{
  "Id": "77da2089-b981-40d0-b33f-788560cdcfe0",
  "Title": "Fractions Mastery: Parts, Equivalence, and Operations",
  "Subject": "Mathematics",
  "Topic": "Fractions\u2014parts of a whole, equivalence, comparison, and basic operations",
  "Instructions": "Read each question carefully and answer to the best of your ability. Show all working for word problems.",
  "EstimatedMinutes": 35,
  "StudentProfileId": "dd186faa-f489-46ee-84e4-26e2d01e2691",
  "SourceFileName": " fractions.pdf",
  "SessionMaterialId": "8499eeea-dc89-4b86-86d3-ec710e4ce069",
  "GeneratedAt": "2026-07-25T11:56:24.450426Z",
  "Questions": [
    {
      "Id": 1,
      "Type": "true_false",
      "Text": "A unit fraction is any fraction with numerator equal to 1.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 2,
      "Type": "true_false",
      "Text": "The fractions 3/5 and 6/10 represent the same value.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 3,
      "Type": "true_false",
      "Text": "A mixed number is always less than 1.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 4,
      "Type": "true_false",
      "Text": "To compare 2/7 and 3/7, you only need to compare the numerators.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 5,
      "Type": "true_false",
      "Text": "Adding 4/9 and 2/9 gives 6/18.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 6,
      "Type": "true_false",
      "Text": "The fraction 5/4 is an improper fraction.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 7,
      "Type": "true_false",
      "Text": "Reducing a fraction to lowest terms changes its value.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 8,
      "Type": "true_false",
      "Text": "Zero can be written as 0/9 for any nonzero denominator.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 9,
      "Type": "true_false",
      "Text": "To add 1/3 and 1/4, you can add the denominators to get 1/7.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 10,
      "Type": "true_false",
      "Text": "On a number line, 5/6 is to the right of 3/4.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 11,
      "Type": "multiple_choice",
      "Text": "Which of the following is a proper fraction?",
      "Options": [
        "A. 7/5",
        "B. 9/9",
        "C. 4/7",
        "D. 12/12"
      ],
      "Answer": "C. 4/7",
      "Points": 2
    },
    {
      "Id": 12,
      "Type": "multiple_choice",
      "Text": "Convert 17/5 to a mixed number.",
      "Options": [
        "A. 3 1/5",
        "B. 3 2/5",
        "C. 2 3/5",
        "D. 4 2/5"
      ],
      "Answer": "B. 3 2/5",
      "Points": 2
    },
    {
      "Id": 13,
      "Type": "multiple_choice",
      "Text": "Which pair are like fractions?",
      "Options": [
        "A. 3/8 and 5/8",
        "B. 2/7 and 3/9",
        "C. 4/5 and 4/7",
        "D. 1/3 and 2/6"
      ],
      "Answer": "A. 3/8 and 5/8",
      "Points": 2
    },
    {
      "Id": 14,
      "Type": "multiple_choice",
      "Text": "Simplify 18/24 to lowest terms.",
      "Options": [
        "A. 3/4",
        "B. 2/5",
        "C. 4/9",
        "D. 5/8"
      ],
      "Answer": "A. 3/4",
      "Points": 2
    },
    {
      "Id": 15,
      "Type": "multiple_choice",
      "Text": "What is 2/3 \u002B 1/6?",
      "Options": [
        "A. 3/9",
        "B. 1/2",
        "C. 5/6",
        "D. 7/6"
      ],
      "Answer": "C. 5/6",
      "Points": 2
    },
    {
      "Id": 16,
      "Type": "multiple_choice",
      "Text": "Which fraction is equal to 0.25?",
      "Options": [
        "A. 1/3",
        "B. 1/4",
        "C. 2/5",
        "D. 3/8"
      ],
      "Answer": "B. 1/4",
      "Points": 2
    },
    {
      "Id": 17,
      "Type": "multiple_choice",
      "Text": "Which fraction is greatest?",
      "Options": [
        "A. 3/4",
        "B. 4/5",
        "C. 7/9",
        "D. 5/6"
      ],
      "Answer": "D. 5/6",
      "Points": 2
    },
    {
      "Id": 18,
      "Type": "multiple_choice",
      "Text": "Compute 5/8 \u2212 1/4.",
      "Options": [
        "A. 1/2",
        "B. 3/8",
        "C. 1/8",
        "D. 5/12"
      ],
      "Answer": "B. 3/8",
      "Points": 2
    },
    {
      "Id": 19,
      "Type": "multiple_choice",
      "Text": "Which is equivalent to 9/12?",
      "Options": [
        "A. 3/4",
        "B. 2/3",
        "C. 6/10",
        "D. 4/5"
      ],
      "Answer": "A. 3/4",
      "Points": 2
    },
    {
      "Id": 20,
      "Type": "multiple_choice",
      "Text": "The least common denominator of 2/9 and 5/12 is:",
      "Options": [
        "A. 21",
        "B. 36",
        "C. 108",
        "D. 18"
      ],
      "Answer": "B. 36",
      "Points": 2
    },
    {
      "Id": 21,
      "Type": "fill_blank",
      "Text": "The number on the top of a fraction is called the _____.",
      "Options": [],
      "Answer": "numerator",
      "Points": 2
    },
    {
      "Id": 22,
      "Type": "fill_blank",
      "Text": "Fractions with the same denominator are called _____.",
      "Options": [],
      "Answer": "like fractions",
      "Points": 2
    },
    {
      "Id": 23,
      "Type": "fill_blank",
      "Text": "To add 1/5 and 2/3, use a common _____.",
      "Options": [],
      "Answer": "denominator",
      "Points": 2
    },
    {
      "Id": 24,
      "Type": "fill_blank",
      "Text": "The fraction 10/15 in lowest terms is _____.",
      "Options": [],
      "Answer": "2/3",
      "Points": 2
    },
    {
      "Id": 25,
      "Type": "fill_blank",
      "Text": "One whole written as an improper fraction with denominator 9 is _____.",
      "Options": [],
      "Answer": "9/9",
      "Points": 2
    },
    {
      "Id": 26,
      "Type": "fill_blank",
      "Text": "The mixed number 4 3/8 written as an improper fraction is _____.",
      "Options": [],
      "Answer": "35/8",
      "Points": 2
    },
    {
      "Id": 27,
      "Type": "fill_blank",
      "Text": "The fraction halfway between 1/4 and 1/2 is _____.",
      "Options": [],
      "Answer": "3/8",
      "Points": 2
    },
    {
      "Id": 28,
      "Type": "fill_blank",
      "Text": "The symbol to show 7/11 is greater than 5/11 is _____.",
      "Options": [],
      "Answer": "\u003E",
      "Points": 2
    },
    {
      "Id": 29,
      "Type": "fill_blank",
      "Text": "A fraction with a numerator larger than its denominator is called an _____.",
      "Options": [],
      "Answer": "improper fraction",
      "Points": 2
    },
    {
      "Id": 30,
      "Type": "fill_blank",
      "Text": "The reciprocal of 3/5 is _____.",
      "Options": [],
      "Answer": "5/3",
      "Points": 2
    },
    {
      "Id": 31,
      "Type": "word_problem",
      "Text": "A recipe needs 3/4 cup of sugar. You only have 1/2 cup. How much more sugar do you need? Show your working.",
      "Options": [],
      "Answer": "Step 1: Find a common denominator: 1/2 = 2/4\nStep 2: Subtract: 3/4 \u2212 2/4 = 1/4\nAnswer: 1/4 cup more",
      "Points": 5
    },
    {
      "Id": 32,
      "Type": "word_problem",
      "Text": "Maya jogs 1 1/4 km in the morning and 3/8 km in the evening. How far does she jog in total each day? Show your working.",
      "Options": [],
      "Answer": "Step 1: Convert 1 1/4 to an improper fraction: 1 1/4 = 5/4\nStep 2: Find common denominator for 5/4 and 3/8: LCD = 8; 5/4 = 10/8\nStep 3: Add: 10/8 \u002B 3/8 = 13/8 = 1 5/8\nAnswer: 1 5/8 km",
      "Points": 5
    },
    {
      "Id": 33,
      "Type": "word_problem",
      "Text": "A shelf holds 24 books. If 5/8 of them are fiction, how many fiction books are there? Show your working.",
      "Options": [],
      "Answer": "Step 1: Multiply total by the fraction: 24 \u00D7 5/8\nStep 2: Simplify: (24 \u00F7 8) \u00D7 5 = 3 \u00D7 5 = 15\nAnswer: 15 fiction books",
      "Points": 5
    },
    {
      "Id": 34,
      "Type": "word_problem",
      "Text": "How many minutes are in 2/3 of an hour? Show your working.",
      "Options": [],
      "Answer": "Step 1: 1 hour = 60 minutes\nStep 2: Compute 2/3 of 60: (2/3) \u00D7 60 = 40\nAnswer: 40 minutes",
      "Points": 5
    },
    {
      "Id": 35,
      "Type": "word_problem",
      "Text": "What fraction of a full turn (360\u00B0) is a right angle (90\u00B0)? Show your working.",
      "Options": [],
      "Answer": "Step 1: Form the fraction: 90/360\nStep 2: Simplify by 90: 90/360 = 1/4\nAnswer: 1/4 of a full turn",
      "Points": 5
    },
    {
      "Id": 36,
      "Type": "word_problem",
      "Text": "There are 3 pizzas, each cut into 8 slices. Four friends eat 5 slices each. How many pizzas are left uneaten? Show your working.",
      "Options": [],
      "Answer": "Step 1: Total slices: 3 \u00D7 8 = 24\nStep 2: Slices eaten: 4 \u00D7 5 = 20\nStep 3: Slices remaining: 24 \u2212 20 = 4\nStep 4: Convert to pizzas: 4/8 = 1/2 pizza\nAnswer: 1/2 pizza left",
      "Points": 5
    },
    {
      "Id": 37,
      "Type": "word_problem",
      "Text": "Which is greater, 7/12 or 5/8, and by how much? Show your working.",
      "Options": [],
      "Answer": "Step 1: Find a common denominator: LCD of 12 and 8 is 24\nStep 2: Convert: 7/12 = 14/24; 5/8 = 15/24\nStep 3: Compare and subtract: 15/24 \u2212 14/24 = 1/24\nAnswer: 5/8 is greater by 1/24",
      "Points": 5
    },
    {
      "Id": 38,
      "Type": "word_problem",
      "Text": "A can has 3 1/2 L of paint. You use 1 3/4 L on a wall and 2/5 L for touch-ups. How much paint remains? Show your working.",
      "Options": [],
      "Answer": "Step 1: Convert to improper fractions: 3 1/2 = 7/2; 1 3/4 = 7/4\nStep 2: Express all with LCD 20: 7/2 = 70/20; 7/4 = 35/20; 2/5 = 8/20\nStep 3: Subtract: 70/20 \u2212 35/20 \u2212 8/20 = 27/20\nStep 4: Convert to mixed number: 27/20 = 1 7/20\nAnswer: 1 7/20 L remains",
      "Points": 5
    },
    {
      "Id": 39,
      "Type": "word_problem",
      "Text": "A class period is 50 minutes. The teacher spends 12 minutes reviewing and 3/10 of the period on group work. How many minutes are left for practice? Show your working.",
      "Options": [],
      "Answer": "Step 1: Compute group work time: (3/10) \u00D7 50 = 15 minutes\nStep 2: Total used: 12 \u002B 15 = 27 minutes\nStep 3: Remaining: 50 \u2212 27 = 23 minutes\nAnswer: 23 minutes",
      "Points": 5
    },
    {
      "Id": 40,
      "Type": "word_problem",
      "Text": "In a garden, 2/5 is planted with carrots and 1/4 with beans. The rest is for flowers. What fraction is for flowers? Show your working.",
      "Options": [],
      "Answer": "Step 1: Total fraction planted: 2/5 \u002B 1/4\nStep 2: Find LCD 20: 2/5 = 8/20; 1/4 = 5/20\nStep 3: Sum planted: 8/20 \u002B 5/20 = 13/20\nStep 4: Flowers: 1 \u2212 13/20 = 7/20\nAnswer: 7/20 of the garden",
      "Points": 5
    }
  ],
  "TotalPoints": 100
}