193 lines
7.1 KiB
TypeScript
193 lines
7.1 KiB
TypeScript
import type { MathProblem, Difficulty } from "../types";
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import { randomInt, randomChoice } from "@/lib/utils";
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import * as frac from "@/lib/math/fractions";
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let counter = 0;
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function nextId() {
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return `fp-${++counter}-${Date.now()}`;
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}
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export function generateFractionAddSubtract(difficulty: Difficulty): MathProblem {
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const operation = randomChoice(["add", "subtract"] as const);
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const op = operation === "add" ? "+" : "-";
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let n1: number, d1: number, n2: number, d2: number;
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if (difficulty === 1) {
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// Common denominators
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d1 = randomChoice([2, 3, 4, 5, 6, 8, 10, 12]);
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d2 = d1;
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n1 = randomInt(1, d1 - 1);
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n2 = operation === "subtract" ? randomInt(1, n1) : randomInt(1, d1 - n1);
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} else if (difficulty === 2) {
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// One denominator is a multiple of the other
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d1 = randomChoice([2, 3, 4, 5, 6]);
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const multiplier = randomChoice([2, 3]);
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d2 = d1 * multiplier;
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n1 = randomInt(1, d1 - 1);
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n2 = randomInt(1, d2 - 1);
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} else {
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// Unlike denominators
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d1 = randomChoice([3, 4, 5, 7, 8, 9]);
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d2 = randomChoice([3, 4, 5, 7, 8, 9].filter((d) => d !== d1));
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n1 = randomInt(1, d1 - 1);
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n2 = randomInt(1, d2 - 1);
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}
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const prompt = `\\frac{${n1}}{${d1}} ${op} \\frac{${n2}}{${d2}}`;
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const commonDen = frac.lcm(d1, d2);
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const convertedN1 = n1 * (commonDen / d1);
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const convertedN2 = n2 * (commonDen / d2);
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const rawNum = operation === "add"
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? convertedN1 + convertedN2
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: convertedN1 - convertedN2;
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const [ansNum, ansDen] = frac.simplify(rawNum, commonDen);
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const steps = d1 === d2
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? [
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{
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explanation: `The denominators already match, so keep ${d1} as the denominator.`,
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math: `\\frac{${n1}}{${d1}} ${op} \\frac{${n2}}{${d2}}`,
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},
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{
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explanation: `${operation === "add" ? "Add" : "Subtract"} the numerators and keep the denominator the same.`,
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math: `\\frac{${n1}}{${d1}} ${op} \\frac{${n2}}{${d2}} = \\frac{${rawNum}}{${d1}}`,
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},
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...(ansNum !== rawNum || ansDen !== d1
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? [{
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explanation: "Simplify the fraction.",
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math: `\\frac{${rawNum}}{${d1}} = \\frac{${ansNum}}{${ansDen}}`,
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}]
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: []),
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]
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: [
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{
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explanation: `Find the lowest common denominator: LCM(${d1}, ${d2}) = ${commonDen}.`,
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math: `\\text{LCD} = ${commonDen}`,
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},
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{
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explanation: "Rewrite both fractions with that denominator.",
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math: `\\frac{${n1}}{${d1}} = \\frac{${convertedN1}}{${commonDen}} \\quad \\frac{${n2}}{${d2}} = \\frac{${convertedN2}}{${commonDen}}`,
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},
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{
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explanation: `${operation === "add" ? "Add" : "Subtract"} the numerators and keep the common denominator.`,
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math: `\\frac{${convertedN1}}{${commonDen}} ${op} \\frac{${convertedN2}}{${commonDen}} = \\frac{${rawNum}}{${commonDen}}`,
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},
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...(ansNum !== rawNum || ansDen !== commonDen
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? [{
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explanation: "Simplify the fraction.",
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math: `\\frac{${rawNum}}{${commonDen}} = \\frac{${ansNum}}{${ansDen}}`,
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}]
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: []),
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];
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return {
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id: nextId(),
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prompt,
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answer: { kind: "fraction", numerator: ansNum, denominator: ansDen },
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hints: [
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d1 === d2 ? "The denominators are already the same!" : "Find a common denominator first",
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d1 !== d2 ? "Rewrite both fractions using that denominator" : `Just ${operation} the numerators`,
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],
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steps,
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};
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}
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export function generateFractionMultiply(difficulty: Difficulty): MathProblem {
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const denChoices = difficulty === 1 ? [2, 3, 4, 5] : difficulty === 2 ? [2, 3, 4, 5, 6, 7, 8] : [3, 5, 7, 9, 11, 12, 15];
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const d1 = randomChoice(denChoices);
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const d2 = randomChoice(denChoices);
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const n1 = randomInt(1, d1 - 1);
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const n2 = randomInt(1, d2 - 1);
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const [ansNum, ansDen] = frac.multiply(n1, d1, n2, d2);
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return {
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id: nextId(),
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prompt: `\\frac{${n1}}{${d1}} \\times \\frac{${n2}}{${d2}}`,
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answer: { kind: "fraction", numerator: ansNum, denominator: ansDen },
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hints: [
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"Multiply numerator × numerator",
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"Multiply denominator × denominator",
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"Simplify if possible",
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],
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steps: [
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{ explanation: `Multiply numerators: ${n1} × ${n2} = ${n1 * n2}` },
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{ explanation: `Multiply denominators: ${d1} × ${d2} = ${d1 * d2}` },
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{ explanation: "Simplify", math: `\\frac{${ansNum}}{${ansDen}}` },
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],
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};
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}
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export function generateFractionDivide(difficulty: Difficulty): MathProblem {
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const denChoices = difficulty === 1 ? [2, 3, 4, 5] : difficulty === 2 ? [2, 3, 4, 5, 6, 7, 8] : [3, 5, 7, 9, 11, 14, 15];
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const d1 = randomChoice(denChoices);
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const d2 = randomChoice(denChoices);
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const n1 = randomInt(1, d1 - 1);
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const n2 = randomInt(1, d2 - 1);
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const [ansNum, ansDen] = frac.divide(n1, d1, n2, d2);
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return {
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id: nextId(),
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prompt: `\\frac{${n1}}{${d1}} \\div \\frac{${n2}}{${d2}}`,
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answer: { kind: "fraction", numerator: ansNum, denominator: ansDen },
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hints: [
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"Keep the first fraction the same",
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"Flip the second fraction (reciprocal)",
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"Then multiply",
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],
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steps: [
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{ explanation: `Keep ${n1}/${d1}, flip ${n2}/${d2} to ${d2}/${n2}` },
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{ explanation: `Multiply: ${n1}×${d2} / ${d1}×${n2}` },
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{ explanation: "Simplify", math: `\\frac{${ansNum}}{${ansDen}}` },
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],
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};
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}
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export function generateFractionOfQuantity(difficulty: Difficulty): MathProblem {
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const denChoices = difficulty === 1 ? [2, 4, 5, 10] : difficulty === 2 ? [3, 4, 5, 6, 8] : [7, 8, 9, 12, 15];
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const den = randomChoice(denChoices);
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const num = randomInt(1, den - 1);
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const multiplier = randomChoice(difficulty === 1 ? [2, 4, 5, 10] : [3, 6, 7, 8, 9, 12]);
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const quantity = den * multiplier;
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const answer = num * multiplier;
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return {
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id: nextId(),
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prompt: `\\frac{${num}}{${den}} \\text{ of } ${quantity}`,
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answer: { kind: "integer", value: answer },
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hints: [
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`Divide ${quantity} by ${den} first`,
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`Then multiply by ${num}`,
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],
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steps: [
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{ explanation: `Divide the quantity by the denominator: ${quantity} ÷ ${den} = ${quantity / den}` },
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{ explanation: `Multiply by the numerator: ${quantity / den} × ${num} = ${answer}` },
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],
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};
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}
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export function generateWholeFromFraction(difficulty: Difficulty): MathProblem {
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const denChoices = difficulty === 1 ? [2, 3, 4, 5] : difficulty === 2 ? [3, 5, 6, 8] : [7, 8, 9, 12];
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const den = randomChoice(denChoices);
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const num = randomInt(1, den - 1);
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const whole = den * randomChoice(difficulty === 1 ? [2, 3, 4, 5] : [3, 5, 6, 7, 8, 10]);
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const part = (num / den) * whole;
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return {
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id: nextId(),
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prompt: `\\frac{${num}}{${den}} \\text{ of a number is } ${part}\\text{. Find the number.}`,
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answer: { kind: "integer", value: whole },
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hints: [
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`If ${num}/${den} of the number is ${part}...`,
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`Find 1/${den} first by dividing ${part} by ${num}`,
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`Then multiply by ${den} to get the whole`,
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],
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steps: [
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{ explanation: `1/${den} of the number = ${part} ÷ ${num} = ${part / num}` },
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{ explanation: `The whole number = ${part / num} × ${den} = ${whole}` },
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],
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};
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}
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