Fraction Calculator Guide

What This Calculator Does

This fraction calculator covers three common tasks in one place: reducing a fraction to lowest terms, performing addition, subtraction, multiplication, or division on two fractions, and comparing two fractions. Depending on the mode, it adds a simplified fraction, mixed-number view, decimal, percentage, or common-denominator comparison, making it useful for classwork, homework checks, and everyday arithmetic.

The input model is deliberately explicit: enter the numerator and denominator separately, and make both integers. The page does not parse mixed numbers or decimal numerators and denominators directly. If your source value is a decimal, use the decimal fraction converter instead.

When to Use It

• You want to reduce 18/24 to lowest terms.
• You need to add, subtract, multiply, or divide two fractions.
• You want to check which of two fractions is larger or whether they are equal.
• You want to see an improper fraction as a mixed number, decimal, or percentage when that view applies.

Inputs Explained

Mode

The page has three modes: simplify, operation, and compare. Simplify needs only the first fraction; the other two modes also need a second fraction. Choosing the mode first keeps the required fields clear.

Numerators and Denominators

Every numerator and denominator field must contain an integer, and denominators cannot be 0. Negative values are allowed. If the negative sign is placed in a denominator, the page moves it to the numerator so the displayed denominator stays positive. A zero fraction is normalized to 0/1.

Operator and Second Fraction

In operation mode, choose addition, subtraction, multiplication, or division and enter the second fraction. Division also requires the second fraction to have a non-zero value. Compare mode has no operator; it reports the relationship between the two normalized fractions.

The page recalculates as inputs change. The Calculate button runs the same logic explicitly and stores the current parameters in the URL, which helps with checking or sharing a calculation.

How the Calculation Works

The page first keeps each denominator positive and reduces each fraction with the greatest common divisor. For normalized fractions a/b and c/d, the core rules are:

• Simplification: divide by gcd(|a|, b).
• Addition: a/b + c/d = (ad + bc) / bd, then reduce.
• Subtraction: a/b - c/d = (ad - bc) / bd, then reduce.
• Multiplication: a/b × c/d = ac / bd, then reduce.
• Division: a/b ÷ c/d = ad / bc, with c ≠ 0.

Compare mode finds a common denominator using the least common multiple, scales both numerators, and compares those integers. It also keeps both decimal values as a secondary check. The fraction result remains the exact representation; decimal and percent values are display forms.

Example

Calculate 1/2 + 3/4

Choose operation mode, enter 1/2 as the first fraction and 3/4 as the second, then choose addition:

1. Cross-multiply to get (1×4 + 3×2) / (2×4).
2. This gives 10/8, which reduces to 5/4.
3. The page also shows the mixed number 1 1/4 and decimal 1.25.

Compare 2/3 and 3/5

Compare mode rewrites them over a shared denominator: 2/3 = 10/15 and 3/5 = 9/15. The result is therefore 2/3 > 3/5, with decimal values 0.66666667 and 0.6 as a second way to check the relationship.

How to Understand the Result

Original and Simplified Fractions

Simplify mode keeps both the normalized input fraction and the reduced fraction. For example, -6/-8 is first normalized to 6/8, then reduced to 3/4.

Mixed Number, Decimal, and Percentage

When an improper fraction has a useful mixed-number form, the page shows it. Simplify mode also shows decimal and percentage views. These are alternate representations of the same value, not new results. Repeating decimals are displayed to at most 8 decimal places, so the fraction is the authoritative exact form.

Comparison Result

Compare mode reports >, <, or = and shows both the common-denominator fractions and decimal values. The common denominator is useful for checking the reasoning; the decimals provide a quick sense of size.

Common Mistakes

• Typing 1 1/2 or 0.75 into a numerator field; the current page expects separate integer fields.
• Entering a denominator of 0.
• Dividing by a second fraction whose value is 0.
• Reading only a rounded decimal when the exact fraction is required.
• Switching modes without filling the second fraction when it is needed.

FAQ

Are results reduced automatically?

Yes. Simplification and operation results are normalized and reduced to lowest terms before they are displayed.

Can it compare negative fractions?

Yes. The page accepts signed numerators and denominators, normalizes the sign placement, and then compares the numeric values.

Why does simplify mode show an original fraction too?

The original value lets you compare the normalized input with the final reduced form, which makes sign and entry mistakes easier to spot.

Can I enter a mixed number directly?

No. Convert 2 1/3 to 7/3, then enter 7 and 3 in the separate numerator and denominator fields. For decimal input, use the decimal fraction converter.

When should I use a GCF or LCM calculator instead?

Use the GCF calculator when you only need the greatest common factor of the numerator and denominator. Use the LCM calculator when you need the least common multiple of several denominators separately.

Notes

This tool is designed for ordinary integer-based fractions, basic arithmetic, and comparison of two fractions. It does not directly accept mixed numbers, decimal numerators or denominators, algebraic expressions, or symbolic derivations. Decimal and percentage views have finite display precision, and very large integers can be affected by JavaScript number precision in the browser.

If you need every handwritten common-denominator or reduction line, use the formulas and results here as a checking aid; the page is a fast calculator and review tool, not a full symbolic-step engine.