Simplified Fraction
3/2
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Simplify Calculator
Switch between fraction reduction and radical simplification with instant clean outputs.
Mixed Number
1 1/2
Decimal
1.5
Simplified Radical
6√2
Decimal Approximation
8.485281
The Ultimate Simplify Calculator: Clean Up Your Math
Whether you are a student tackling a grueling algebra assignment, a carpenter measuring cuts for a custom cabinet, or a home chef trying to scale down a baking recipe, dealing with messy, unsimplified numbers is a recipe for disaster. Unwieldy fractions and complex square roots lead to calculation errors and confusion.
Our comprehensive Simplify Calculator is designed to instantly clean up your mathematical expressions. By toggling between our fraction reducer and our radical simplifier, you can instantly find the lowest common terms, convert improper fractions to mixed numbers, and pull perfect squares out of root equations. Stop guessing with mental math and start getting standardized, textbook-perfect answers in seconds.
How to Simplify Fractions (Lowest Terms)
Simplifying a fraction means finding an equivalent fraction where the numerator (the top number) and the denominator (the bottom number) are as small as possible. To do this manually, you must find the Greatest Common Factor (GCF)—the largest number that divides evenly into both parts of the fraction.
Step-by-Step Example: Simplifying 24/36
- List the factors of the numerator (24): 1, 2, 3, 4, 6, 8, 12, 24.
- List the factors of the denominator (36): 1, 2, 3, 4, 6, 9, 12, 18, 36.
- Identify the GCF: The largest number appearing on both lists is 12.
- Divide both parts by the GCF:
- 24 ÷ 12 = 2
- 36 ÷ 12 = 3
- The simplified fraction is 2/3.
How to Simplify Radicals (Square Roots)
Simplifying a radical is very different from simplifying a fraction. Instead of looking for division factors, you are looking for perfect squares (numbers like 4, 9, 16, 25, 36) hiding inside the number under the root (the radicand).
The goal is to pull the largest perfect square out of the radical. For example, let's simplify √72:
- 1. Find the largest perfect square factor: 72 can be divided by 36 (a perfect square, since 6 × 6 = 36).
- 2. Rewrite the radical: √72 becomes √(36 × 2).
- 3. Pull out the root: The square root of 36 is 6. The 2 stays trapped inside.
- 4. Final Answer: 6√2.
Quick Reference: Common Simplifications
Memorizing the most common fraction and radical reductions will dramatically speed up your ability to solve complex math problems. Use this quick reference chart for standard conversions.
| Unsimplified Fraction | Simplified Form |
|---|---|
| 2/4, 3/6, 4/8, 50/100 | 1/2 |
| 3/12, 4/16, 25/100 | 1/4 |
| 2/6, 4/12, 10/30 | 1/3 |
| 15/10 (Improper) | 1 1/2 (Mixed) |
| Unsimplified Radical | Simplified Form |
|---|---|
| √8 | 2√2 |
| √12 | 2√3 |
| √20 | 2√5 |
| √50 | 5√2 |
Frequently Asked Questions
What is the difference between simplifying and solving?
Solving an equation means finding the specific value of a variable (like discovering that x = 4). Simplifying an expression simply means rewriting it in its most compact, easy-to-read format without changing its actual mathematical value. 2/4 and 1/2 are the exact same amount, but 1/2 is simplified.
Do I always have to convert an improper fraction to a mixed number?
It depends on your context. In advanced algebra and calculus, it is usually preferred to leave the answer as a simplified improper fraction (e.g., 5/2). However, in lower-level math classes, baking, or carpentry, mixed numbers (e.g., 2 1/2) are standard because they are easier to visualize in the real world.
How do I know if a fraction is fully simplified?
A fraction is fully simplified (in its lowest terms) when the only common factor between the numerator and the denominator is the number 1. For example, with 3/5, no whole number other than 1 can divide evenly into both 3 and 5.
Can a radical be simplified if there are no perfect squares?
No. If the number under the square root does not contain any perfect square factors (4, 9, 16, 25, etc.), it is already in its simplest radical form. For example, √15 cannot be simplified because its only factors are 1, 3, 5, and 15—none of which are perfect squares.
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