fractions add/sub fix

lib/math/validation.ts

@@ -15,6 +15,20 @@ export function parseStrictInt(input: string): number | null {
   return parseInt(s, 10);
 }
 
+/** Parse a strict signed integer string. Reject decimals, scientific notation, and trailing text. */
+export function parseStrictSignedInt(input: string): number | null {
+  const s = input.trim();
+  if (!/^-?\d+$/.test(s)) return null;
+  return parseInt(s, 10);
+}
+
+/** Parse a strict signed decimal string. Reject scientific notation and trailing text. */
+export function parseStrictSignedDecimal(input: string): number | null {
+  const s = input.trim();
+  if (!/^-?\d+(\.\d+)?$/.test(s)) return null;
+  return parseFloat(s);
+}
+
 export type AnswerResult =
   | { correct: true; simplified: boolean }
   | { correct: false; message: string };
@@ -37,6 +51,11 @@ export function checkFractionAnswer(
     return { correct: false, message: "That's not quite right. Try again!" };
   }
 
+  // Any non-zero denominator gives the same value for zero, so don't force 0/1 in the UI.
+  if (userNum === 0) {
+    return { correct: true, simplified: true };
+  }
+
   const isSimplified = gcd(Math.abs(userNum), Math.abs(userDen)) === 1;
 
   if (requireSimplified && !isSimplified) {

lib/problems/generators/fraction-problems.ts

@@ -34,22 +34,51 @@ export function generateFractionAddSubtract(difficulty: Difficulty): MathProblem
     n2 = randomInt(1, d2 - 1);
   }
 
-  const [ansNum, ansDen] = operation === "add"
-    ? frac.add(n1, d1, n2, d2)
-    : frac.subtract(n1, d1, n2, d2);
-
   const prompt = `\\frac{${n1}}{${d1}} ${op} \\frac{${n2}}{${d2}}`;
-
   const commonDen = frac.lcm(d1, d2);
+  const convertedN1 = n1 * (commonDen / d1);
+  const convertedN2 = n2 * (commonDen / d2);
+  const rawNum = operation === "add"
+    ? convertedN1 + convertedN2
+    : convertedN1 - convertedN2;
+  const [ansNum, ansDen] = frac.simplify(rawNum, commonDen);
+
   const steps = d1 === d2
     ? [
-        { explanation: "Denominators are the same, so just " + (operation === "add" ? "add" : "subtract") + " the numerators" },
-        { explanation: `${n1} ${op} ${n2} = ${operation === "add" ? n1 + n2 : n1 - n2}`, math: `\\frac{${operation === "add" ? n1 + n2 : n1 - n2}}{${d1}}` },
+        {
+          explanation: `The denominators already match, so keep ${d1} as the denominator.`,
+          math: `\\frac{${n1}}{${d1}} ${op} \\frac{${n2}}{${d2}}`,
+        },
+        {
+          explanation: `${operation === "add" ? "Add" : "Subtract"} the numerators and keep the denominator the same.`,
+          math: `\\frac{${n1}}{${d1}} ${op} \\frac{${n2}}{${d2}} = \\frac{${rawNum}}{${d1}}`,
+        },
+        ...(ansNum !== rawNum || ansDen !== d1
+          ? [{
+              explanation: "Simplify the fraction.",
+              math: `\\frac{${rawNum}}{${d1}} = \\frac{${ansNum}}{${ansDen}}`,
+            }]
+          : []),
       ]
     : [
-        { explanation: `Find the common denominator: LCM(${d1}, ${d2}) = ${commonDen}` },
-        { explanation: `Convert: ${n1}×${commonDen / d1}/${d1}×${commonDen / d1} and ${n2}×${commonDen / d2}/${d2}×${commonDen / d2}` },
-        { explanation: `${op === "+" ? "Add" : "Subtract"} numerators`, math: `\\frac{${ansNum}}{${ansDen}}` },
+        {
+          explanation: `Find the lowest common denominator: LCM(${d1}, ${d2}) = ${commonDen}.`,
+          math: `\\text{LCD} = ${commonDen}`,
+        },
+        {
+          explanation: "Rewrite both fractions with that denominator.",
+          math: `\\frac{${n1}}{${d1}} = \\frac{${convertedN1}}{${commonDen}} \\quad \\frac{${n2}}{${d2}} = \\frac{${convertedN2}}{${commonDen}}`,
+        },
+        {
+          explanation: `${operation === "add" ? "Add" : "Subtract"} the numerators and keep the common denominator.`,
+          math: `\\frac{${convertedN1}}{${commonDen}} ${op} \\frac{${convertedN2}}{${commonDen}} = \\frac{${rawNum}}{${commonDen}}`,
+        },
+        ...(ansNum !== rawNum || ansDen !== commonDen
+          ? [{
+              explanation: "Simplify the fraction.",
+              math: `\\frac{${rawNum}}{${commonDen}} = \\frac{${ansNum}}{${ansDen}}`,
+            }]
+          : []),
       ];
 
   return {
@@ -58,7 +87,7 @@ export function generateFractionAddSubtract(difficulty: Difficulty): MathProblem
     answer: { kind: "fraction", numerator: ansNum, denominator: ansDen },
     hints: [
       d1 === d2 ? "The denominators are already the same!" : "Find a common denominator first",
-      d1 !== d2 ? `Try using the Butterfly Method: cross multiply` : `Just ${operation} the numerators`,
+      d1 !== d2 ? "Rewrite both fractions using that denominator" : `Just ${operation} the numerators`,
     ],
     steps,
   };

lib/problems/generators/ratio-problems.ts

@@ -93,7 +93,7 @@ export function generateRatioWordProblem(difficulty: Difficulty): MathProblem {
 
   return {
     id: nextId(),
-    prompt: `\\text{${ctx.item.charAt(0).toUpperCase() + ctx.item.slice(1)} were shared between ${ctx.nameA} and ${ctx.nameB} in the ratio ${a}:${b}. If ${bigger} received ${extraAmount} more ${ctx.item}, find the total shared.}`,
+    prompt: `\\begin{array}{l}\\text{${ctx.item.charAt(0).toUpperCase() + ctx.item.slice(1)} were shared between ${ctx.nameA} and ${ctx.nameB}}\\\\\\text{in the ratio ${a}:${b}. If ${bigger} received ${extraAmount} more ${ctx.item}, find the total shared.}\\end{array}`,
     answer: { kind: "integer", value: total },
     hints: [
       `The difference in ratio parts is ${biggerRatio} - ${smallerRatio} = ${diff}`,