Simplifying the Fraction $\frac{25}{225}$ Using the Euclidean Algorithm

Overview

A short visual guide that demonstrates how to reduce the fraction $\frac{25}{225}$ to its simplest form by finding the greatest common divisor (GCD) with the Euclidean algorithm and then performing the division step‑by‑step. The key takeaway is that $\frac{25}{225}=\frac{1}{9}$.

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Phases

#	Phase Name	Duration	Description
1	Intro	~3 s	Title fades in: “Simplifying $\frac{25}{225}$”. A blank fraction appears centered.
2	Show Original Fraction	~4 s	The fraction $\frac{25}{225}$ is drawn with numerator and denominator as large numbers. A subtle pulse highlights the whole fraction.
3	Euclidean Algorithm (Find GCD)	~6 s	A step‑by‑step Euclidean calculation is displayed: 1️⃣ Show “$225 \div 25 = 9$ R 0”. 2️⃣ Highlight the remainder “0” and announce that the GCD is the last non‑zero divisor, 25. Visuals include a sliding division bar, a highlighted divisor box, and a brief “✓ GCD = 25” pop‑up.
4	Divide by GCD	~5 s	The numerator and denominator each animate a division by 25: numbers shrink to $1$ and $9$ respectively. The fraction morphs into $\frac{1}{9}$.
5	Outro	~3 s	The simplified fraction $\frac{1}{9}$ stays on screen while a check‑mark appears, confirming the result. Fade out.

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Layout

┌─────────────────────────────────────┐
│               TOP AREA               │
├─────────────────────────────────────┤
│               MAIN AREA               │
│   (centered fraction and animations) │
├─────────────────────────────────────┤
│               BOTTOM AREA            │
└─────────────────────────────────────┘

Area Descriptions

Area	Content	Notes
Top	Title text “Simplifying $\frac{25}{225}$”	Fades in during Intro, remains visible until end of Phase 2
Main	The fraction itself, Euclidean‑algorithm calculation, highlights, arrows, and division animation	Central focus; all steps occur here
Bottom	Small caption “Result: $\frac{1}{9}$” that appears in the Outro	Appears only in the final phase

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Notes

• Keep the total runtime under 20 seconds to maintain brevity.
• Use a consistent color scheme: original fraction in blue, Euclidean‑algorithm steps in orange, division steps in green, final result in dark blue.
• No explanatory text is required beyond the title and final caption; the visual steps convey the process.
• The Euclidean algorithm visualization should be clear and quick (e.g., a division bar with remainder appearing, then a “GCD = 25” badge).
• The scene must be implemented as a single Manim Scene class.