Fraction Calculator

Master the math of parts. Handle complex operations with mixed numbers and unlike denominators. Get step-by-step solutions for homework, carpentry, or recipes using standard US math rules.

Fractions are often the first major stumbling block in mathematics. Unlike whole numbers, you cannot simply add the tops and bottoms. You need a "Common Denominator." The Fraction Calculator is your automated tutor. It handles the "Least Common Multiple" (LCM) for addition, performs the "Reciprocal" flip for division, and automatically simplifies the final result to its lowest terms.

Whether you are a student checking your homework or a carpenter measuring 5/8 of an inch, this tool ensures your fractional math is precise.

[Image of parts of a fraction numerator denominator]

➗ The Golden Rules of Fraction Math

The rules change depending on the operation. Here is the US Common Core standard approach:

        Addition/Subtraction: Must find LCD (Least Common Denominator).

        Multiplication: Multiply straight across (Top×Top, Bottom×Bottom).

        Division: "Keep, Change, Flip." (Multiply by the reciprocal).

Key Terms:

Numerator: The top number (How many parts you have).
Denominator: The bottom number (Total parts in a whole).
Mixed Number: A whole number combined with a fraction (e.g., 1 ½).

👨‍🏫 Scenario: The "Unlike Denominator" Challenge

The most common error is adding fractions with different bottoms. Let's solve: 2/3 + 3/4.

CLASSROOM SOLVER: 2/3 + 3/4
Step 1: Find LCD	Multiples of 3: 3, 6, 9, 12 Multiples of 4: 4, 8, 12 LCD = 12
Step 2: Rename Fractions	2/3 becomes 8/12 (×4) 3/4 becomes 9/12 (×3)
Step 3: Add Numerators	8 + 9 = 17 Result: 17/12 (Improper)
FINAL ANSWER	1 5/12 (Mixed Number)

Academic Insight: In higher-level algebra, "Improper Fractions" (17/12) are often preferred because they are easier to calculate with. However, in daily life (like cooking or carpentry), "Mixed Numbers" (1 5/12) are easier to visualize.

Common US Fraction Standards

Keep-Change-Flip: The standard mnemonic taught in US schools for dividing fractions. You Keep the first fraction, Change division to multiplication, and Flip the second fraction (Reciprocal).
Lowest Terms: A fraction is not considered "done" until it is simplified. 4/8 is mathematically correct, but 1/2 is the accepted answer. You divide the top and bottom by the Greatest Common Factor (GCF).
Decimal Conversion: Fractions are just division problems waiting to happen. 1/2 literally means "1 divided by 2," which equals 0.5.

Frequently Asked Questions (FAQs)

What is an Improper Fraction?

An improper fraction is a "top-heavy" fraction where the numerator is larger than the denominator (e.g., 5/4). It means you have more than one whole item. It can be converted into a Mixed Number (1 1/4).

How do I calculate 20% as a fraction?

Percent means "per 100." So 20% is 20/100. To simplify, divide both top and bottom by 20. The result is 1/5.

Why do we need a common denominator for adding?

Imagine trying to add "3 apples" and "2 oranges." You can't say "5 apple-oranges." You need a common unit (like "5 pieces of fruit"). In fractions, the denominator is the unit. You can't add Thirds to Fourths until they both become Twelfths.

Can calculators handle mixed numbers directly?

Most basic calculators cannot. You usually have to convert mixed numbers to improper fractions first (Multiply whole number by denominator, add numerator) to perform the calculation, then convert back.

What is the Reciprocal?

The Reciprocal is simply flipping the fraction upside down. The reciprocal of 3/4 is 4/3. This is used exclusively for division.

Fraction Calculator