Add mixed-denominator fraction worksheets

apps/web/src/app/create/worksheets/components/config-panel/OperatorSection.tsx

@@ -2,8 +2,8 @@ import { css } from '@styled/css'
 import { OperatorIcon } from './OperatorIcon'
 
 export interface OperatorSectionProps {
-  operator: 'addition' | 'subtraction' | 'mixed' | undefined
+  operator: 'addition' | 'subtraction' | 'mixed' | 'fractions' | undefined
-  onChange: (operator: 'addition' | 'subtraction' | 'mixed') => void
+  onChange: (operator: 'addition' | 'subtraction' | 'mixed' | 'fractions') => void
   isDark?: boolean
 }
 
@@ -187,6 +187,67 @@ export function OperatorSection({ operator, onChange, isDark = false }: Operator
             </span>
           </div>
         </label>
+
+        {/* Fractions Toggle */}
+        <label
+          data-action="toggle-fractions"
+          className={css({
+            display: 'flex',
+            alignItems: 'center',
+            gap: '3',
+            cursor: 'pointer',
+            px: '3',
+            py: '2.5',
+            rounded: 'lg',
+            border: '2px solid',
+            transition: 'all 0.2s',
+            bg:
+              operator === 'fractions'
+                ? isDark
+                  ? 'brand.900'
+                  : 'brand.50'
+                : isDark
+                  ? 'gray.700'
+                  : 'white',
+            borderColor: operator === 'fractions' ? 'brand.500' : isDark ? 'gray.600' : 'gray.300',
+            _hover: {
+              borderColor: 'brand.400',
+            },
+          })}
+        >
+          <input
+            type="radio"
+            checked={operator === 'fractions'}
+            onChange={() => onChange('fractions')}
+            className={css({
+              width: '5',
+              height: '5',
+              cursor: 'pointer',
+              accentColor: 'brand.600',
+              flexShrink: 0,
+            })}
+          />
+          <div
+            className={css({
+              display: 'flex',
+              alignItems: 'center',
+              gap: '2',
+              flex: 1,
+              minWidth: 0,
+            })}
+          >
+            <OperatorIcon operator="addition" isDark={isDark} />
+            <span
+              className={css({
+                fontSize: 'sm',
+                fontWeight: 'semibold',
+                color: isDark ? 'gray.200' : 'gray.700',
+              })}
+            >
+              Mixed Denominator Fractions
+            </span>
+          </div>
+        </label>
       </div>
 
       <p
@@ -196,11 +257,13 @@ export function OperatorSection({ operator, onChange, isDark = false }: Operator
           lineHeight: '1.5',
         })}
       >
-        {additionChecked && subtractionChecked
+        {operator === 'fractions'
-          ? 'Problems will randomly use addition or subtraction'
+          ? 'All problems will add fractions with different denominators'
-          : subtractionChecked
+          : additionChecked && subtractionChecked
-            ? 'All problems will be subtraction'
+            ? 'Problems will randomly use addition or subtraction'
-            : 'All problems will be addition'}
+            : subtractionChecked
+              ? 'All problems will be subtraction'
+              : 'All problems will be addition'}
       </p>
     </div>
   )

apps/web/src/app/create/worksheets/components/config-sidebar/ProblemPreview.tsx

@@ -8,7 +8,7 @@ import type { DisplayRules } from '../../displayRules'
 interface ProblemPreviewProps {
   displayRules: DisplayRules
   resolvedDisplayRules?: DisplayRules
-  operator?: 'addition' | 'subtraction' | 'mixed'
+  operator?: 'addition' | 'subtraction' | 'mixed' | 'fractions'
   digitRange?: { min: number; max: number }
   className?: string
 }

apps/web/src/app/create/worksheets/components/config-sidebar/TabNavigation.tsx

@@ -9,7 +9,10 @@ import { ProblemPreview } from './ProblemPreview'
 export interface Tab {
   id: string
   label: string
-  icon: string | ((operator?: 'addition' | 'subtraction' | 'mixed') => string) | 'preview'
+  icon:
+    | string
+    | ((operator?: 'addition' | 'subtraction' | 'mixed' | 'fractions') => string)
+    | 'preview'
   subtitle?: (props: {
     mode?: 'custom' | 'manual' | 'mastery'
     difficultyProfile?: string
@@ -20,7 +23,7 @@ export interface Tab {
     pages?: number
     displayRules?: DisplayRules
     resolvedDisplayRules?: DisplayRules
-    operator?: 'addition' | 'subtraction' | 'mixed'
+    operator?: 'addition' | 'subtraction' | 'mixed' | 'fractions'
   }) => string | null
 }
 
@@ -31,6 +34,7 @@ export const TABS: Tab[] = [
     icon: (operator) => {
       if (operator === 'mixed') return '±'
       if (operator === 'subtraction') return '−'
+      if (operator === 'fractions') return '⅟'
       return '+'
     },
   },
@@ -115,7 +119,7 @@ export const TABS: Tab[] = [
 interface TabNavigationProps {
   activeTab: string
   onChange: (tabId: string) => void
-  operator?: 'addition' | 'subtraction' | 'mixed'
+  operator?: 'addition' | 'subtraction' | 'mixed' | 'fractions'
   mode?: 'custom' | 'manual' | 'mastery'
   difficultyProfile?: string
   interpolate?: boolean

apps/web/src/app/create/worksheets/config-schemas.ts

@@ -343,7 +343,7 @@ const additionConfigV4BaseSchema = z.object({
     }),
 
   // V4: Operator selection (addition, subtraction, or mixed)
-  operator: z.enum(['addition', 'subtraction', 'mixed']).default('addition'),
+  operator: z.enum(['addition', 'subtraction', 'mixed', 'fractions']).default('addition'),
 
   // Regrouping probabilities (shared between modes)
   pAnyStart: z.number().min(0).max(1),

apps/web/src/app/create/worksheets/difficultyProfiles.ts

@@ -243,7 +243,7 @@ function describeScaffoldingChange(
   fromRules: DisplayRules,
   toRules: DisplayRules,
   direction: 'added' | 'reduced',
-  operator?: 'addition' | 'subtraction' | 'mixed'
+  operator?: 'addition' | 'subtraction' | 'mixed' | 'fractions'
 ): string {
   const changes: string[] = []
 
@@ -786,7 +786,7 @@ export function makeHarder(
     displayRules: DisplayRules
   },
   mode: DifficultyMode = 'both',
-  operator?: 'addition' | 'subtraction' | 'mixed'
+  operator?: 'addition' | 'subtraction' | 'mixed' | 'fractions'
 ): {
   pAnyStart: number
   pAllStart: number
@@ -989,7 +989,7 @@ export function makeEasier(
     displayRules: DisplayRules
   },
   mode: DifficultyMode = 'both',
-  operator?: 'addition' | 'subtraction' | 'mixed'
+  operator?: 'addition' | 'subtraction' | 'mixed' | 'fractions'
 ): {
   pAnyStart: number
   pAllStart: number

apps/web/src/app/create/worksheets/generatePreview.ts

@@ -5,6 +5,7 @@ import type { WorksheetFormState } from '@/app/create/worksheets/types'
 import {
   generateMasteryMixedProblems,
   generateMixedProblems,
+  generateFractionProblems,
   generateProblems,
   generateSubtractionProblems,
 } from './problemGenerator'
@@ -86,7 +87,9 @@ export async function generateWorksheetPreview(
     let problems
 
     // Special handling for mastery + mixed mode
-    if (mode === 'mastery' && operator === 'mixed') {
+    if (operator === 'fractions') {
+      problems = generateFractionProblems(validatedConfig.total, validatedConfig.seed ?? Date.now())
+    } else if (mode === 'mastery' && operator === 'mixed') {
       // Query both skill configs
       const addSkillId = config.currentAdditionSkillId
       const subSkillId = config.currentSubtractionSkillId

apps/web/src/app/create/worksheets/problemGenerator.ts

@@ -2,6 +2,7 @@
 
 import type {
   AdditionProblem,
+  FractionProblem,
   ProblemCategory,
   SubtractionProblem,
   WorksheetProblem,
@@ -1269,3 +1270,49 @@ export function generateMixedProblems(
 
   return problems
 }
+
+export function generateFractionProblems(
+  total: number,
+  seed: number,
+  options: {
+    minNumerator?: number
+    maxNumerator?: number
+    minDenominator?: number
+    maxDenominator?: number
+  } = {}
+): FractionProblem[] {
+  const {
+    minNumerator = 1,
+    maxNumerator = 9,
+    minDenominator = 2,
+    maxDenominator = 12,
+  } = options
+
+  const rand = createPRNG(seed)
+  const problems: FractionProblem[] = []
+
+  const randomFraction = () => {
+    const denominator = randint(minDenominator, maxDenominator, rand)
+    const numerator = randint(minNumerator, Math.max(minNumerator, denominator - 1), rand)
+    return { numerator, denominator }
+  }
+
+  for (let i = 0; i < total; i++) {
+    let a = randomFraction()
+    let b = randomFraction()
+
+    while (a.denominator === b.denominator) {
+      b = randomFraction()
+    }
+
+    problems.push({
+      aNumerator: a.numerator,
+      aDenominator: a.denominator,
+      bNumerator: b.numerator,
+      bDenominator: b.denominator,
+      operator: 'fractions',
+    })
+  }
+
+  return problems
+}

apps/web/src/app/create/worksheets/types.ts

@@ -116,7 +116,7 @@ export type WorksheetFormState = Partial<Omit<AdditionConfigV4Custom, 'version'>
 /**
  * Worksheet operator type
  */
-export type WorksheetOperator = 'addition' | 'subtraction' | 'mixed'
+export type WorksheetOperator = 'addition' | 'subtraction' | 'mixed' | 'fractions'
 
 /**
  * A single addition problem
@@ -136,10 +136,21 @@ export interface SubtractionProblem {
   operator: 'sub'
 }
 
+/**
+ * Fraction addition problem (mixed denominators)
+ */
+export interface FractionProblem {
+  aNumerator: number
+  aDenominator: number
+  bNumerator: number
+  bDenominator: number
+  operator: 'fractions'
+}
+
 /**
  * Unified problem type (addition or subtraction)
  */
-export type WorksheetProblem = AdditionProblem | SubtractionProblem
+export type WorksheetProblem = AdditionProblem | SubtractionProblem | FractionProblem
 
 /**
  * Validation result

apps/web/src/app/create/worksheets/typstGenerator.ts

@@ -1,6 +1,6 @@
 // Typst document generator for addition worksheets
 
-import type { WorksheetConfig, WorksheetProblem } from '@/app/create/worksheets/types'
+import type { FractionProblem, WorksheetConfig, WorksheetProblem } from '@/app/create/worksheets/types'
 import { resolveDisplayForProblem } from './displayRules'
 import { analyzeProblem, analyzeSubtractionProblem } from './problemAnalysis'
 import { generateQRCodeSVG } from './qrCodeGenerator'
@@ -24,6 +24,13 @@ function generateWorksheetDescription(config: WorksheetConfig): {
   title: string
   scaffolding: string
 } {
+  if (config.operator === 'fractions') {
+    return {
+      title: 'Fraction addition (mixed denominators)',
+      scaffolding: 'No scaffolding elements required',
+    }
+  }
+
   // Line 1: Digit range + operator + regrouping percentage
   const parts: string[] = []
 
@@ -116,6 +123,26 @@ function chunkProblems(problems: WorksheetProblem[], pageSize: number): Workshee
   return pages
 }
 
+function gcd(a: number, b: number): number {
+  return b === 0 ? Math.abs(a) : gcd(b, a % b)
+}
+
+function lcm(a: number, b: number): number {
+  return Math.abs((a * b) / gcd(a, b))
+}
+
+function addAndSimplifyFractions(problem: FractionProblem) {
+  const commonDenominator = lcm(problem.aDenominator, problem.bDenominator)
+  const numerator =
+    problem.aNumerator * (commonDenominator / problem.aDenominator) +
+    problem.bNumerator * (commonDenominator / problem.bDenominator)
+  const divisor = gcd(numerator, commonDenominator)
+  return {
+    numerator: numerator / divisor,
+    denominator: commonDenominator / divisor,
+  }
+}
+
 /**
  * Calculate maximum number of digits in any problem on this page
  * Returns max digits across all operands (handles both addition and subtraction)
@@ -128,12 +155,21 @@ function calculateMaxDigits(problems: WorksheetProblem[]): number {
       const digitsB = problem.b.toString().length
       const maxProblemDigits = Math.max(digitsA, digitsB)
       maxDigits = Math.max(maxDigits, maxProblemDigits)
-    } else {
+    } else if (problem.operator === 'sub') {
       // Subtraction
       const digitsMinuend = problem.minuend.toString().length
       const digitsSubtrahend = problem.subtrahend.toString().length
       const maxProblemDigits = Math.max(digitsMinuend, digitsSubtrahend)
       maxDigits = Math.max(maxDigits, maxProblemDigits)
+    } else {
+      const fractionProblem = problem as FractionProblem
+      const maxProblemDigits = Math.max(
+        fractionProblem.aNumerator.toString().length,
+        fractionProblem.aDenominator.toString().length,
+        fractionProblem.bNumerator.toString().length,
+        fractionProblem.bDenominator.toString().length
+      )
+      maxDigits = Math.max(maxDigits, maxProblemDigits)
     }
   }
   return maxDigits
@@ -596,6 +632,12 @@ export async function generateTypstSource(
   shareUrl?: string,
   domain?: string
 ): Promise<string[]> {
+  const hasFractionProblems = problems.some((p) => (p as WorksheetProblem).operator === 'fractions')
+
+  if (hasFractionProblems) {
+    return await generateFractionTypstSource(config, problems as FractionProblem[], shareUrl, domain)
+  }
+
   // Use the problemsPerPage directly from config (primary state)
   const problemsPerPage = config.problemsPerPage
   const rowsPerPage = problemsPerPage / config.cols
@@ -651,3 +693,133 @@ export async function generateTypstSource(
 
   return worksheetPages
 }
+
+function generateFractionPageTypst(
+  config: WorksheetConfig,
+  pageProblems: FractionProblem[],
+  problemOffset: number,
+  qrCodeSvg?: string,
+  shareCode?: string,
+  domain?: string
+): string {
+  const margin = 0.4
+  const problemData = pageProblems
+    .map((p, idx) => {
+      const answer = addAndSimplifyFractions(p)
+      return `  (number: ${problemOffset + idx + 1}, aNum: ${p.aNumerator}, aDen: ${p.aDenominator}, bNum: ${p.bNumerator}, bDen: ${p.bDenominator}, ansNum: ${answer.numerator}, ansDen: ${answer.denominator}),`
+    })
+    .join('\n')
+
+  return `#let fraction-problems = (
+${problemData}
+)
+
+#page(
+  paper: (${config.page.wIn}in, ${config.page.hIn}in),
+  margin: (${margin}in, ${margin}in),
+  header: align(center)[
+    #text(size: 14pt, weight: 'bold')[${config.name}]
+    #v(6pt)
+    #text(size: 10pt)[Fraction Addition (Mixed Denominators)]
+  ],
+  footer: align(center)[
+    #text(size: 8pt)[${domain || 'abaci.one'}]
+  ],
+)[
+  #grid(columns: ${config.cols}, gutter: 0.3in)[
+    ..for p in fraction-problems {
+      box(stroke: 0.5pt, inset: 10pt)[
+        #stack(dir: ttb, spacing: 6pt)[
+          #align(center)[
+            #text(size: 13pt)[#frac(p.aNum, p.aDen) + #frac(p.bNum, p.bDen) = \h(30pt)]
+          ]
+          #align(right)[#text(size: 8pt)[#p.number]]
+        ]
+      ]
+    }
+  ]
+  ${
+    qrCodeSvg
+      ? `#place(bottom + left, dx: 0.1in, dy: -0.05in)[#stack(dir: ttb, spacing: 2pt, align(center)[#image(bytes("${qrCodeSvg.replace(/"/g, '\\"').replace(/\n/g, '')}"), format: "svg", width: 0.63in, height: 0.63in)], align(center)[#text(size: 7pt, font: "Courier New")[${shareCode || 'PREVIEW'}]])]`
+      : ''
+  }
+]
+`
+}
+
+function generateFractionAnswerKey(
+  config: WorksheetConfig,
+  problems: FractionProblem[],
+  qrCodeSvg?: string,
+  shareCode?: string
+): string[] {
+  const margin = 0.4
+  const answerLines = problems
+    .map((p, idx) => {
+      const answer = addAndSimplifyFractions(p)
+      return `  #text(size: 11pt)[${idx + 1}. #frac(${p.aNumerator}, ${p.aDenominator}) + #frac(${p.bNumerator}, ${p.bDenominator}) = #frac(${answer.numerator}, ${answer.denominator})]`
+    })
+    .join('\n')
+
+  const qrBlock =
+    qrCodeSvg && shareCode
+      ? `#place(bottom + left, dx: 0.1in, dy: -0.05in)[#stack(dir: ttb, spacing: 2pt, align(center)[#image(bytes("${qrCodeSvg.replace(/"/g, '\\"').replace(/\n/g, '')}"), format: "svg", width: 0.63in, height: 0.63in)], align(center)[#text(size: 7pt, font: "Courier New")[${shareCode}])])]`
+      : ''
+
+  return [
+    `#page(
+  paper: (${config.page.wIn}in, ${config.page.hIn}in),
+  margin: (${margin}in, ${margin}in),
+  header: align(center)[#text(size: 14pt, weight: 'bold')[Answer Key - Fractions]],
+)[
+  #stack(dir: ttb, spacing: 6pt)[
+${answerLines}
+  ]
+  ${qrBlock}
+]
+`,
+  ]
+}
+
+async function generateFractionTypstSource(
+  config: WorksheetConfig,
+  problems: FractionProblem[],
+  shareUrl?: string,
+  domain?: string
+): Promise<string[]> {
+  const problemsPerPage = config.problemsPerPage
+  const pages = chunkProblems(problems, problemsPerPage)
+
+  let qrCodeSvg: string | undefined
+  let shareCode: string | undefined
+  if (config.includeQRCode && shareUrl) {
+    qrCodeSvg = await generateQRCodeSVG(shareUrl, 200)
+    shareCode = extractShareCode(shareUrl)
+  }
+
+  let brandDomain = domain
+  if (!brandDomain && shareUrl) {
+    try {
+      brandDomain = new URL(shareUrl).hostname
+    } catch {
+      // Ignore invalid URL and fall back to default
+    }
+  }
+
+  const fractionPages = pages.map((page, pageIndex) =>
+    generateFractionPageTypst(
+      config,
+      page,
+      pageIndex * problemsPerPage,
+      qrCodeSvg,
+      shareCode,
+      brandDomain
+    )
+  )
+
+  if (config.includeAnswerKey) {
+    return [...fractionPages, ...generateFractionAnswerKey(config, problems, qrCodeSvg, shareCode)]
+  }
+
+  return fractionPages
+}

apps/web/src/app/create/worksheets/utils/validateProblemSpace.ts

@@ -112,7 +112,7 @@ export function validateProblemSpace(
   pages: number,
   digitRange: { min: number; max: number },
   pAnyStart: number,
-  operator: 'addition' | 'subtraction' | 'mixed'
+  operator: 'addition' | 'subtraction' | 'mixed' | 'fractions'
 ): ProblemSpaceValidation {
   const requestedProblems = problemsPerPage * pages
   const warnings: string[] = []
@@ -123,12 +123,15 @@ export function validateProblemSpace(
     const addSpace = estimateUniqueProblemSpace(digitRange, pAnyStart, 'addition')
     const subSpace = estimateUniqueProblemSpace(digitRange, pAnyStart, 'subtraction')
     estimatedSpace = addSpace + subSpace
+  } else if (operator === 'fractions') {
+    // Fractions have extremely large combinatorial space; treat as effectively infinite
+    estimatedSpace = Number.POSITIVE_INFINITY
   } else {
     estimatedSpace = estimateUniqueProblemSpace(digitRange, pAnyStart, operator)
   }
 
   // Calculate duplicate risk
-  const ratio = requestedProblems / estimatedSpace
+  const ratio = estimatedSpace === Number.POSITIVE_INFINITY ? 0 : requestedProblems / estimatedSpace
   let duplicateRisk: 'none' | 'low' | 'medium' | 'high' | 'extreme'
 
   if (ratio < 0.3) {

apps/web/src/app/create/worksheets/validation.ts

@@ -167,8 +167,8 @@ export function validateWorksheetConfig(formState: WorksheetFormState): Validati
 
   // V4: Validate operator (addition, subtraction, or mixed)
   const operator = formState.operator ?? 'addition'
-  if (!['addition', 'subtraction', 'mixed'].includes(operator)) {
+  if (!['addition', 'subtraction', 'mixed', 'fractions'].includes(operator)) {
-    errors.push('Operator must be "addition", "subtraction", or "mixed"')
+    errors.push('Operator must be "addition", "subtraction", "fractions", or "mixed"')
   }
 
   // Validate seed (must be positive integer)