481 lines
20 KiB
TypeScript
481 lines
20 KiB
TypeScript
import React, { useRef, useState, useEffect } from "react";
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import {
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ArrowDown,
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Check,
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BookOpen,
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Scale,
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Calculator,
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ArrowLeftRight,
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Percent,
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} from "lucide-react";
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import RatioVisualizerWidget from "../../../components/lessons/RatioVisualizerWidget";
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import UnitConversionWidget from "../../../components/lessons/UnitConversionWidget";
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import PercentChangeWidget from "../../../components/lessons/PercentChangeWidget";
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import MultiStepPercentWidget from "../../../components/lessons/MultiStepPercentWidget";
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import Quiz from "../../../components/lessons/Quiz";
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import {
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PROPORTIONAL_QUIZ_DATA,
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PERCENTAGES_ADV_QUIZ,
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PERCENTAGES_QUIZ_DATA,
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} from "../../../utils/constants";
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import { Frac } from "../../../components/Math";
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interface LessonProps {
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onFinish?: () => void;
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}
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const ProportionalLesson: React.FC<LessonProps> = ({ onFinish }) => {
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const [activeSection, setActiveSection] = useState(0);
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const sectionsRef = useRef<(HTMLElement | null)[]>([]);
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const scrollToSection = (index: number) => {
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setActiveSection(index);
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sectionsRef.current[index]?.scrollIntoView({
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behavior: "smooth",
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block: "start",
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});
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};
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useEffect(() => {
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const observer = new IntersectionObserver(
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(entries) => {
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entries.forEach((entry) => {
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if (entry.isIntersecting) {
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const index = sectionsRef.current.indexOf(
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entry.target as HTMLElement,
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);
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if (index !== -1) {
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setActiveSection(index);
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}
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}
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});
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},
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{ rootMargin: "-20% 0px -60% 0px" },
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);
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sectionsRef.current.forEach((section) => {
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if (section) observer.observe(section);
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});
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return () => observer.disconnect();
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}, []);
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const SectionMarker = ({
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index,
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title,
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icon: Icon,
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}: {
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index: number;
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title: string;
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icon: any;
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}) => {
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const isActive = activeSection === index;
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const isPast = activeSection > index;
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return (
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<button
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onClick={() => scrollToSection(index)}
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className={`flex items-center gap-3 p-3 w-full rounded-lg transition-all ${isActive ? "bg-white shadow-md border border-amber-100" : "hover:bg-slate-100"}`}
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>
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<div
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className={`w-8 h-8 rounded-full flex items-center justify-center shrink-0 ${isActive ? "bg-amber-600 text-white" : isPast ? "bg-amber-400 text-white" : "bg-slate-200 text-slate-500"}`}
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>
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{isPast ? (
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<Check className="w-4 h-4" />
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) : (
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<Icon className="w-4 h-4" />
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)}
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</div>
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<div className="text-left">
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<p
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className={`text-sm font-bold ${isActive ? "text-amber-900" : "text-slate-600"}`}
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>
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{title}
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</p>
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</div>
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</button>
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);
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};
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const allQuizzes = [
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...PROPORTIONAL_QUIZ_DATA,
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...PERCENTAGES_ADV_QUIZ,
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...PERCENTAGES_QUIZ_DATA,
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];
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return (
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<div className="flex flex-col lg:flex-row min-h-screen">
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<aside className="w-full lg:w-64 lg:fixed lg:top-20 lg:bottom-0 lg:overflow-y-auto p-4 border-r border-slate-200 bg-slate-50 z-0 hidden lg:block">
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<nav className="space-y-2">
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<SectionMarker index={0} title="Ratios" icon={Scale} />
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<SectionMarker
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index={1}
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title="Unit Conversions"
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icon={ArrowLeftRight}
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/>
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<SectionMarker index={2} title="Percent Changes" icon={Percent} />
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<SectionMarker
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index={3}
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title="Multi-Step & Interest"
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icon={Calculator}
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/>
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<SectionMarker index={4} title="Practice" icon={BookOpen} />
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</nav>
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</aside>
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<div className="flex-1 lg:ml-64 p-6 md:p-12 max-w-4xl mx-auto">
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{/* Section 1: Ratios */}
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<section
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ref={(el) => {
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sectionsRef.current[0] = el;
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}}
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className="min-h-screen flex flex-col justify-center mb-24 pt-20 lg:pt-0"
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>
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<h2 className="text-4xl font-extrabold text-slate-900 mb-6">
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Ratios & Proportions
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</h2>
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<div className="prose prose-slate text-lg text-slate-600 mb-8">
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<p>
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A <strong>Ratio</strong> compares two quantities. A critical SAT
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skill is distinguishing between <strong>Part-to-Part</strong> and{" "}
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<strong>Part-to-Whole</strong> ratios, and knowing which one a
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question is asking for.
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</p>
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<div className="grid md:grid-cols-2 gap-4 mt-4">
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<div className="bg-amber-50 border border-amber-200 rounded-xl p-5">
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<p className="font-bold text-amber-900 mb-2">Part-to-Part</p>
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<p className="text-sm text-slate-700 mb-2">
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Compares one part of a whole to another part. Neither number
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is the total.
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</p>
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<div className="font-mono text-center bg-white py-1 rounded text-amber-700 text-sm">
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Boys : Girls = 3 : 2
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</div>
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<p className="text-xs text-slate-500 mt-2">
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Means: for every 3 boys there are 2 girls. Total parts = 5.
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</p>
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</div>
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<div className="bg-amber-50 border border-amber-200 rounded-xl p-5">
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<p className="font-bold text-amber-900 mb-2">Part-to-Whole</p>
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<p className="text-sm text-slate-700 mb-2">
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Compares one part to the total. This is equivalent to a
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fraction or percentage.
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</p>
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<div className="font-mono text-center bg-white py-1 rounded text-amber-700 text-sm">
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Boys : Total = 3 : 5
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</div>
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<p className="text-xs text-slate-500 mt-2">
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Means: boys make up 3 out of 5 = 60% of the total group.
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</p>
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</div>
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</div>
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<div className="mt-4 bg-slate-100 p-4 rounded-xl border-l-4 border-amber-500 text-sm">
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<p className="font-bold text-amber-900 mb-1">
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Cross-Multiplication for Proportions
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</p>
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<p className="text-slate-700 mb-2">
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When two ratios are equal (a proportion), cross-multiply to
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solve for an unknown:
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</p>
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<div className="font-mono text-center bg-white py-2 rounded text-slate-700 font-bold mb-1">
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<Frac n="a" d="b" /> = <Frac n="c" d="d" /> → a × d = b × c
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</div>
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<p className="text-xs text-slate-500">
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Example: <Frac n="3" d="4" /> = <Frac n="x" d="20" /> → 3 × 20 =
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4 × x → 60 = 4x → x = <strong>15</strong>
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</p>
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</div>
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<div className="mt-4 bg-amber-50 border border-amber-200 rounded-xl p-4 text-sm">
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<p className="font-bold text-amber-900 mb-1">
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The k-Multiplier Method
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</p>
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<p className="text-slate-700">
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If a ratio is a : b, the actual amounts are <strong>ak</strong>{" "}
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and <strong>bk</strong> for some positive number k. Use this
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when you know the ratio and the total.
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</p>
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<div className="font-mono text-center bg-white py-1 rounded text-amber-700 text-sm mt-2">
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Ratio 3:2, Total = 25 → 3k + 2k = 25 → k = 5 → Parts: 15 and 10
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</div>
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</div>
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<p className="text-base text-slate-600 mt-4">
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Use the tool below to see how scaling a ratio (multiplying by{" "}
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<em>k</em>) keeps the proportions the same.
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</p>
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</div>
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<RatioVisualizerWidget />
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<button
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onClick={() => scrollToSection(1)}
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className="mt-12 group flex items-center text-amber-600 font-bold hover:text-amber-800 transition-colors"
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>
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Next: Unit Conversions{" "}
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<ArrowDown className="ml-2 w-5 h-5 group-hover:translate-y-1 transition-transform" />
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</button>
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</section>
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{/* Section 2: Unit Conversions */}
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<section
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ref={(el) => {
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sectionsRef.current[1] = el;
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}}
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className="min-h-screen flex flex-col justify-center mb-24"
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>
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<h2 className="text-4xl font-extrabold text-slate-900 mb-6">
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Dimensional Analysis
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</h2>
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<div className="prose prose-slate text-lg text-slate-600 mb-8">
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<p>
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To convert units, multiply by conversion fractions equal to 1
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(like <strong>5280 ft per mile</strong>). Arrange the fractions so
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the units you <em>don't</em> want cancel out (top and bottom).
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</p>
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<div className="mt-4 bg-amber-50 border border-amber-200 rounded-xl p-5">
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<p className="font-bold text-amber-900 mb-2">
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Step-by-Step Chain Multiplication
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</p>
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<ol className="list-decimal list-inside space-y-1 text-sm text-slate-700">
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<li>
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Write the starting value as a fraction (e.g., 60 miles / 1
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hour).
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</li>
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<li>
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Multiply by a conversion fraction that cancels the unit you
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want to remove.
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</li>
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<li>Repeat until only the desired units remain.</li>
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<li>
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Multiply all numerators, multiply all denominators, then
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divide.
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</li>
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</ol>
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</div>
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<div className="mt-4 bg-slate-100 p-4 rounded-xl border-l-4 border-amber-500 text-sm">
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<p className="font-bold text-amber-900 mb-2">
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Worked Example: Convert 60 miles/hour to feet/second
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</p>
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<div className="font-mono text-slate-700 space-y-2 text-xs">
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<div className="bg-white rounded p-2">
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<span className="text-amber-700 font-bold">Step 1:</span>{" "}
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Start with 60 miles/hr
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</div>
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<div className="bg-white rounded p-2">
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<span className="text-amber-700 font-bold">Step 2:</span> ×
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(5280 ft / 1 mile) ← cancels "miles"
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</div>
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<div className="bg-white rounded p-2">
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<span className="text-amber-700 font-bold">Step 3:</span> × (1
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hr / 3600 sec) ← cancels "hours"
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</div>
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<div className="bg-white rounded p-3 border-2 border-amber-300">
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<span className="text-amber-700 font-bold">Result:</span>{" "}
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<Frac n="60 × 5280" d="1 × 3600" /> ={" "}
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<Frac n="316,800" d="3600" /> ={" "}
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<strong className="text-amber-800">88 feet per second</strong>
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</div>
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</div>
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<p className="text-xs text-slate-500 mt-2">
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Notice how miles and hours both cancel, leaving only feet/second
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— exactly what was asked for.
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</p>
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</div>
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</div>
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<UnitConversionWidget />
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<button
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onClick={() => scrollToSection(2)}
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className="mt-12 group flex items-center text-amber-600 font-bold hover:text-amber-800 transition-colors"
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>
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Next: Percent Changes{" "}
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<ArrowDown className="ml-2 w-5 h-5 group-hover:translate-y-1 transition-transform" />
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</button>
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</section>
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{/* Section 3: Percent Increases & Decreases */}
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<section
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ref={(el) => {
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sectionsRef.current[2] = el;
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}}
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className="min-h-screen flex flex-col justify-center mb-24"
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>
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<h2 className="text-4xl font-extrabold text-slate-900 mb-6">
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Percent Increases & Decreases
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</h2>
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<div className="prose prose-slate text-lg text-slate-600 mb-8">
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<p>
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The most important SAT skill for percentages is using{" "}
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<strong>multipliers</strong> — a single number that captures both
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the original value and the change.
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</p>
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<div className="grid md:grid-cols-2 gap-4 mt-4">
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<div className="bg-amber-50 border border-amber-200 rounded-xl p-5">
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<p className="font-bold text-amber-900 mb-2">
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Percent Increase
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</p>
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<div className="font-mono text-center bg-white py-2 rounded text-amber-700 font-bold mb-2">
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New = Original × (1 + r)
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</div>
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<p className="text-xs text-slate-600">
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Where r is the rate as a decimal (e.g., 30% → r = 0.30)
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</p>
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<p className="text-xs text-slate-500 mt-1">
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Example: $200 increased by 15% → 200 × 1.15 ={" "}
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<strong>$230</strong>
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</p>
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</div>
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<div className="bg-amber-50 border border-amber-200 rounded-xl p-5">
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<p className="font-bold text-amber-900 mb-2">
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Percent Decrease
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</p>
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<div className="font-mono text-center bg-white py-2 rounded text-amber-700 font-bold mb-2">
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New = Original × (1 − r)
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</div>
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<p className="text-xs text-slate-600">
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Where r is the rate as a decimal (e.g., 25% → r = 0.25)
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</p>
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<p className="text-xs text-slate-500 mt-1">
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Example: $200 decreased by 25% → 200 × 0.75 ={" "}
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<strong>$150</strong>
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</p>
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</div>
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</div>
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<div className="mt-4 bg-slate-100 p-4 rounded-xl border-l-4 border-amber-500 text-sm">
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<p className="font-bold text-amber-900 mb-1">
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Finding the Percent Change
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</p>
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<div className="font-mono text-center bg-white py-2 rounded text-slate-700 font-bold mb-1">
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% Change = <Frac n="New − Old" d="Old" /> × 100
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</div>
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<p className="text-xs text-slate-600">
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Positive result = increase. Negative result = decrease.
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</p>
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<p className="text-xs text-slate-500 mt-1">
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Example: Old = 80, New = 100 → <Frac n="100 − 80" d="80" /> ×
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100 = <strong>25% increase</strong>
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</p>
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</div>
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</div>
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<PercentChangeWidget />
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<button
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onClick={() => scrollToSection(3)}
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className="mt-12 group flex items-center text-amber-600 font-bold hover:text-amber-800 transition-colors"
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>
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Next: Multi-Step Changes{" "}
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<ArrowDown className="ml-2 w-5 h-5 group-hover:translate-y-1 transition-transform" />
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</button>
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</section>
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{/* Section 4: Multi-Step Changes */}
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<section
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ref={(el) => {
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sectionsRef.current[3] = el;
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}}
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className="min-h-screen flex flex-col justify-center mb-24"
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>
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<h2 className="text-4xl font-extrabold text-slate-900 mb-6">
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Multi-Step Percent Changes
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</h2>
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<div className="prose prose-slate text-lg text-slate-600 mb-8">
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<p>
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<strong>Trap Alert:</strong> Percentages do not simply add up. An
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increase of 20% followed by a decrease of 20% does{" "}
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<strong>not</strong> bring you back to the start!
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</p>
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<div className="mt-4 bg-rose-50 border border-rose-200 rounded-xl p-5">
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<p className="font-bold text-rose-900 mb-2">
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Why 20% Up then 20% Down ≠ 0%
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</p>
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<div className="font-mono text-sm text-slate-700 space-y-1">
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<div>
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Start: <strong>$100</strong>
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</div>
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<div>
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+20%: 100 × 1.20 = <strong>$120</strong>
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</div>
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<div>
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−20%: 120 × 0.80 = <strong>$96</strong> ← not $100!
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</div>
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</div>
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<p className="text-xs text-slate-600 mt-2">
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The decrease applies to the <em>new</em> (larger) amount, not
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the original.
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</p>
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</div>
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<div className="mt-4 bg-amber-50 border border-amber-200 rounded-xl p-5">
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<p className="font-bold text-amber-900 mb-2">
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The Multiplier Chain Method
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</p>
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<p className="text-sm text-slate-700 mb-2">
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For any sequence of percent changes, multiply all the
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multipliers together:
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</p>
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<div className="font-mono text-center bg-white py-2 rounded text-amber-700 font-bold mb-2">
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Final = Original × m₁ × m₂ × m₃ × ...
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</div>
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<div className="font-mono text-sm text-slate-700 space-y-1">
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<div>
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+20% then −20%: 1.20 × 0.80 = <strong>0.96</strong> →{" "}
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<strong>4% net decrease</strong>
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</div>
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<div>
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+50% then −50%: 1.50 × 0.50 = <strong>0.75</strong> →{" "}
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<strong>25% net decrease</strong>
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</div>
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</div>
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</div>
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<div className="mt-4 bg-slate-100 p-4 rounded-xl border-l-4 border-amber-500 text-sm">
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<p className="font-bold text-amber-900 mb-1">
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Compound Interest (Same Idea!)
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</p>
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<div className="font-mono text-center bg-white py-2 rounded text-slate-700 font-bold mb-1">
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A = P × (1 + r)ⁿ
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</div>
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<p className="text-xs text-slate-600">
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P = principal, r = annual rate (decimal), n = number of years.
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This is just the multiplier chain with the same multiplier
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repeated n times.
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</p>
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<p className="text-xs text-slate-500 mt-1">
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Example: $1,000 at 5% for 3 years → 1000 × (1.05)³ ={" "}
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<strong>$1,157.63</strong>
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</p>
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</div>
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</div>
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<MultiStepPercentWidget />
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<button
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onClick={() => scrollToSection(4)}
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className="mt-12 group flex items-center text-amber-600 font-bold hover:text-amber-800 transition-colors"
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>
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Next: Practice Quiz{" "}
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<ArrowDown className="ml-2 w-5 h-5 group-hover:translate-y-1 transition-transform" />
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</button>
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</section>
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{/* Section 5: Quiz */}
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<section
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||
ref={(el) => {
|
||
sectionsRef.current[4] = el;
|
||
}}
|
||
className="min-h-screen flex flex-col justify-center"
|
||
>
|
||
<h2 className="text-4xl font-extrabold text-slate-900 mb-8">
|
||
Practice Time
|
||
</h2>
|
||
{allQuizzes.map((quiz, idx) => (
|
||
<div key={`quiz-${idx}`} className="mb-12">
|
||
<Quiz data={quiz} />
|
||
</div>
|
||
))}
|
||
<div className="p-8 bg-amber-900 rounded-2xl text-white text-center mt-12">
|
||
<h3 className="text-2xl font-bold mb-4">Topic Mastered!</h3>
|
||
<button
|
||
onClick={onFinish}
|
||
className="px-6 py-3 bg-white text-amber-900 font-bold rounded-full hover:bg-amber-50 transition-colors"
|
||
>
|
||
Finish Lesson ✓
|
||
</button>
|
||
</div>
|
||
</section>
|
||
</div>
|
||
</div>
|
||
);
|
||
};
|
||
|
||
export default ProportionalLesson;
|