

Do I always need to find the LCM when subtracting fractions?

No, you only need to find the LCM when the denominators are different. If the fractions already have the same denominator, you can directly subtract the numerators. For example, 5/6 - 2/6 = 3/6 = 1/2. The LCM method is used to convert fractions with different denominators to equivalent fractions with a common denominator.

How do I simplify the result after subtracting fractions?

To simplify a fraction, find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both by this number. For example, if the result is 6/8, the GCD of 6 and 8 is 2, so 6/8 = (6÷2)/(8÷2) = 3/4. The simplified form is always preferred unless you need the exact decimal value.