Students are shown how to simplify fractions by reducing them to lowest terms. Examples include both proper and improper fractions. GCF is shown to be the most efficient method for simplifying.

For more help, check out our Introduction to Fractions Lessons Page

Credit goes to Math Antics.

## Reducing Fractions to Lowest Terms

Reducing a fraction to its lowest terms, also known as simplifying or reducing to simplest form, involves dividing both the numerator and the denominator by their greatest common divisor (GCD). The greatest common divisor is the largest number that evenly divides both the numerator and the denominator without leaving a remainder. Reducing a fraction to its lowest terms is crucial for various mathematical operations and ensures that the fraction is expressed in its simplest and most concise form.

Here’s a detailed step-by-step guide on how to reduce a fraction to its lowest terms:

**Step 1) Identify the Numerator and Denominator** – Start by identifying the numerator (the number on the top of the fraction) and the denominator (the number on the bottom of the fraction).

Example: Let’s say we want to reduce the fraction 24 / 36 to its lowest terms:

Identify the numerator and denominator: Numerator = 24, Denominator = 36.

**Step 2) Find the Greatest Common Divisor (GCD)** – Determine the greatest common divisor (GCD) of the numerator and the denominator. The GCD is the largest number that evenly divides both the numerator and the denominator.

**Step 3) List Factors** – List all the factors of both the numerator and the denominator. Factors are the numbers that can be multiplied together to get a certain number.

**Step 4) Identify Common Factors** – Identify the common factors between the numerator and the denominator. These are the factors that both the numerator and the denominator share.

**Step 5) Determine the GCD** – The greatest common divisor (GCD) is the largest of these common factors. It’s the largest number that divides both the numerator and the denominator evenly.

**Step 6) Divide by the GCD** – Divide both the numerator and the denominator by the greatest common divisor (GCD). This step ensures that the fraction is reduced to its simplest form.

**Step 7) Write the Reduced Fraction** – Write down the fraction with the numerator and denominator divided by the greatest common divisor. This is the fraction in its lowest terms.

**Step 8) Check for Further Simplification** – After dividing by the greatest common divisor, check if the fraction can be further simplified. If there are still common factors between the numerator and the denominator, repeat steps 2 through 7 until the fraction can no longer be simplified.

### Why Do We Reduce Fractions?

Reducing fractions to their simplest form is a crucial practice across various mathematical contexts. Simplifying fractions enhances clarity and simplifies comprehension by presenting relationships between parts and wholes in their most straightforward terms. By ensuring fractions are expressed in their lowest terms, comparisons become more precise, facilitating accurate assessments of relative sizes.

This standardization not only aids in clarity but also helps to avoid errors, as simplified fractions reduce the likelihood of mistakes in calculations, especially during complex mathematical operations. Expressing fractions in their simplest form promotes efficiency, streamlining computations and enhancing overall problem-solving processes.

Simplified fractions play a pivotal role in understanding proportions and ratios intuitively, as they provide a clearer picture of the proportional relationship between different quantities. Therefore, reducing fractions to their lowest terms is essential for promoting clarity, accuracy, efficiency, and comprehension in mathematical endeavors.