Simplify Fractions Calculator (Step-by-Step)

Free Simplify Fractions Calculator with Steps

GoMim's simplify fractions calculator helps you reduce any fraction to its lowest terms and see every step in the process.

Just type your fraction (or paste your math problem), and our AI math solver will:

• Find the greatest common divisor (GCD)
• Reduce the fraction step by step
• Explain each step in clear, simple language

What Does It Mean to Simplify Fractions?

In mathematics, "simplify" means reducing a mathematical expression to its simplest form. This can involve combining like terms, factoring, or using the distributive property. For example, $2x + 3x$ simplifies to $5x$ by combining like terms. A fraction such as $\frac{6}{8}$ simplifies to $\frac{3}{4}$ by dividing both numerator and denominator by their greatest common divisor. Tools like a Simplify Calculator or a simplifying calculator can assist in performing these steps quickly, but understanding the underlying concepts is key to mastering math.

Simplifying Fractions to Lowest Terms

Lowest terms means a fraction has been simplified as much as possible. In other words, the numerator and denominator have no common factor other than 1. To simplify a fraction to its lowest terms, you divide both numbers by their greatest common divisor (GCD). Once the GCD is 1, the fraction is fully reduced.

How to Simplify Fractions Step by Step

Simplifying a fraction means reducing it to its lowest terms, where the numerator and denominator share no common factor except 1. Here’s the standard method students can follow:

General Steps

1. Find the Greatest Common Divisor (GCD)

Identify the largest number that divides both the numerator and denominator.

1. Divide both the numerator and denominator by the GCD

This reduces the fraction in one clean step.

1. Check whether the fraction can be simplified further
2. If the GCD becomes 1, the fraction is already in its lowest terms.

Example 1: Simplify 24/36

1. The GCD of 24 and 36 is 12.
2. Divide both by 12:
3. 24 ÷ 12 = 2
4. 36 ÷ 12 = 3
5. Result: 24/36 → 2/3

Example 2: Simplify 45/60

1. The GCD of 45 and 60 is 15.
2. Divide both by 15:
3. 45 ÷ 15 = 3
4. 60 ÷ 15 = 4
5. Result: 45/60 → 3/4

Using the GCD to Reduce Fractions

Steps to simplify a fraction using the GCD:

1. Identify the numerator and denominator of the fraction.
2. Find the Greatest Common Divisor (GCD) of the two numbers.
3. Divide both numerator and denominator by the GCD.
4. Write the resulting fraction—this is the fraction in its lowest terms.

Example: Simplify 24/36

• GCD of 24 and 36 is 12
• Divide both by 12 → 24 ÷ 12 = 2, 36 ÷ 12 = 3
• Simplified fraction = 2/3

Simplifying Fractions Mentally vs. Using a Calculator

Steps to simplify mentally:

1. Look for common factors between the numerator and the denominator.
2. Divide both numbers by a common factor.
3. Repeat if necessary until no common factors remain.

Steps using a calculator:

1. Enter the numerator and denominator into the calculator.
2. Compute the GCD using a built-in function or online tool.
3. Divide both numbers by the GCD to get the fraction in lowest terms.

Example (mental): 15/25 → divide both by 5 → 3/5

Examples: Simplifying Fractions to Lowest Terms

Here are some typical practice problems where you reduce fractions to their simplest form. Try them yourself first, then compare your work with the step-by-step solutions.

Fractions

Simplify by reducing to lowest terms or converting improper fractions to mixed numbers.

Example 1: Simplify $\frac{9}{6}$

Solution:

• Step 1: Find the greatest common divisor (GCD) of 9 and 6 (GCD = 3).
• Step 2: Divide numerator and denominator by 3: $\frac{9 \div 3}{6 \div 3} = \frac{3}{2}$

Answer: $\frac{3}{2}$

Example 2: Convert $\frac{7}{4}$ to a mixed number

Solution:

• Step 1: Divide 7 by 4: $7 \div 4 = 1$ with a remainder of 3.
• Step 2: Write as a mixed number: $1\frac{3}{4}$

Answer: $1\frac{3}{4}$

Converting Improper Fractions and Mixed Numbers

Improper fractions and mixed numbers express the same value in different forms.

An improper fraction has a numerator larger than (or equal to) the denominator, while a mixed number combines a whole number with a proper fraction. Converting between them is a key skill in arithmetic and algebra.

Convert Improper Fractions to Mixed Numbers

To convert an improper fraction into a mixed number:

1. Divide the numerator by the denominator to find the whole number.
2. Use the remainder as the new numerator.
3. Keep the same denominator for the fractional part.
4. Write the result as: whole number + remainder/denominator.

Example 1: Convert 17/5

• 17 ÷ 5 = 3 remainder 2
• Result: 3 2/5

Example 2: Convert 22/6

• 22 ÷ 6 = 3 remainder 4
• Result: 3 4/6 → can be simplified to 3 2/3

Convert Mixed Numbers to Improper Fractions

To convert a mixed number back into an improper fraction:

1. Multiply the whole number by the denominator.
2. Add the numerator of the fractional part.
3. Place the result over the original denominator.

Examples: Convert Mixed Numbers to Improper Fractions

These questions ask you to convert mixed numbers into improper fractions. Follow the step-by-step process to turn each mixed number into a single fraction.

Example 1: Convert 4 1/3

• 4 × 3 = 12
• 12 + 1 = 13
• Result: 13/3

Examples: Convert Improper Fractions to Mixed Numbers

In these examples, the numerator is larger than the denominator. We rewrite each improper fraction as a mixed number and show the steps.

Example 2: Convert 2 5/8

• 2 × 8 = 16
• 16 + 5 = 21
• Result: 21/8

Working with Decimal Fractions

Here are a few examples where we switch between decimal and fraction forms. See how each decimal can be written as a fraction and simplified.

Convert Decimals to Fractions

Converting decimals helps in exact calculations.

Example: Convert $0.75$ to a fraction

Solution:

• Step 1: Write $0.75 = \frac{75}{100}$
• Step 2: Reduce by the GCD (25): $\frac{75}{100} = \frac{3}{4}$

Answer: $\frac{3}{4}$

Convert Fractions to Decimals

Converting fractions to decimals makes calculations easier when working with measurements, percentages, and comparisons.

Example: Convert $\frac{3}{8}$ to a decimal

Solution:

Step 1: Divide the numerator by the denominator: $3 \div 8 = 0.375$

Step 2: If needed, round to the desired decimal place.

Answer: 0.375

Simplifying Algebraic Expressions (Bonus Feature)

Here are some typical practice problems where you reduce fractions to their simplest form. Try them yourself first, then compare your work with the step-by-step solutions

Examples: Simplifying Algebraic Expressions Step by Step

Simplify by combining like terms and factoring (when possible).

Example 1: Simplify $2x^2 + 5x + 3x^2$

Solution:

• Step 1: Combine like terms: $2x^2 + 3x^2 = 5x^2$
• Step 2: Add remaining terms: $5x^2 + 5x$

Answer: $5x^2 + 5x$

Example 2: Simplify $6y + 2y - 3y$

Solution:

• Step 1: Combine like terms: $6y + 2y = 8y$
• Step 2: Subtract $3y$: $8y - 3y = 5y$

Answer: $5y$

Practice Problems: Simplify Fractions with Solutions

Practice: Simplify These Fractions with GoMim

Use the problems below as extra practice. You can enter any of them into the GoMim simplify fractions calculator to see the full step-by-step solution and check your work.

Exponents

Simplify by applying exponent rules (e.g., adding exponents for same-base multiplication, multiplying exponents for powers of powers).

Example 1: Simplify $x^3 \cdot x^2$

Solution:

• Step 1: Add exponents of the same base: $3 + 2 = 5$

Answer: $x^5$

Example 2: Simplify $(x^2)^3$

Solution:

• Step 1: Multiply exponents: $2 \cdot 3 = 6$

Answer: $x^6$

Positive and Negative Fractions

Simplify by finding a common denominator first, then combining terms carefully.

Simplifying Positive and Negative Fractions

The following problems involve negative fractions and signs. Pay attention to how the sign changes as you simplify each fraction.

Example 1: Simplify $\frac{3}{4} - \frac{5}{6}$

Solution:

• Step 1: Find the least common multiple (LCM) of 4 and 6 (LCM = 12).
• Step 2: Convert fractions to have the common denominator: $\frac{3}{4} = \frac{9}{12}$, $\frac{5}{6} = \frac{10}{12}$
• Step 3: Subtract: $\frac{9}{12} - \frac{10}{12} = -\frac{1}{12}$

Answer: $-\frac{1}{12}$

Example 2: Simplify $-\frac{2}{5} + \frac{7}{10}$

Solution:

• Step 1: Find the LCM of 5 and 10 (LCM = 10).
• Step 2: Convert fractions to have the common denominator: $-\frac{2}{5} = -\frac{4}{10}$
• Step 3: Add: $-\frac{4}{10} + \frac{7}{10} = \frac{3}{10}$

Answer: $\frac{3}{10}$

Using a simplifying calculator or simplify fractions calculator can verify these results, but working through each step strengthens your understanding of algebra, fractions, exponents, and combined operations.

Distributive Property

Apply the distributive property, combine like terms, and factor if possible.

Example: Simplify $2(x + 3) + 4x$

Solution:

• Step 1: Apply the distributive property: $2x + 6 + 4x$
• Step 2: Combine like terms: $6x + 6$
• Step 3: Factor out the common term (6): $6(x + 1)$

Answer: $6(x + 1)$

Mixed Fraction Problems

Simplify by converting to a common denominator or rewriting improper fractions as mixed numbers.

Example: Simplify $\frac{11}{4} + \frac{3}{2}$

Solution:

• Step 1: Convert to a common denominator (4): $\frac{11}{4} + \frac{6}{4}$
• Step 2: Add the numerators: $\frac{17}{4}$
• Step 3: Convert the improper fraction to a mixed number: $4\frac{1}{4}$

Answer: $4\frac{1}{4}$

These examples show how systematic steps lead to correct results. A Simplify Calculator with steps can guide you through each stage, and many students rely on free step-by-step math calculators to double-check answers. While tools help, practicing the process builds a deeper understanding.

Related Fraction Calculators and Topics

More Fraction Tools on GoMim

• Common Denominator Calculator
• Fraction to Decimal Calculator
• Mixed Number to Improper Fraction Calculator

Why is Simplification Important?

Simplifying expressions is a core skill in mathematics because it reduces problems to their simplest form and makes calculations faster. Whether you use a Simplify calculator with steps or solve manually, the goal is to make equations clearer and avoid mistakes. For example, the simplify calculator will then show you the steps clearly, but understanding the process ensures long-term mastery. In exams, simplifying expressions can save valuable time and reduce errors. In engineering, simplified models allow for more efficient analysis and design. In data analysis, breaking down complex formulas into simpler terms leads to better predictions. Overall, to simplify an expression is not just a classroom exercise—it is a tool that enhances accuracy and problem-solving in many fields.

Use GoMim Math AI Solver for Simplifying Tasks

To make learning easier, you can use GoMim Math AI Solver for simplify tasks. The AI solver instantly reduces fractions, applies exponent rules, and organizes each step with clear explanations. For students, it works like a free step-by-step math calculator that not only gives the answer but also explains how to reach it. It supports different needs, whether you want to handle decimals using a decimal to fraction method, work with a mixed fraction calculator, or practice with an adding positive and negative fraction calculator. Most importantly, AI shows detailed reasoning, so you learn the rules while practicing. With GoMim, the simplify calculator will then show you the steps in a way that feels like having a real tutor.

⚠Explore more math solutions today❗ Try GoMim Math Calculator

FAQ

Q: What does it mean to simplify a fraction?

A: To simplify a fraction means to reduce it to its lowest terms so that the numerator and denominator have no common factor other than 1. For example, $\frac{8}{12}$ can be simplified to $\frac{2}{3}$ by dividing both 8 and 12 by their greatest common divisor, which is 4.

Q: How do I simplify fractions step by step?

A: The usual steps are:

1. Find the greatest common divisor (GCD) of the numerator and denominator.
2. Divide both the numerator and denominator by the GCD.
3. Check whether the fraction can be reduced any further.
4. GoMim’s simplify fractions calculator follows these steps for you and shows each step clearly.

Q: Is this simplify fractions calculator free to use?

A: Yes. You can use GoMim’s simplify fractions calculator for free. Just enter your fraction or paste a full problem, and the AI solver will generate the answer with step-by-step explanations.

Q: Can I use this tool to check my homework answers?

A: Absolutely. You can enter the same fraction or problem you have in your homework and compare your steps with the solution shown by GoMim. This helps you see where you did well and where you might have made a mistake.

Q: Can GoMim simplify more than fractions, like algebraic expressions?

A: Yes. Besides simplifying numerical fractions, GoMim can also simplify many algebraic expressions. It can combine like terms, remove brackets, and handle exponents, while still explaining each step so you can learn the underlying method.