{
  "Id": "d5ba92d8-3845-449d-806a-b9399704e5d3",
  "Title": "Fractions: Concepts and Operations (Grade 6)",
  "Subject": "Mathematics",
  "Topic": "Fractions \u2014 parts of a whole, equivalence, simplification, comparison, and addition/subtraction",
  "Instructions": "Read each question carefully and answer to the best of your ability. Show all working for word problems.",
  "EstimatedMinutes": 60,
  "StudentProfileId": "",
  "SourceFileName": " fractions.pdf",
  "SessionMaterialId": "8499eeea-dc89-4b86-86d3-ec710e4ce069",
  "GeneratedAt": "2026-07-25T12:05:40.35558Z",
  "Questions": [
    {
      "Id": 1,
      "Type": "true_false",
      "Text": "When a whole is divided into equal parts, each part is a fraction of the whole.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 2,
      "Type": "true_false",
      "Text": "7/3 is greater than 2.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 3,
      "Type": "true_false",
      "Text": "0/9 is equal to 0.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 4,
      "Type": "true_false",
      "Text": "Multiplying 2/5 by 2/2 creates an equivalent fraction.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 5,
      "Type": "true_false",
      "Text": "3/4 and 6/8 represent the same quantity.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 6,
      "Type": "true_false",
      "Text": "To add 1/3 and 1/4, using 7 as a common denominator is correct.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 7,
      "Type": "true_false",
      "Text": "Twenty minutes is one-third of an hour.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 8,
      "Type": "true_false",
      "Text": "A fraction in simplest form has no common factor greater than 1 between its numerator and denominator.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 9,
      "Type": "true_false",
      "Text": "On the number line, 1/4 is to the right of 1/3.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "False",
      "Points": 1
    },
    {
      "Id": 10,
      "Type": "true_false",
      "Text": "Subtracting 5/6 from 1/2 gives a negative result.",
      "Options": [
        "True",
        "False"
      ],
      "Answer": "True",
      "Points": 1
    },
    {
      "Id": 11,
      "Type": "multiple_choice",
      "Text": "Which fraction is equivalent to 3/5?",
      "Options": [
        "A. 9/15",
        "B. 12/25",
        "C. 6/11",
        "D. 15/18"
      ],
      "Answer": "A. 9/15",
      "Points": 2
    },
    {
      "Id": 12,
      "Type": "multiple_choice",
      "Text": "18/24 in lowest terms is:",
      "Options": [
        "A. 3/4",
        "B. 2/3",
        "C. 6/8",
        "D. 9/12"
      ],
      "Answer": "A. 3/4",
      "Points": 2
    },
    {
      "Id": 13,
      "Type": "multiple_choice",
      "Text": "Which of the following is a mixed number?",
      "Options": [
        "A. 11/4",
        "B. 4 2/9",
        "C. 7/7",
        "D. 9/2"
      ],
      "Answer": "B. 4 2/9",
      "Points": 2
    },
    {
      "Id": 14,
      "Type": "multiple_choice",
      "Text": "Which is greater?",
      "Options": [
        "A. 5/12",
        "B. 4/9",
        "C. They are equal",
        "D. Cannot be compared"
      ],
      "Answer": "B. 4/9",
      "Points": 2
    },
    {
      "Id": 15,
      "Type": "multiple_choice",
      "Text": "2 3/5 expressed as an improper fraction is:",
      "Options": [
        "A. 13/5",
        "B. 12/5",
        "C. 7/5",
        "D. 23/5"
      ],
      "Answer": "A. 13/5",
      "Points": 2
    },
    {
      "Id": 16,
      "Type": "multiple_choice",
      "Text": "3/8 \u002B 1/4 equals:",
      "Options": [
        "A. 1/2",
        "B. 5/8",
        "C. 3/12",
        "D. 7/8"
      ],
      "Answer": "B. 5/8",
      "Points": 2
    },
    {
      "Id": 17,
      "Type": "multiple_choice",
      "Text": "9/10 \u2212 7/10 equals:",
      "Options": [
        "A. 1/5",
        "B. 2/10",
        "C. 1/10",
        "D. 2/5"
      ],
      "Answer": "A. 1/5",
      "Points": 2
    },
    {
      "Id": 18,
      "Type": "multiple_choice",
      "Text": "Arrange in ascending order: 1/2, 3/10, 2/5",
      "Options": [
        "A. 1/2, 2/5, 3/10",
        "B. 3/10, 2/5, 1/2",
        "C. 2/5, 3/10, 1/2",
        "D. 2/5, 1/2, 3/10"
      ],
      "Answer": "B. 3/10, 2/5, 1/2",
      "Points": 2
    },
    {
      "Id": 19,
      "Type": "multiple_choice",
      "Text": "Find the missing numerator: __/12 = 5/6",
      "Options": [
        "A. 9",
        "B. 10",
        "C. 12",
        "D. 15"
      ],
      "Answer": "B. 10",
      "Points": 2
    },
    {
      "Id": 20,
      "Type": "multiple_choice",
      "Text": "Which fraction is not in lowest terms?",
      "Options": [
        "A. 9/14",
        "B. 4/7",
        "C. 8/12",
        "D. 7/9"
      ],
      "Answer": "C. 8/12",
      "Points": 2
    },
    {
      "Id": 21,
      "Type": "fill_blank",
      "Text": "The fraction \u0022one-half\u0022 is written as _____.",
      "Options": [],
      "Answer": "1/2",
      "Points": 2
    },
    {
      "Id": 22,
      "Type": "fill_blank",
      "Text": "A fraction greater than 1 is called an _____ fraction.",
      "Options": [],
      "Answer": "improper",
      "Points": 2
    },
    {
      "Id": 23,
      "Type": "fill_blank",
      "Text": "Fifteen minutes is _____ of an hour.",
      "Options": [],
      "Answer": "1/4",
      "Points": 2
    },
    {
      "Id": 24,
      "Type": "fill_blank",
      "Text": "To reduce 21/28 to lowest terms, divide by their _____ common factor.",
      "Options": [],
      "Answer": "greatest",
      "Points": 2
    },
    {
      "Id": 25,
      "Type": "fill_blank",
      "Text": "On a number line, the midpoint between 0 and 1 is _____.",
      "Options": [],
      "Answer": "1/2",
      "Points": 2
    },
    {
      "Id": 26,
      "Type": "fill_blank",
      "Text": "The least common multiple of 6 and 8 is _____.",
      "Options": [],
      "Answer": "24",
      "Points": 2
    },
    {
      "Id": 27,
      "Type": "fill_blank",
      "Text": "3 1/4 written as an improper fraction is _____.",
      "Options": [],
      "Answer": "13/4",
      "Points": 2
    },
    {
      "Id": 28,
      "Type": "fill_blank",
      "Text": "Multiplying the numerator and denominator of 4/9 by _____ makes a fraction with denominator 27.",
      "Options": [],
      "Answer": "3",
      "Points": 2
    },
    {
      "Id": 29,
      "Type": "fill_blank",
      "Text": "Between 5/8 and 2/3, the greater fraction is _____.",
      "Options": [],
      "Answer": "2/3",
      "Points": 2
    },
    {
      "Id": 30,
      "Type": "fill_blank",
      "Text": "A juice mix uses 2/5 L of water and 3/10 L of syrup; the total is _____ L.",
      "Options": [],
      "Answer": "7/10",
      "Points": 2
    },
    {
      "Id": 31,
      "Type": "word_problem",
      "Text": "A runner jogs 3/5 km in the morning and 1/5 km in the evening. How far does the runner travel in total? Show your working.",
      "Options": [],
      "Answer": "Step 1: Add like denominators: 3/5 \u002B 1/5 = (3 \u002B 1)/5\nStep 2: Simplify the sum: 4/5\nAnswer: 4/5 km",
      "Points": 5
    },
    {
      "Id": 32,
      "Type": "word_problem",
      "Text": "A pizza is cut into 12 equal slices. Maya eats 5 slices and Omar eats 2 slices. What fraction of the pizza remains? Show your working.",
      "Options": [],
      "Answer": "Step 1: Total eaten = (5 \u002B 2)/12 = 7/12\nStep 2: Remaining fraction = 1 \u2212 7/12 = 5/12\nAnswer: 5/12 of the pizza remains",
      "Points": 5
    },
    {
      "Id": 33,
      "Type": "word_problem",
      "Text": "What fraction of an hour is 18 minutes? Express your answer in simplest form. Show your working.",
      "Options": [],
      "Answer": "Step 1: Write the fraction of the hour: 18/60\nStep 2: Simplify by dividing by 6: 18/60 = 3/10\nAnswer: 3/10 of an hour",
      "Points": 5
    },
    {
      "Id": 34,
      "Type": "word_problem",
      "Text": "Ali ran 7/12 km and Bea ran 5/8 km. Who ran farther and by how much (in km)? Show your working.",
      "Options": [],
      "Answer": "Step 1: Find a common denominator (24): 7/12 = 14/24, 5/8 = 15/24\nStep 2: Compare and find difference: 15/24 \u2212 14/24 = 1/24\nAnswer: Bea ran farther by 1/24 km",
      "Points": 5
    },
    {
      "Id": 35,
      "Type": "word_problem",
      "Text": "A wooden board is 1 2/3 m long. If 3/4 m is cut off, how much length remains? Show your working.",
      "Options": [],
      "Answer": "Step 1: Convert 1 2/3 to improper: 1 2/3 = 5/3\nStep 2: Subtract with common denominator 12: 5/3 = 20/12, 3/4 = 9/12, so 20/12 \u2212 9/12 = 11/12\nAnswer: 11/12 m remains",
      "Points": 5
    },
    {
      "Id": 36,
      "Type": "word_problem",
      "Text": "A ribbon 2/3 m long is cut into 3 equal pieces. What is the length of each piece? Show your working.",
      "Options": [],
      "Answer": "Step 1: Divide 2/3 by 3: 2/3 \u00F7 3 = 2/3 \u00D7 1/3\nStep 2: Multiply numerators and denominators: 2/9\nAnswer: Each piece is 2/9 m",
      "Points": 5
    },
    {
      "Id": 37,
      "Type": "word_problem",
      "Text": "What fraction of a right angle (90\u00B0) is 30\u00B0? Write your answer in simplest form. Show your working.",
      "Options": [],
      "Answer": "Step 1: Form the fraction: 30/90\nStep 2: Simplify by dividing by 30: 1/3\nAnswer: 1/3 of a right angle",
      "Points": 5
    },
    {
      "Id": 38,
      "Type": "word_problem",
      "Text": "A 5/6-liter bottle of juice is shared equally among 3 friends. How much juice does each friend get? Show your working.",
      "Options": [],
      "Answer": "Step 1: Divide 5/6 by 3: 5/6 \u00F7 3 = 5/6 \u00D7 1/3\nStep 2: Compute: 5/18\nAnswer: Each friend gets 5/18 L",
      "Points": 5
    },
    {
      "Id": 39,
      "Type": "word_problem",
      "Text": "Starting at 0 on a straight path, Riya walks 3/10 km east and then 1/5 km west. Where is she relative to the start? Show your working.",
      "Options": [],
      "Answer": "Step 1: Convert 1/5 to tenths: 1/5 = 2/10\nStep 2: Net displacement: 3/10 \u2212 2/10 = 1/10\nAnswer: 1/10 km east of the start",
      "Points": 5
    },
    {
      "Id": 40,
      "Type": "word_problem",
      "Text": "A chef wants a total of 5/6 L of marinade. If 2/9 L is lemon juice and the rest is water, how much water must be added? Show your working.",
      "Options": [],
      "Answer": "Step 1: Rewrite 5/6 with denominator 18: 5/6 = 15/18; 2/9 = 4/18\nStep 2: Find missing part: 15/18 \u2212 4/18 = 11/18\nAnswer: 11/18 L of water",
      "Points": 5
    }
  ],
  "TotalPoints": 100
}