[{"data":1,"prerenderedAt":869},["ShallowReactive",2],{"questions:order-of-operations":3},{"bank":4,"contentHash":859,"dependencyHashes":860,"releaseId":868},{"schemaVersion":5,"conceptId":6,"revision":5,"title":7,"intro":8,"sections":9,"questions":42,"sourceIds":848,"reviewStatus":855,"authoring":856},1,"order-of-operations","Order of operations: question bank","Practise the order of operations from first steps to olympiad puzzles. The rule used throughout: **brackets first (innermost first), then × and ÷ from left to right, then + and − from left to right**. \"Of\" (as in ½ of 10) is done before ordinary × and ÷, following the BODMAS textbook convention; questions say so where it matters. Every solution shows the working one step per line, the best habit for this topic. Questions start at **foundation** and rise through **core** and **stretch** to **challenge**.",[10,14,18,22,26,30,34,38],{"id":11,"title":12,"description":13},"why-order","Why an order is needed","Why one agreed order matters, what DMAS and BODMAS stand for, and how the rule matches real meaning.",{"id":15,"title":16,"description":17},"mul-div","× and ÷, left to right","Multiplication and division share a level: do them in the order they appear, from the left.",{"id":19,"title":20,"description":21},"add-sub","+ and −, left to right","Addition and subtraction share a level and are done left to right, after all × and ÷.",{"id":23,"title":24,"description":25},"mixed","Mixed operations","Expressions with all four operations: × and ÷ first, then + and −.",{"id":27,"title":28,"description":29},"brackets","Brackets","Round, curly and square brackets, nested brackets, \"of\" and the bar: innermost first.",{"id":31,"title":32,"description":33},"word-problems","Expressions from word problems","Turn shopping, travel, cricket and sharing stories into one expression and evaluate it.",{"id":35,"title":36,"description":37},"spot-mistake","Spot the mistake","Find the exact step where a piece of working goes wrong, and correct it.",{"id":39,"title":40,"description":41},"puzzles","Puzzles and targets","Insert brackets, fill in missing signs, make a target, four fours and other puzzles.",[43,68,86,100,121,139,156,175,186,195,204,213,222,230,239,248,266,275,283,292,301,310,329,338,346,354,364,373,381,389,398,407,416,425,434,444,452,461,470,479,488,498,508,517,527,536,547,557,567,576,585,595,603,612,620,629,638,648,658,666,683,692,709,719,738,746,755,772,781,789,798,807,820,830,839],{"id":44,"section":11,"level":45,"prompt":46,"check":47,"hints":63,"solution":65,"skills":66},"order-of-operations.q001","foundation","Using the agreed order of operations, what is **2 + 3 × 4**?",{"kind":48,"options":49,"correct":62},"choice",[50,53,56,59],{"id":51,"label":52},"a","20",{"id":54,"label":55},"b","14",{"id":57,"label":58},"c","24",{"id":60,"label":61},"d","9",[54],[64],"Which is done first, × or +?","× comes before +. So 3 × 4 = 12 first, then 2 + 12 = **14**.\n\nThe answer 20 comes from reading left to right like a sentence (2 + 3 = 5, then 5 × 4). That would be written (2 + 3) × 4.",[67],"precedence",{"id":69,"section":11,"level":45,"prompt":70,"check":71,"hints":82,"solution":83,"skills":84},"order-of-operations.q002","Why do mathematicians agree on one order of operations?",{"kind":48,"options":72,"correct":81},[73,75,77,79],{"id":51,"label":74},"So that an expression means the same thing to everyone",{"id":54,"label":76},"Because multiplication is more important than addition",{"id":57,"label":78},"To make questions harder",{"id":60,"label":80},"Because calculators cannot add",[51],[],"Without an agreed order, 2 + 3 × 4 could be 14 or 20. Like driving on the left in India, the rule works because **everyone follows the same one**, so an expression has exactly one meaning everywhere.",[85],"convention",{"id":87,"section":11,"level":45,"prompt":88,"check":89,"hints":95,"solution":97,"skills":98},"order-of-operations.q003","What does the **D** in DMAS stand for?",{"kind":90,"accept":91},"text",[92,93,94],"division","divide","dividing",[96],"It is one of the four operations.","DMAS stands for **Division**, Multiplication, Addition, Subtraction. (Some notes say \"Distributive\", but that is a mix-up: the distributive property is a separate idea.)",[99],"vocabulary",{"id":101,"section":11,"level":102,"prompt":103,"check":104,"hints":115,"solution":117,"skills":118},"order-of-operations.q004","core","Riya buys **1 pencil for ₹2** and **3 erasers at ₹4 each**. Which expression gives her bill, and what is it?",{"kind":48,"options":105,"correct":114},[106,108,110,112],{"id":51,"label":107},"2 + 3 × 4 = ₹14",{"id":54,"label":109},"(2 + 3) × 4 = ₹20",{"id":57,"label":111},"2 × 3 + 4 = ₹10",{"id":60,"label":113},"2 + 3 + 4 = ₹9",[51],[116],"What do the erasers cost altogether?","The erasers cost 3 × 4 = ₹12, which is one chunk. Add the pencil: 2 + 12 = **₹14**. So the bill is 2 + 3 × 4, and the order of operations gives exactly the real cost. (2 + 3) × 4 would mean 3 sets of a pencil and an eraser.",[119,120],"meaning","word problems",{"id":122,"section":11,"level":102,"prompt":123,"check":124,"hints":135,"solution":137,"skills":138},"order-of-operations.q005","Which story matches the expression **(5 + 3) × 10**?",{"kind":48,"options":125,"correct":134},[126,128,130,132],{"id":51,"label":127},"5 pens and 3 pencils, each costing ₹10",{"id":54,"label":129},"A ₹5 pen and 3 pencils at ₹10 each",{"id":57,"label":131},"5 pens at ₹3 each and a ₹10 bag",{"id":60,"label":133},"5 friends each paying ₹3 and ₹10 more",[51],[136],"The bracket is worked out first. What does 5 + 3 count?","The brackets make 5 + 3 = 8 things, and each costs ₹10: 8 × 10 = ₹80. Story (b) would be 5 + 3 × 10 = ₹35.",[119],{"id":140,"section":11,"level":102,"prompt":141,"check":142,"hints":153,"solution":154,"skills":155},"order-of-operations.q006","In the BODMAS version taught in Indian school books, what does the **O** stand for?",{"kind":48,"options":143,"correct":152},[144,146,148,150],{"id":51,"label":145},"Order",{"id":54,"label":147},"Of, as in ½ of 10",{"id":57,"label":149},"Operation",{"id":60,"label":151},"Odd numbers",[54],[],"O stands for **of**, as in \"half of 10\". \"Of\" means multiply, and BODMAS-style textbooks do it before ordinary ÷ and ×: ½ of 10 = 5. (Many other books, and sites such as Math is Fun, read the same O as \"Orders\", meaning powers — so always check which convention a book uses.)",[99],{"id":157,"section":11,"level":158,"prompt":159,"check":160,"hints":169,"solution":171,"skills":172},"order-of-operations.q007","stretch","True or false: in BODMAS, all divisions must be done before any multiplication, because D comes before M.",{"kind":48,"options":161,"correct":168},[162,165],{"id":163,"label":164},"t","True",{"id":166,"label":167},"f","False",[166],[170],"Compare with PEMDAS.","**False.** Division and multiplication share one level and are done **left to right**. The letters have to be written in some order, that is all. Proof: PEMDAS (used in the USA) puts M before D, yet everyone agrees 8 ÷ 4 × 2 = 2 × 2 = 4.",[173,174],"left to right","mnemonics",{"id":176,"section":15,"level":45,"prompt":177,"check":178,"hints":182,"solution":184,"skills":185},"order-of-operations.q008","Evaluate **12 ÷ 3 × 2**.",{"kind":179,"answer":180,"tolerance":181},"number",8,0,[183],"÷ and × share a level: go left to right.","Start from 12 ÷ 3 × 2.\n\nWork one step at a time:\n\n1. 4 × 2\n2. 8\n\n**Answer: 8**\n\nDoing 3 × 2 first would give 12 ÷ 6 = 2, which is the letter trap.",[173],{"id":187,"section":15,"level":45,"prompt":188,"check":189,"hints":191,"solution":193,"skills":194},"order-of-operations.q009","Evaluate **8 ÷ 4 × 2**.",{"kind":179,"answer":190,"tolerance":181},4,[192],"Start with the operation on the left.","Start from 8 ÷ 4 × 2.\n\nWork one step at a time:\n\n1. 2 × 2\n2. 4\n\n**Answer: 4**",[173],{"id":196,"section":15,"level":45,"prompt":197,"check":198,"hints":200,"solution":202,"skills":203},"order-of-operations.q010","Evaluate **5 × 6 ÷ 3**.",{"kind":179,"answer":199,"tolerance":181},10,[201],"Left to right: 5 × 6 first.","Start from 5 × 6 ÷ 3.\n\nWork one step at a time:\n\n1. 30 ÷ 3\n2. 10\n\n**Answer: 10**",[173],{"id":205,"section":15,"level":102,"prompt":206,"check":207,"hints":209,"solution":211,"skills":212},"order-of-operations.q011","Evaluate **36 ÷ 6 ÷ 2**.",{"kind":179,"answer":208,"tolerance":181},3,[210],"Two divisions: the left one first.","Start from 36 ÷ 6 ÷ 2.\n\nWork one step at a time:\n\n1. 6 ÷ 2\n2. 3\n\n**Answer: 3**\n\n36 ÷ (6 ÷ 2) would be 36 ÷ 3 = 12, a different expression.",[173],{"id":214,"section":15,"level":102,"prompt":215,"check":216,"hints":218,"solution":220,"skills":221},"order-of-operations.q012","Evaluate **60 ÷ 5 × 3**.",{"kind":179,"answer":217,"tolerance":181},36,[219],"60 ÷ 5 first.","Start from 60 ÷ 5 × 3.\n\nWork one step at a time:\n\n1. 12 × 3\n2. 36\n\n**Answer: 36**",[173],{"id":223,"section":15,"level":102,"prompt":224,"check":225,"hints":226,"solution":228,"skills":229},"order-of-operations.q013","Evaluate **48 ÷ 8 × 2 ÷ 3**.",{"kind":179,"answer":190,"tolerance":181},[227],"Work left to right, one operation at a time.","Start from 48 ÷ 8 × 2 ÷ 3.\n\nWork one step at a time:\n\n1. 6 × 2 ÷ 3\n2. 12 ÷ 3\n3. 4\n\n**Answer: 4**",[173],{"id":231,"section":15,"level":102,"prompt":232,"check":233,"hints":235,"solution":237,"skills":238},"order-of-operations.q014","Evaluate **72 ÷ 9 ÷ 2 × 5**.",{"kind":179,"answer":234,"tolerance":181},20,[236],"72 ÷ 9 = 8 first.","Start from 72 ÷ 9 ÷ 2 × 5.\n\nWork one step at a time:\n\n1. 8 ÷ 2 × 5\n2. 4 × 5\n3. 20\n\n**Answer: 20**",[173],{"id":240,"section":15,"level":158,"prompt":241,"check":242,"hints":244,"solution":246,"skills":247},"order-of-operations.q015","Evaluate **100 ÷ 4 × 2 ÷ 5 × 3**.",{"kind":179,"answer":243,"tolerance":181},30,[245],"Five numbers, four operations: keep going left to right.","Start from 100 ÷ 4 × 2 ÷ 5 × 3.\n\nWork one step at a time:\n\n1. 25 × 2 ÷ 5 × 3\n2. 50 ÷ 5 × 3\n3. 10 × 3\n4. 30\n\n**Answer: 30**",[173],{"id":249,"section":15,"level":158,"prompt":250,"check":251,"hints":262,"solution":264,"skills":265},"order-of-operations.q016","Which expression has the **same value** as **96 ÷ 4 ÷ 2**?",{"kind":48,"options":252,"correct":261},[253,255,257,259],{"id":51,"label":254},"96 ÷ (4 ÷ 2)",{"id":54,"label":256},"96 ÷ (4 × 2)",{"id":57,"label":258},"96 ÷ 4 × 2",{"id":60,"label":260},"(96 ÷ 4) × 2",[54],[263],"Dividing by 4 then by 2 is dividing by what?","96 ÷ 4 ÷ 2 = 24 ÷ 2 = **12**. Dividing by 4 and then by 2 is the same as dividing by 4 × 2 = 8: 96 ÷ 8 = 12. The others give 48, 48 and 48.",[173,27],{"id":267,"section":19,"level":45,"prompt":268,"check":269,"hints":271,"solution":273,"skills":274},"order-of-operations.q017","Evaluate **10 − 3 + 2**.",{"kind":179,"answer":270,"tolerance":181},9,[272],"+ and − share a level: left to right.","Start from 10 − 3 + 2.\n\nWork one step at a time:\n\n1. 7 + 2\n2. 9\n\n**Answer: 9**\n\nIf you got 5, you added 3 + 2 first. Think: ₹10, spend ₹3, get ₹2: you have ₹9.",[173],{"id":276,"section":19,"level":45,"prompt":277,"check":278,"hints":279,"solution":281,"skills":282},"order-of-operations.q018","Evaluate **20 − 5 − 5**.",{"kind":179,"answer":199,"tolerance":181},[280],"Two subtractions: the left one first.","Start from 20 − 5 − 5.\n\nWork one step at a time:\n\n1. 15 − 5\n2. 10\n\n**Answer: 10**",[173],{"id":284,"section":19,"level":45,"prompt":285,"check":286,"hints":288,"solution":290,"skills":291},"order-of-operations.q019","Evaluate **15 − 6 + 4**.",{"kind":179,"answer":287,"tolerance":181},13,[289],"15 − 6 first.","Start from 15 − 6 + 4.\n\nWork one step at a time:\n\n1. 9 + 4\n2. 13\n\n**Answer: 13**",[173],{"id":293,"section":19,"level":102,"prompt":294,"check":295,"hints":297,"solution":299,"skills":300},"order-of-operations.q020","Evaluate **50 − 20 + 10 − 5**.",{"kind":179,"answer":296,"tolerance":181},35,[298],"Keep going left to right.","Start from 50 − 20 + 10 − 5.\n\nWork one step at a time:\n\n1. 30 + 10 − 5\n2. 40 − 5\n3. 35\n\n**Answer: 35**",[173],{"id":302,"section":19,"level":102,"prompt":303,"check":304,"hints":306,"solution":308,"skills":309},"order-of-operations.q021","Evaluate **100 − 35 + 15 − 40**.",{"kind":179,"answer":305,"tolerance":181},40,[307],"100 − 35 = 65 first.","Start from 100 − 35 + 15 − 40.\n\nWork one step at a time:\n\n1. 65 + 15 − 40\n2. 80 − 40\n3. 40\n\n**Answer: 40**",[173],{"id":311,"section":19,"level":102,"prompt":312,"check":313,"hints":324,"solution":326,"skills":327},"order-of-operations.q022","Which expression equals **40 − 12 + 8** (value 36)?",{"kind":48,"options":314,"correct":323},[315,317,319,321],{"id":51,"label":316},"40 − (12 + 8)",{"id":54,"label":318},"40 + 8 − 12",{"id":57,"label":320},"40 − 8 + 12",{"id":60,"label":322},"40 − 20",[54],[325],"Each number must keep the sign in front of it.","40 − 12 + 8 = 28 + 8 = **36**. You may reorder terms if each number keeps its own sign: 40 + 8 − 12 = 48 − 12 = 36. Options (a) and (d) take away 20 (giving 20), and (c) swaps the signs (giving 44).",[173,328],"reordering",{"id":330,"section":19,"level":158,"prompt":331,"check":332,"hints":333,"solution":335,"skills":336},"order-of-operations.q023","Evaluate **1000 − 999 + 998 − 997 + 996 − 995**.",{"kind":179,"answer":208,"tolerance":181},[334],"Group the numbers in pairs from the left.","Left to right works, but pairing is quicker: (1000 − 999) + (998 − 997) + (996 − 995) = 1 + 1 + 1 = **3**. Pairing from the left keeps each − attached to its own number.",[337,173],"structure",{"id":339,"section":23,"level":45,"prompt":340,"check":341,"hints":342,"solution":344,"skills":345},"order-of-operations.q024","Evaluate **6 + 8 ÷ 2**.",{"kind":179,"answer":199,"tolerance":181},[343],"÷ before +.","Start from 6 + 8 ÷ 2.\n\nWork one step at a time:\n\n1. 6 + 4\n2. 10\n\n**Answer: 10**",[67],{"id":347,"section":23,"level":45,"prompt":348,"check":349,"hints":350,"solution":352,"skills":353},"order-of-operations.q025","Evaluate **10 − 2 × 3**.",{"kind":179,"answer":190,"tolerance":181},[351],"× before −.","Start from 10 − 2 × 3.\n\nWork one step at a time:\n\n1. 10 − 6\n2. 4\n\n**Answer: 4**",[67],{"id":355,"section":23,"level":45,"prompt":356,"check":357,"hints":359,"solution":361,"skills":362},"order-of-operations.q026","Evaluate **5 × 2 + 3 × 4**.",{"kind":179,"answer":358,"tolerance":181},22,[360],"Work out both × chunks, then add.","Start from 5 × 2 + 3 × 4.\n\nWork one step at a time:\n\n1. 10 + 3 × 4\n2. 10 + 12\n3. 22\n\n**Answer: 22**",[67,363],"terms",{"id":365,"section":23,"level":102,"prompt":366,"check":367,"hints":369,"solution":371,"skills":372},"order-of-operations.q027","Evaluate **20 − 12 ÷ 4 × 2**.",{"kind":179,"answer":368,"tolerance":181},14,[370],"÷ and × left to right, then −.","Start from 20 − 12 ÷ 4 × 2.\n\nWork one step at a time:\n\n1. 20 − 3 × 2\n2. 20 − 6\n3. 14\n\n**Answer: 14**",[67,173],{"id":374,"section":23,"level":102,"prompt":375,"check":376,"hints":377,"solution":379,"skills":380},"order-of-operations.q028","Evaluate **7 + 18 ÷ 3 × 2 − 6**.",{"kind":179,"answer":287,"tolerance":181},[378],"First the × ÷ chunk: 18 ÷ 3 × 2.","Start from 7 + 18 ÷ 3 × 2 − 6.\n\nWork one step at a time:\n\n1. 7 + 6 × 2 − 6\n2. 7 + 12 − 6\n3. 19 − 6\n4. 13\n\n**Answer: 13**",[67,363],{"id":382,"section":23,"level":102,"prompt":383,"check":384,"hints":385,"solution":387,"skills":388},"order-of-operations.q029","Evaluate **48 ÷ 6 + 7 × 3 − 45 ÷ 9 × 2 + 1**.",{"kind":179,"answer":234,"tolerance":181},[386],"Split into terms at the + and − signs.","Start from 48 ÷ 6 + 7 × 3 − 45 ÷ 9 × 2 + 1.\n\nWork one step at a time:\n\n1. 8 + 7 × 3 − 45 ÷ 9 × 2 + 1\n2. 8 + 21 − 45 ÷ 9 × 2 + 1\n3. 8 + 21 − 5 × 2 + 1\n4. 8 + 21 − 10 + 1\n5. 29 − 10 + 1\n6. 19 + 1\n7. 20\n\n**Answer: 20**",[363],{"id":390,"section":23,"level":102,"prompt":391,"check":392,"hints":394,"solution":396,"skills":397},"order-of-operations.q030","Evaluate **6 × 7 − 36 ÷ 4 + 2 × 5**.",{"kind":179,"answer":393,"tolerance":181},43,[395],"Terms: 6 × 7, 36 ÷ 4, 2 × 5.","Start from 6 × 7 − 36 ÷ 4 + 2 × 5.\n\nWork one step at a time:\n\n1. 42 − 36 ÷ 4 + 2 × 5\n2. 42 − 9 + 2 × 5\n3. 42 − 9 + 10\n4. 33 + 10\n5. 43\n\n**Answer: 43**",[363],{"id":399,"section":23,"level":102,"prompt":400,"check":401,"hints":403,"solution":405,"skills":406},"order-of-operations.q031","Evaluate **90 − 45 ÷ 5 × 3 + 12**.",{"kind":179,"answer":402,"tolerance":181},75,[404],"45 ÷ 5 × 3 first.","Start from 90 − 45 ÷ 5 × 3 + 12.\n\nWork one step at a time:\n\n1. 90 − 9 × 3 + 12\n2. 90 − 27 + 12\n3. 63 + 12\n4. 75\n\n**Answer: 75**",[67,173],{"id":408,"section":23,"level":102,"prompt":409,"check":410,"hints":412,"solution":414,"skills":415},"order-of-operations.q032","How many **terms** does **4 × 5 − 6 ÷ 2 + 3 × 3 × 3** have, and what is its value? Enter the value.",{"kind":179,"answer":411,"tolerance":181},44,[413],"Terms are separated by + and − signs.","The top-level + and − split it into **3 terms**: 4 × 5, 6 ÷ 2 and 3 × 3 × 3.\n\nTerm values: 20, 3 and 27.\n\nCombine left to right: 20 − 3 + 27 = 17 + 27 = **44**.",[363],{"id":417,"section":23,"level":158,"prompt":418,"check":419,"hints":420,"solution":422,"skills":423},"order-of-operations.q033","Evaluate **9 − 9 × 0 + 1**.",{"kind":179,"answer":199,"tolerance":181},[421],"What is 9 × 0?","Start from 9 − 9 × 0 + 1.\n\nWork one step at a time:\n\n1. 9 − 0 + 1\n2. 9 + 1\n3. 10\n\n**Answer: 10**\n\nA common wrong answer is 1, from doing 9 − 9 first.",[424,67],"zero",{"id":426,"section":23,"level":158,"prompt":427,"check":428,"hints":430,"solution":432,"skills":433},"order-of-operations.q034","Evaluate **100 − 4 × 5 × 2 + 64 ÷ 8 ÷ 2**.",{"kind":179,"answer":429,"tolerance":181},64,[431],"Two × ÷ chunks: 4 × 5 × 2 and 64 ÷ 8 ÷ 2.","Start from 100 − 4 × 5 × 2 + 64 ÷ 8 ÷ 2.\n\nWork one step at a time:\n\n1. 100 − 20 × 2 + 64 ÷ 8 ÷ 2\n2. 100 − 40 + 64 ÷ 8 ÷ 2\n3. 100 − 40 + 8 ÷ 2\n4. 100 − 40 + 4\n5. 60 + 4\n6. 64\n\n**Answer: 64**",[363,173],{"id":435,"section":23,"level":158,"prompt":436,"check":437,"hints":439,"solution":441,"skills":442},"order-of-operations.q035","In Python, `2 + 3 * 4 - 10 \u002F 5` gives a decimal answer. Using school maths (× is *, ÷ is \u002F), what is its value?",{"kind":179,"answer":438,"tolerance":181},12,[440],"* means × and \u002F means ÷.","Translate: 2 + 3 × 4 − 10 ÷ 5.\n\n× and ÷ first: 3 × 4 = 12 and 10 ÷ 5 = 2.\n\nThen 2 + 12 − 2 = **12**. (Python prints 12.0 because \u002F always gives a decimal.)",[443,67],"programming",{"id":445,"section":27,"level":45,"prompt":446,"check":447,"hints":448,"solution":450,"skills":451},"order-of-operations.q036","Evaluate **(2 + 3) × 4**.",{"kind":179,"answer":234,"tolerance":181},[449],"Brackets first.","Start from (2 + 3) × 4.\n\nWork one step at a time:\n\n1. 5 × 4\n2. 20\n\n**Answer: 20**",[27],{"id":453,"section":27,"level":45,"prompt":454,"check":455,"hints":457,"solution":459,"skills":460},"order-of-operations.q037","Evaluate **3 × (2 + 4)**.",{"kind":179,"answer":456,"tolerance":181},18,[458],"2 + 4 first.","Start from 3 × (2 + 4).\n\nWork one step at a time:\n\n1. 3 × 6\n2. 18\n\n**Answer: 18**",[27],{"id":462,"section":27,"level":102,"prompt":463,"check":464,"hints":465,"solution":467,"skills":468},"order-of-operations.q038","Evaluate **[20 − (3 + 5)] ÷ 4**.",{"kind":179,"answer":208,"tolerance":181},[466],"Innermost bracket first: 3 + 5.","Start from [20 − (3 + 5)] ÷ 4.\n\nWork one step at a time:\n\n1. [20 − 8] ÷ 4\n2. 12 ÷ 4\n3. 3\n\n**Answer: 3**",[469],"nested brackets",{"id":471,"section":27,"level":102,"prompt":472,"check":473,"hints":475,"solution":477,"skills":478},"order-of-operations.q039","Evaluate **100 − [6 × (8 − 3) + 10]**.",{"kind":179,"answer":474,"tolerance":181},60,[476],"8 − 3 first, then the square bracket.","Start from 100 − [6 × (8 − 3) + 10].\n\nWork one step at a time:\n\n1. 100 − [6 × 5 + 10]\n2. 100 − [30 + 10]\n3. 100 − 40\n4. 60\n\n**Answer: 60**",[469],{"id":480,"section":27,"level":102,"prompt":481,"check":482,"hints":484,"solution":486,"skills":487},"order-of-operations.q040","Evaluate **(7 + 5) × (9 − 4) − [36 ÷ (2 + 4)]**.",{"kind":179,"answer":483,"tolerance":181},54,[485],"Three innermost brackets: do all of them.","Start from (7 + 5) × (9 − 4) − [36 ÷ (2 + 4)].\n\nWork one step at a time:\n\n1. 12 × (9 − 4) − [36 ÷ (2 + 4)]\n2. 12 × 5 − [36 ÷ (2 + 4)]\n3. 12 × 5 − [36 ÷ 6]\n4. 12 × 5 − 6\n5. 60 − 6\n6. 54\n\n**Answer: 54**",[469],{"id":489,"section":27,"level":102,"prompt":490,"check":491,"hints":493,"solution":496,"skills":497},"order-of-operations.q041","Evaluate **[50 − {12 + (18 − 6) ÷ 4}] × 2**.",{"kind":179,"answer":492,"tolerance":181},70,[494,495],"( ) first, then { }, then [ ].","Inside { }, ÷ before +.","Start from [50 − {12 + (18 − 6) ÷ 4}] × 2.\n\nWork one step at a time:\n\n1. [50 − {12 + 12 ÷ 4}] × 2\n2. [50 − {12 + 3}] × 2\n3. [50 − 15] × 2\n4. 35 × 2\n5. 70\n\n**Answer: 70**",[469],{"id":499,"section":27,"level":102,"prompt":500,"check":501,"hints":503,"solution":505,"skills":506},"order-of-operations.q042","In BODMAS-style working (\"of\" before ÷ and ×), evaluate **60 − ½ of 40 + 5**.",{"kind":179,"answer":502,"tolerance":181},45,[504],"½ of 40 = ?","\"Of\" first: ½ of 40 = 20.\n\nThen left to right: 60 − 20 = 40, and 40 + 5 = **45**.",[507],"of",{"id":509,"section":27,"level":158,"prompt":510,"check":511,"hints":513,"solution":515,"skills":516},"order-of-operations.q043","In BODMAS-style working, evaluate **40 ÷ ½ of 16**. (Do \"of\" before ÷.)",{"kind":179,"answer":512,"tolerance":181},5,[514],"Work out ½ of 16 first.","\"Of\" first: ½ of 16 = 8.\n\nThen 40 ÷ 8 = **5**.\n\nCompare 40 ÷ ½ × 16 (with × instead of \"of\"): left to right that is 80 × 16 = 1,280. This is why many mathematicians prefer brackets: 40 ÷ (½ × 16).",[507],{"id":518,"section":27,"level":158,"prompt":519,"check":520,"hints":522,"solution":524,"skills":525},"order-of-operations.q044","A bar (vinculum) drawn over **5 − 2** means it is worked out first. Simplify **40 − [10 + {12 − (8 − *bar over 5 − 2*)}]**.",{"kind":179,"answer":521,"tolerance":181},23,[523],"The bar is the innermost grouping.","Bar first: 5 − 2 = 3.\n\nRound: 8 − 3 = 5.\n\nCurly: 12 − 5 = 7.\n\nSquare: 10 + 7 = 17.\n\nFinally 40 − 17 = **23**.",[526,469],"vinculum",{"id":528,"section":27,"level":158,"prompt":529,"check":530,"hints":532,"solution":534,"skills":535},"order-of-operations.q045","Evaluate **[84 ÷ {3 × (9 − 2)} + 5] × (18 − 4 × 4) − 6 ÷ 3**.",{"kind":179,"answer":531,"tolerance":181},16,[533],"Two innermost brackets: (9 − 2) and (18 − 4 × 4).","Start from [84 ÷ {3 × (9 − 2)} + 5] × (18 − 4 × 4) − 6 ÷ 3.\n\nWork one step at a time:\n\n1. [84 ÷ {3 × 7} + 5] × (18 − 4 × 4) − 6 ÷ 3\n2. [84 ÷ 21 + 5] × (18 − 4 × 4) − 6 ÷ 3\n3. [4 + 5] × (18 − 4 × 4) − 6 ÷ 3\n4. 9 × (18 − 4 × 4) − 6 ÷ 3\n5. 9 × (18 − 16) − 6 ÷ 3\n6. 9 × 2 − 6 ÷ 3\n7. 18 − 6 ÷ 3\n8. 18 − 2\n9. 16\n\n**Answer: 16**",[469],{"id":537,"section":27,"level":538,"prompt":539,"check":540,"hints":542,"solution":544,"skills":545},"order-of-operations.q046","challenge","Without working out the brackets, rewrite **75 − (25 − 10) + 3 × (6 ÷ 2)** with no brackets at all, keeping its value. What is the value?",{"kind":179,"answer":541,"tolerance":181},69,[543],"Removing a bracket after − flips + and − inside.","After a −, the signs inside flip: 75 − (25 − 10) = 75 − 25 + 10.\n\nAfter a ×, a bracket holding only ÷ can go: 3 × (6 ÷ 2) = 3 × 6 ÷ 2.\n\nSo the expression is 75 − 25 + 10 + 3 × 6 ÷ 2 = 75 − 25 + 10 + 9 = **69**.\n\nCheck with brackets: 75 − 15 + 3 × 3 = 60 + 9 = 69 ✓.",[546],"removing brackets",{"id":548,"section":31,"level":45,"prompt":549,"check":550,"hints":553,"solution":555,"skills":556},"order-of-operations.q047","Kabir buys **3 pens at ₹12 each** and **2 notebooks at ₹40 each**. What is the total bill in rupees?",{"kind":179,"answer":551,"tolerance":181,"unit":552},116,"₹",[554],"Pens: 3 × 12. Notebooks: 2 × 40.","Expression: **3 × 12 + 2 × 40**\n\n1. 36 + 2 × 40\n2. 36 + 80\n3. 116\n\n**Answer: ₹116.**\n\nEach \"how many × price\" is a chunk; the chunks are added.",[120],{"id":558,"section":31,"level":45,"prompt":559,"check":560,"hints":563,"solution":565,"skills":566},"order-of-operations.q048","A batter hits **4 fours**, **3 sixes** and **5 singles**. How many runs?",{"kind":179,"answer":561,"tolerance":181,"unit":562},39,"runs",[564],"Fours: 4 × 4. Sixes: 3 × 6.","Expression: **4 × 4 + 3 × 6 + 5**\n\n1. 16 + 3 × 6 + 5\n2. 16 + 18 + 5\n3. 34 + 5\n4. 39\n\n**Answer: 39 runs.**",[120],{"id":568,"section":31,"level":45,"prompt":569,"check":570,"hints":572,"solution":574,"skills":575},"order-of-operations.q049","An auto charges **₹30 to start** plus **₹15 for each km**. What is the fare for **6 km**?",{"kind":179,"answer":571,"tolerance":181,"unit":552},120,[573],"The km make one chunk: 15 × 6.","Expression: **30 + 15 × 6**\n\n1. 30 + 90\n2. 120\n\n**Answer: ₹120.**",[120],{"id":577,"section":31,"level":102,"prompt":578,"check":579,"hints":581,"solution":583,"skills":584},"order-of-operations.q050","Kabir pays for **3 pens at ₹12** and **2 notebooks at ₹40** with a **₹200** note. How much change does he get?",{"kind":179,"answer":580,"tolerance":181,"unit":552},84,[582],"Change = 200 − (whole bill).","Expression: **200 − (3 × 12 + 2 × 40)**\n\n1. 200 − (36 + 2 × 40)\n2. 200 − (36 + 80)\n3. 200 − 116\n4. 84\n\n**Answer: ₹84.**\n\nThe whole bill is taken away, so it goes in brackets. Without them, 200 − 3 × 12 + 2 × 40 = 244 would add the notebooks back.",[120],{"id":586,"section":31,"level":102,"prompt":587,"check":588,"hints":591,"solution":593,"skills":594},"order-of-operations.q051","A teacher has **5 boxes of 12 laddoos**. **4** are broken. The rest are shared equally among **8** children. How many does each get?",{"kind":179,"answer":589,"tolerance":181,"unit":590},7,"laddoos",[592],"Total minus broken, then share.","Expression: **(5 × 12 − 4) ÷ 8**\n\n1. (60 − 4) ÷ 8\n2. 56 ÷ 8\n3. 7\n\n**Answer: 7 laddoos.**\n\nThe whole remainder is shared, so bracket it.",[120],{"id":596,"section":31,"level":102,"prompt":597,"check":598,"hints":600,"solution":601,"skills":602},"order-of-operations.q052","A family buys **2 adult** train tickets at **₹245** and **3 child** tickets at **₹125**, plus a **₹30** booking fee. Total?",{"kind":179,"answer":599,"tolerance":181,"unit":552},895,[],"Expression: **2 × 245 + 3 × 125 + 30**\n\n1. 490 + 3 × 125 + 30\n2. 490 + 375 + 30\n3. 865 + 30\n4. 895\n\n**Answer: ₹895.**\n\nEstimate: 500 + 375 + 30 ≈ 900. ✓",[120],{"id":604,"section":31,"level":102,"prompt":605,"check":606,"hints":608,"solution":610,"skills":611},"order-of-operations.q053","A team wins **₹5,000**, spends **₹1,400** on a party, and shares the rest equally among **12** players. How much each?",{"kind":179,"answer":607,"tolerance":181,"unit":552},300,[609],"What is left after the party?","Expression: **(5,000 − 1,400) ÷ 12**\n\n1. 3,600 ÷ 12\n2. 300\n\n**Answer: ₹300.**",[120],{"id":613,"section":31,"level":102,"prompt":614,"check":615,"hints":616,"solution":618,"skills":619},"order-of-operations.q054","Ravi buys **5 kg sugar at ₹45 a kg** and **2 packets of tea at ₹120** and pays with **₹500**. Change?",{"kind":179,"answer":296,"tolerance":181,"unit":552},[617],"Bill first, in brackets.","Expression: **500 − (5 × 45 + 2 × 120)**\n\n1. 500 − (225 + 2 × 120)\n2. 500 − (225 + 240)\n3. 500 − 465\n4. 35\n\n**Answer: ₹35.**",[120],{"id":621,"section":31,"level":158,"prompt":622,"check":623,"hints":625,"solution":627,"skills":628},"order-of-operations.q055","Asha buys **3 pens (₹12 each) and 2 notebooks (₹40 each)** for herself and **the same again** for her brother. She pays with **₹500**. Change?",{"kind":179,"answer":624,"tolerance":181,"unit":552},268,[626],"One set costs 3 × 12 + 2 × 40.","Expression: **500 − 2 × (3 × 12 + 2 × 40)**\n\n1. 500 − 2 × (36 + 2 × 40)\n2. 500 − 2 × (36 + 80)\n3. 500 − 2 × 116\n4. 500 − 232\n5. 268\n\n**Answer: ₹268.**\n\nOne set is 3 × 12 + 2 × 40; two sets need brackets: 2 × (…).",[120],{"id":630,"section":31,"level":158,"prompt":631,"check":632,"hints":635,"solution":636,"skills":637},"order-of-operations.q056","A hall has **12 rows of 15 seats** and a balcony of **4 rows of 20 seats**. **25** seats are broken. How many seats can be used?",{"kind":179,"answer":633,"tolerance":181,"unit":634},235,"seats",[],"Expression: **12 × 15 + 4 × 20 − 25**\n\n1. 180 + 4 × 20 − 25\n2. 180 + 80 − 25\n3. 260 − 25\n4. 235\n\n**Answer: 235 seats.**",[120],{"id":639,"section":31,"level":538,"prompt":640,"check":641,"hints":643,"solution":645,"skills":646},"order-of-operations.q057","A shop sells an item for **₹500** before tax. **GST is 18%**. Which expression gives the price with tax, and what is it? Enter the price in rupees.",{"kind":179,"answer":642,"tolerance":181,"unit":552},590,[644],"Add 18% means multiply by 118 and divide by 100.","Price with tax = 500 × (100 + 18) ÷ 100.\n\n1. Bracket: 100 + 18 = 118.\n2. Left to right: 500 × 118 = 59,000.\n3. 59,000 ÷ 100 = 590.\n\n**Answer: ₹590.**\n\nWithout brackets, 500 × 100 + 18 ÷ 100 = 50,000.18, an absurd price. Estimating (a bit more than ₹500) catches that at once.",[120,647],"percent",{"id":649,"section":35,"level":45,"prompt":650,"check":651,"hints":653,"solution":655,"skills":656},"order-of-operations.q058","Arjun wrote **6 + 4 × 5 = 10 × 5 = 50**. What is the correct value?",{"kind":179,"answer":652,"tolerance":181},26,[654],"Which should come first, + or ×?","Arjun added first. × comes before +: 4 × 5 = 20, then 6 + 20 = **26**.",[657],"error analysis",{"id":659,"section":35,"level":45,"prompt":660,"check":661,"hints":662,"solution":664,"skills":665},"order-of-operations.q059","Meena wrote **20 − 8 + 2 = 20 − 10 = 10**. What is the correct value?",{"kind":179,"answer":368,"tolerance":181},[663],"+ and − share a level.","Meena did + before −, the \"letter trap\". + and − share a level: left to right, 20 − 8 = 12, then 12 + 2 = **14**.",[657,173],{"id":667,"section":35,"level":102,"prompt":668,"check":669,"hints":680,"solution":681,"skills":682},"order-of-operations.q060","Where is the mistake? **2 × (5 + 3) = 10 + 3 = 13**",{"kind":48,"options":670,"correct":679},[671,673,675,677],{"id":51,"label":672},"The bracket was ignored: 2 multiplied only the 5",{"id":54,"label":674},"Should have done 5 + 3 after multiplying",{"id":57,"label":676},"No mistake",{"id":60,"label":678},"Should have added 2 + 5 first",[51],[],"Brackets first: 5 + 3 = 8, then 2 × 8 = **16**. The working multiplied only the 5 and left the 3 out.",[657,27],{"id":684,"section":35,"level":102,"prompt":685,"check":686,"hints":688,"solution":690,"skills":691},"order-of-operations.q061","Neha wrote **45 − 3 × (2 + 8) = 45 − 3 × 2 + 8 = 45 − 6 + 8 = 47**. What is the correct value?",{"kind":179,"answer":687,"tolerance":181},15,[689],"What should (2 + 8) become first?","She dropped the brackets in the first step. Correct: (2 + 8) = 10; 3 × 10 = 30; 45 − 30 = **15**.",[657,27],{"id":693,"section":35,"level":102,"prompt":694,"check":695,"hints":706,"solution":707,"skills":708},"order-of-operations.q062","Which piece of working is **correct**?",{"kind":48,"options":696,"correct":705},[697,699,701,703],{"id":51,"label":698},"24 ÷ 6 × 2 = 24 ÷ 12 = 2",{"id":54,"label":700},"24 ÷ 6 × 2 = 4 × 2 = 8",{"id":57,"label":702},"30 − (8 + 2) = 22 + 2 = 24",{"id":60,"label":704},"100 − 4 × 5 × 2 = 96 × 10 = 960",[54],[],"(b) goes left to right through ÷ and ×: 24 ÷ 6 = 4, 4 × 2 = **8**. (a) did × before ÷; (c) dropped the bracket (should be 30 − 10 = 20); (d) subtracted first (should be 100 − 40 = 60).",[657],{"id":710,"section":35,"level":158,"prompt":711,"check":712,"hints":714,"solution":716,"skills":717},"order-of-operations.q063","A shopkeeper types **5 + 2 × 10 =** on a basic (step-by-step) calculator. It shows **70**. What is the correct value, and why does the calculator differ? Enter the correct value.",{"kind":179,"answer":713,"tolerance":181},25,[715],"Which step did the calculator do first?","The correct value multiplies first: 2 × 10 = 20, then 5 + 20 = **25**.\n\nA basic calculator uses *immediate execution*: it finishes 5 + 2 = 7 as soon as × is pressed, then 7 × 10 = 70. To get 25, type 2 × 10 = first, then + 5 =.",[718,657],"calculators",{"id":720,"section":35,"level":158,"prompt":721,"check":722,"hints":733,"solution":735,"skills":736},"order-of-operations.q064","Find the first wrong step: **[12 − (2 + 4)] × 3 ÷ 9 = [12 − 6] × 3 ÷ 9 = 6 × 3 ÷ 9 = 6 × (1\u002F3) = 2**",{"kind":48,"options":723,"correct":732},[724,726,728,730],{"id":51,"label":725},"Step 1: (2 + 4) = 6",{"id":54,"label":727},"Step 2: [12 − 6] = 6",{"id":57,"label":729},"Step 3: doing 3 ÷ 9 before 6 × 3",{"id":60,"label":731},"There is no mistake: the answer 2 is correct",[60],[734],"Check the final answer by going left to right.","Every step is valid and the answer is **2**. Step 3 did 3 ÷ 9 before 6 × 3, which looks like breaking left to right, but 6 × 3 ÷ 9 = 6 × (3 ÷ 9) is always true, because dividing by 9 can be done at any point in a × ÷ chain. Left to right gives 18 ÷ 9 = 2 as well. (The risky move is the other way: a ÷ b × c is not a ÷ (b × c).)",[657,737],"reasoning",{"id":739,"section":35,"level":538,"prompt":740,"check":741,"hints":742,"solution":744,"skills":745},"order-of-operations.q065","A student claims: **\"a − a × 0 = 0 for every number a, because a − a = 0 and 0 × 0 = 0.\"** For a = 7, what is the correct value of a − a × 0?",{"kind":179,"answer":589,"tolerance":181},[743],"Do the × first.","× comes first: 7 × 0 = 0, so 7 − 7 × 0 = 7 − 0 = **7**.\n\nIn general a − a × 0 = a − 0 = a. The claim is only true when a = 0. The student subtracted first, which would be written (a − a) × 0.",[657,424],{"id":747,"section":39,"level":102,"prompt":748,"check":749,"hints":751,"solution":753,"skills":754},"order-of-operations.q066","Add brackets to **2 + 3 × 4 − 1** (keep the order of numbers and signs) to make the **biggest** value. What is it?",{"kind":179,"answer":750,"tolerance":181},19,[752],"Try making the + happen before the ×.","The possible values are 11, 13, 15 and 19.\n\nThe biggest is (2 + 3) × 4 − 1 = 20 − 1 = **19**: adding first makes a bigger number to multiply.",[27,39],{"id":756,"section":39,"level":102,"prompt":757,"check":758,"hints":769,"solution":770,"skills":771},"order-of-operations.q067","Which filling of **6 ▢ 3 ▢ 2** (each box is +, −, × or ÷) gives **12**?",{"kind":48,"options":759,"correct":768},[760,762,764,766],{"id":51,"label":761},"6 + 3 × 2",{"id":54,"label":763},"6 × 3 − 2",{"id":57,"label":765},"6 ÷ 3 × 2",{"id":60,"label":767},"6 − 3 + 2",[51],[],"6 + 3 × 2 = 6 + 6 = **12**. The others: 6 × 3 − 2 = 16, 6 ÷ 3 × 2 = 4, 6 − 3 + 2 = 5. (If you forgot the rule you might think 6 + 3 × 2 = 18.)",[39],{"id":773,"section":39,"level":158,"prompt":774,"check":775,"hints":776,"solution":778,"skills":779},"order-of-operations.q068","Using exactly four 4s, which number does **(4 × 4 + 4) ÷ 4** make?",{"kind":179,"answer":512,"tolerance":181},[777],"Inside the bracket, × before +.","Bracket first: inside, × before +: 4 × 4 = 16, 16 + 4 = 20.\n\nThen 20 ÷ 4 = **5**.",[780],"four fours",{"id":782,"section":39,"level":158,"prompt":783,"check":784,"hints":785,"solution":787,"skills":788},"order-of-operations.q069","Using **1, 2, 3, 4** once each with + and × and any brackets, what is the **biggest** value?",{"kind":179,"answer":217,"tolerance":181},[786],"Is it better to multiply by 1 or add 1?","Multiplying by 1 wastes the 1. Add it instead: (1 + 2) × 3 × 4 = 3 × 12 = **36**. Compare 1 × 2 × 3 × 4 = 24 and (1 + 3) × 2 × 4 = 32.",[39,737],{"id":790,"section":39,"level":158,"prompt":791,"check":792,"hints":793,"solution":795,"skills":796},"order-of-operations.q070","Find the missing number: **▢ × 4 + 3 × 5 = 47**.",{"kind":179,"answer":180,"tolerance":181},[794],"First find what ▢ × 4 must be.","Undo the operations in reverse order. The + is done last, so undo it first: ▢ × 4 = 47 − 3 × 5 = 47 − 15 = 32.\n\nThen ▢ = 32 ÷ 4 = **8**.\n\nCheck: 8 × 4 + 3 × 5 = 32 + 15 = 47 ✓.",[797],"working backwards",{"id":799,"section":39,"level":538,"prompt":800,"check":801,"hints":803,"solution":805,"skills":806},"order-of-operations.q071","Put brackets into **1 + 2 × 3 + 4 × 5 + 6** (order kept) to make the **largest** possible value.",{"kind":179,"answer":802,"tolerance":181},231,[804],"Bracket each + that sits next to a ×.","Add small numbers before multiplying: (1 + 2) × (3 + 4) × (5 + 6) = 3 × 7 × 11 = **231**.\n\nA computer check of all 42 bracketings confirms 231 is the maximum (and the no-bracket value, 33, is the minimum).",[27,39],{"id":808,"section":39,"level":538,"prompt":809,"check":810,"hints":813,"solution":816,"skills":817},"order-of-operations.q072","Make **24** from **3, 3, 8, 8** (each once, + − × ÷ and brackets). The only way uses a fraction on the way. What is the value of **3 − 8 ÷ 3** in that solution? Give it as a fraction.",{"kind":811,"numerator":5,"denominator":208,"acceptEquivalent":812},"fraction",true,[814,815],"8 ÷ 3 = 8\u002F3.","3 = 9\u002F3.","The solution is 8 ÷ (3 − 8 ÷ 3).\n\nInside the bracket, ÷ first: 8 ÷ 3 = 8\u002F3 = 2⅔. Then 3 − 8\u002F3 = 9\u002F3 − 8\u002F3 = **1\u002F3**.\n\nFinally 8 ÷ ⅓ = 24 (there are 24 thirds in 8). ✓",[818,819],"24 game","fractions",{"id":821,"section":39,"level":538,"prompt":822,"check":823,"hints":825,"solution":827,"skills":828},"order-of-operations.q073","Evaluate **2026 − 2025 + 2024 − 2023 + … + 4 − 3 + 2 − 1**.",{"kind":179,"answer":824,"tolerance":181},1013,[826],"Group the numbers in pairs.","Pair from the left: (2026 − 2025) + (2024 − 2023) + … + (2 − 1).\n\nEach pair is 1, and there are 2026 ÷ 2 = 1,013 pairs.\n\n**Answer: 1,013.**",[337,829],"olympiad",{"id":831,"section":39,"level":538,"prompt":832,"check":833,"hints":834,"solution":836,"skills":837},"order-of-operations.q074","Using the strict school rule (implied multiplication treated as an ordinary ×), what is **8 ÷ 2(2 + 2)**?",{"kind":179,"answer":531,"tolerance":181},[835],"Rewrite 2(2 + 2) as 2 × (2 + 2).","Bracket: 2 + 2 = 4. Then 8 ÷ 2 × 4, left to right: 8 ÷ 2 = 4, 4 × 4 = **16**.\n\nBut beware: many people, and some calculators, treat 2(2 + 2) as one unit and get 8 ÷ 8 = 1. Casio’s fx-82ES PLUS manual, for instance, ranks multiplication with the sign left out above ordinary ÷. The expression is badly written. Clear versions: (8 ÷ 2) × (2 + 2) = 16 or 8 ÷ [2 × (2 + 2)] = 1.",[838],"implied multiplication",{"id":840,"section":39,"level":538,"prompt":841,"check":842,"hints":843,"solution":845,"skills":846},"order-of-operations.q075","Using **1, 2, 3, 4, 5 in order**, with **+ or ×** between them and **no brackets**, how many of the 16 possible fillings give an **odd** value?",{"kind":179,"answer":180,"tolerance":181},[844],"Work out each filling with × first, or think about odd and even.","List all 16 (× first in each): sorted, the values are 14, 15, 15, 16, 19, 20, 25, 26, 26, 27, 29, 30, 62, 63, 120, 121.\n\nThe odd ones are 15, 15, 19, 25, 27, 29, 63, 121: **8** fillings.\n\nA shortcut: only the parity (odd\u002Feven) of each term matters. Try to explain why exactly half are odd.",[39,847],"parity",[849,850,851,852,853,854],"order-of-operations-ncert-class7","order-of-operations-wikipedia","order-of-operations-mathsisfun-bodmas","order-of-operations-wikipedia-24-game","order-of-operations-wikipedia-four-fours","order-of-operations-casio-priority","needs_review",{"generatedBy":857,"notes":858},"claude-code","Every numeric answer computed and asserted in Python using the site convention (× ÷ left to right, then + − left to right; \"of\" before × ÷). Pending owner review.","9219a21c16fa84657279582c196695f25c8efe556aa51a3f92c16020f3edaca5",{"logic:questions":861,"source:order-of-operations-casio-priority":862,"source:order-of-operations-mathsisfun-bodmas":863,"source:order-of-operations-ncert-class7":864,"source:order-of-operations-wikipedia":865,"source:order-of-operations-wikipedia-24-game":866,"source:order-of-operations-wikipedia-four-fours":867},"e7fd7c240a65bea1bff6277f7af7cca65e2c7fcb13c6d756cb943d53f3cbc948","2df5e6142624f3ba1931c70a8d8ac63b09cd1eb649fb1ae8757bb36f96452720","92959283b293565e5dbcac7d99680a63df55eef50520c997ab808634afaa0062","e7cadfedc70b54014195d6d8bc2740fb10a7e8aed3509c11f1efbde6e7698ade","88ccf3653f7d9723bbb33a67a6548ccff64980f752cba0cd94a32bc60f72bd44","1022e875bb64d7d92d0b0eb62e2dfa81ff1c82aef5e67c620cafa77e2d0e8e1e","3f1d6a760aa170524009986575f77b1a9af08bf736fab494703b115246a5fded","preview-7e1cbbcc4f",1789899599922]