Rational Numbers

{
  "antigravity_content": "### Lesson on Ratios\n\n**Objective**: To understand what ratios are, how to represent them visually, and how to work with them in word problems.\n\n---\n\n### Step 1: Concrete - Draw a Visual Representation\n\n**Activity**: Let\u2019s start by visualizing a ratio of blue squares and yellow squares.\n\n1. **Draw 3 blue squares** and **1 yellow square** on a piece of paper or a whiteboard.\n   \n   - **Ask the child**: \"Can you draw what you\u0027re thinking based on my description?\"\n\n   Here\u0027s how it should look:\n   \n   ```\n   [\ud83d\udfe6][\ud83d\udfe6][\ud83d\udfe6] [\ud83d\udfe8]\n   ```\n\n2. **Explain**: This drawing shows a ratio of **3 blue squares to 1 yellow square**.\n\n---\n\n### Step 2: Pictorial - Create a Number Line\n\n1. **Draw a number line** to show the ratio visually:\n   \n   ```\n   0 ---- 1 ---- 2 ---- 3 ---- 4 ---- 5\n              |     |\n             (B)   (Y)\n   ```\n\n2. **Label the points**: \n   - Point **3** can represent the **3 blue squares**.\n   - Point **1** can represent the **1 yellow square**.\n   \n3. **Explain**: This number line helps us see the relationship between the two quantities.\n\n---\n\n### Step 3: Abstract - Introduce Numbers and Symbols\n\n1. **Write the ratio** using symbols:\n   - **3 : 1** or **3 to 1**\n\n2. **Discuss** the meaning:\n   - \"This means there are 3 of one thing (blue squares) for every 1 of another (yellow squares).\"\n\n---\n\n### Step 4: Scaling Ratios\n\n1. **Draw another set of squares** to show a scaled-up version:\n   - If we have **12 blue squares** and **4 yellow squares**, visualize it:\n\n   ```\n   [\ud83d\udfe6][\ud83d\udfe6][\ud83d\udfe6][\ud83d\udfe6][\ud83d\udfe6][\ud83d\udfe6][\ud83d\udfe6][\ud83d\udfe6][\ud83d\udfe6][\ud83d\udfe6][\ud83d\udfe6][\ud83d\udfe6] [\ud83d\udfe8][\ud83d\udfe8][\ud83d\udfe8][\ud83d\udfe8]\n   ```\n\n2. **Write the new ratio**:\n   - **12 : 4**\n   - **Explain**: \"We multiplied both parts of the original ratio (3 : 1) by 4.\"\n\n---\n\n### Step 5: Part-to-Part vs. Part-to-Whole Ratios \n\n1. **Draw a new scenario** with 5 puppies: **2 boys and 3 girls**.\n   \n   ```\n   [\ud83d\udc36][\ud83d\udc36] [\ud83d\udc36][\ud83d\udc36][\ud83d\udc36]\n   ```\n\n2. **Label the ratios**:\n   - **Part-to-Part**: Boys to Girls = **2 : 3**\n   - **Part-to-Whole**: Boys to All Puppies = **2 : 5**\n\n3. **Write out the relationships**:\n   - For part-to-whole, convert to fractions:\n     - Boys: \\( \\frac{2}{5} \\)\n     - Girls: \\( \\frac{3}{5} \\)\n\n---\n\n### Step 6: Ratios in Real Life\n\n1. **Discuss using a recipe**:\n   - For pancakes, **3 cups of flour and 2 cups of milk** can be shown with a visual bar model.\n\n   ```\n   [\ud83c\udf3e][\ud83c\udf3e][\ud83c\udf3e] [\ud83e\udd5b][\ud83e\udd5b]\n   ```\n\n2. **Introduce the ratio**:\n   - Flour to Milk = **3 : 2**.\n   - If making more, say **12 cups of flour and 8 cups of milk**, visualize it.\n\n---\n\n### Step 7: Practice\n\n1. **Encourage the child** to create their own ratios using different objects or drawings at home.\n2. **Use a number line** or bar models to show their ratios.\n\n### Final Thoughts\n\n**Ask Questions**:\n- \"Can you think of other situations where you might use ratios?\"\n- \"How can you show a ratio of 4:1 using your toys or drawings?\"\n\n**End with a Summary**: Ratios are a way to compare quantities. We can visualize them through drawings, number lines, and in everyday contexts like recipes!",
  "meta": {
    "difficulty_distribution": {
      "1": 10,
      "2": 10,
      "3": 10,
      "4": 10
    },
    "total_questions": 40
  },
  "prompt_id": "visual_first",
  "prompt_name": "\ud83d\udc41\ufe0f Visual-First Thinker (Research: Bruner CPA 1966)",
  "questions": [
    {
      "correct_answer": "A",
      "difficulty": 1,
      "explanation": "The correct representation of 2 red circles to 3 green circles is [\ud83d\udd34][\ud83d\udd34][\ud83d\udfe2][\ud83d\udfe2][\ud83d\udfe2].",
      "id": 1,
      "options": [
        "A) [\ud83d\udd34][\ud83d\udd34][\ud83d\udfe2][\ud83d\udfe2][\ud83d\udfe2]",
        "B) [\ud83d\udd34][\ud83d\udfe2][\ud83d\udfe2][\ud83d\udfe2][\ud83d\udfe2]",
        "C) [\ud83d\udd34][\ud83d\udd34][\ud83d\udfe2][\ud83d\udfe2]",
        "D) [\ud83d\udfe2][\ud83d\udfe2][\ud83d\udd34][\ud83d\udd34][\ud83d\udfe2]"
      ],
      "question": "Draw a visual representation of a ratio of 2 red circles to 3 green circles."
    },
    {
      "correct_answer": "A",
      "difficulty": 1,
      "explanation": "The correct representation of 4 stars to 1 moon is [\u2b50][\u2b50][\u2b50][\u2b50][\ud83c\udf15].",
      "id": 2,
      "options": [
        "A) [\u2b50][\u2b50][\u2b50][\u2b50][\ud83c\udf15]",
        "B) [\ud83c\udf15][\u2b50][\u2b50][\u2b50][\u2b50]",
        "C) [\u2b50][\ud83c\udf15][\u2b50][\u2b50][\u2b50]",
        "D) [\ud83c\udf15][\ud83c\udf15][\u2b50][\u2b50][\u2b50][\u2b50]"
      ],
      "question": "Draw a visual representation of a ratio of 4 stars to 1 moon."
    },
    {
      "correct_answer": "A",
      "difficulty": 1,
      "explanation": "The correct representation of 1 cat to 2 dogs is [\ud83d\udc31][\ud83d\udc36][\ud83d\udc36].",
      "id": 3,
      "options": [
        "A) [\ud83d\udc31][\ud83d\udc36][\ud83d\udc36]",
        "B) [\ud83d\udc36][\ud83d\udc31][\ud83d\udc36]",
        "C) [\ud83d\udc36][\ud83d\udc36][\ud83d\udc31]",
        "D) [\ud83d\udc31][\ud83d\udc31][\ud83d\udc36]"
      ],
      "question": "Draw a visual representation of a ratio of 1 cat to 2 dogs."
    },
    {
      "correct_answer": "A",
      "difficulty": 1,
      "explanation": "The correct representation of 5 apples to 2 oranges is [\ud83c\udf4f][\ud83c\udf4f][\ud83c\udf4f][\ud83c\udf4f][\ud83c\udf4f][\ud83c\udf4a][\ud83c\udf4a].",
      "id": 4,
      "options": [
        "A) [\ud83c\udf4f][\ud83c\udf4f][\ud83c\udf4f][\ud83c\udf4f][\ud83c\udf4f][\ud83c\udf4a][\ud83c\udf4a]",
        "B) [\ud83c\udf4a][\ud83c\udf4a][\ud83c\udf4f][\ud83c\udf4f][\ud83c\udf4f][\ud83c\udf4f][\ud83c\udf4f]",
        "C) [\ud83c\udf4f][\ud83c\udf4a][\ud83c\udf4f][\ud83c\udf4f][\ud83c\udf4f][\ud83c\udf4f][\ud83c\udf4f]",
        "D) [\ud83c\udf4f][\ud83c\udf4f][\ud83c\udf4f][\ud83c\udf4a][\ud83c\udf4a][\ud83c\udf4f][\ud83c\udf4f]"
      ],
      "question": "Draw a visual representation of a ratio of 5 apples to 2 oranges."
    },
    {
      "correct_answer": "A",
      "difficulty": 1,
      "explanation": "The correct representation of 6 triangles to 3 squares is [\ud83d\udd3a][\ud83d\udd3a][\ud83d\udd3a][\ud83d\udd3a][\ud83d\udd3a][\ud83d\udd3a][\u2b1c][\u2b1c][\u2b1c].",
      "id": 5,
      "options": [
        "A) [\ud83d\udd3a][\ud83d\udd3a][\ud83d\udd3a][\ud83d\udd3a][\ud83d\udd3a][\ud83d\udd3a][\u2b1c][\u2b1c][\u2b1c]",
        "B) [\u2b1c][\ud83d\udd3a][\ud83d\udd3a][\ud83d\udd3a][\ud83d\udd3a][\ud83d\udd3a][\ud83d\udd3a][\u2b1c][\u2b1c]",
        "C) [\ud83d\udd3a][\u2b1c][\ud83d\udd3a][\ud83d\udd3a][\ud83d\udd3a][\ud83d\udd3a][\ud83d\udd3a][\u2b1c]",
        "D) [\u2b1c][\u2b1c][\ud83d\udd3a][\ud83d\udd3a][\ud83d\udd3a][\ud83d\udd3a][\ud83d\udd3a][\ud83d\udd3a]"
      ],
      "question": "Draw a visual representation of a ratio of 6 triangles to 3 squares."
    },
    {
      "correct_answer": "A",
      "difficulty": 1,
      "explanation": "The correct representation of 2 books to 5 notebooks is [\ud83d\udcda][\ud83d\udcda][\ud83d\udcd3][\ud83d\udcd3][\ud83d\udcd3][\ud83d\udcd3][\ud83d\udcd3].",
      "id": 6,
      "options": [
        "A) [\ud83d\udcda][\ud83d\udcda][\ud83d\udcd3][\ud83d\udcd3][\ud83d\udcd3][\ud83d\udcd3][\ud83d\udcd3]",
        "B) [\ud83d\udcd3][\ud83d\udcd3][\ud83d\udcda][\ud83d\udcda][\ud83d\udcd3][\ud83d\udcd3]",
        "C) [\ud83d\udcda][\ud83d\udcd3][\ud83d\udcd3][\ud83d\udcd3][\ud83d\udcd3][\ud83d\udcd3]",
        "D) [\ud83d\udcd3][\ud83d\udcda][\ud83d\udcd3][\ud83d\udcd3][\ud83d\udcd3][\ud83d\udcd3]"
      ],
      "question": "Draw a visual representation of a ratio of 2 books to 5 notebooks."
    },
    {
      "correct_answer": "A",
      "difficulty": 1,
      "explanation": "The correct representation of 1 chair to 4 tables is [\ud83e\ude91][\ud83e\ude91][\ud83e\ude91][\ud83e\ude91][\ud83e\ude91].",
      "id": 7,
      "options": [
        "A) [\ud83e\ude91][\ud83e\ude91][\ud83e\ude91][\ud83e\ude91][\ud83e\ude91]",
        "B) [\ud83e\ude91][\ud83e\ude91][\ud83e\ude91][\ud83e\ude91][\ud83e\ude91][\ud83e\ude91][\ud83e\ude91][\ud83e\ude91]",
        "C) [\ud83e\ude91][\ud83e\ude91][\ud83e\ude91][\ud83e\ude91][\ud83e\ude91][\ud83e\ude91][\ud83e\ude91][\ud83e\ude91][\ud83e\ude91]",
        "D) [\ud83e\ude91][\ud83e\ude91][\ud83e\ude91][\ud83e\ude91][\ud83e\ude91][\ud83e\ude91][\ud83e\ude91][\ud83e\ude91][\ud83e\ude91]"
      ],
      "question": "Draw a visual representation of a ratio of 1 chair to 4 tables."
    },
    {
      "correct_answer": "A",
      "difficulty": 1,
      "explanation": "The correct representation of 3 flowers to 2 leaves is [\ud83c\udf38][\ud83c\udf38][\ud83c\udf38][\ud83c\udf43][\ud83c\udf43].",
      "id": 8,
      "options": [
        "A) [\ud83c\udf38][\ud83c\udf38][\ud83c\udf38][\ud83c\udf43][\ud83c\udf43]",
        "B) [\ud83c\udf43][\ud83c\udf43][\ud83c\udf38][\ud83c\udf38][\ud83c\udf38]",
        "C) [\ud83c\udf38][\ud83c\udf43][\ud83c\udf38][\ud83c\udf38][\ud83c\udf43]",
        "D) [\ud83c\udf43][\ud83c\udf38][\ud83c\udf38][\ud83c\udf38][\ud83c\udf43]"
      ],
      "question": "Draw a visual representation of a ratio of 3 flowers to 2 leaves."
    },
    {
      "correct_answer": "A",
      "difficulty": 1,
      "explanation": "The correct representation of 2 cars to 3 bikes is [\ud83d\ude97][\ud83d\ude97][\ud83d\udeb2][\ud83d\udeb2][\ud83d\udeb2].",
      "id": 9,
      "options": [
        "A) [\ud83d\ude97][\ud83d\ude97][\ud83d\udeb2][\ud83d\udeb2][\ud83d\udeb2]",
        "B) [\ud83d\udeb2][\ud83d\udeb2][\ud83d\ude97][\ud83d\ude97][\ud83d\udeb2]",
        "C) [\ud83d\ude97][\ud83d\udeb2][\ud83d\ude97][\ud83d\udeb2][\ud83d\udeb2]",
        "D) [\ud83d\udeb2][\ud83d\ude97][\ud83d\udeb2][\ud83d\udeb2][\ud83d\ude97]"
      ],
      "question": "Draw a visual representation of a ratio of 2 cars to 3 bikes."
    },
    {
      "correct_answer": "A",
      "difficulty": 1,
      "explanation": "The correct representation of 4 birds to 1 fish is [\ud83d\udc26][\ud83d\udc26][\ud83d\udc26][\ud83d\udc26][\ud83d\udc20].",
      "id": 10,
      "options": [
        "A) [\ud83d\udc26][\ud83d\udc26][\ud83d\udc26][\ud83d\udc26][\ud83d\udc20]",
        "B) [\ud83d\udc20][\ud83d\udc26][\ud83d\udc26][\ud83d\udc26][\ud83d\udc26]",
        "C) [\ud83d\udc26][\ud83d\udc26][\ud83d\udc26][\ud83d\udc20][\ud83d\udc26]",
        "D) [\ud83d\udc26][\ud83d\udc26][\ud83d\udc20][\ud83d\udc26][\ud83d\udc26]"
      ],
      "question": "Draw a visual representation of a ratio of 4 birds to 1 fish."
    },
    {
      "correct_answer": "A",
      "difficulty": 2,
      "explanation": "The representation is [\ud83d\udd34][\ud83d\udd34][\ud83d\udd35][\ud83d\udd35][\ud83d\udd35], and the ratio is 2:3.",
      "id": 11,
      "options": [
        "A) 2:3",
        "B) 3:2",
        "C) 5:2",
        "D) 2:5"
      ],
      "question": "Draw a visual representation of a ratio of 2 red balls to 3 blue balls, then write the ratio in numbers."
    },
    {
      "correct_answer": "B",
      "difficulty": 2,
      "explanation": "The representation is [\u270f\ufe0f][\u270f\ufe0f][\u270f\ufe0f][\ud83e\uddfd][\ud83e\uddfd], and the ratio is 3:2.",
      "id": 12,
      "options": [
        "A) 2:3",
        "B) 3:2",
        "C) 5:2",
        "D) 2:5"
      ],
      "question": "Draw a visual representation of a ratio of 3 pencils to 2 erasers, then write the ratio in numbers."
    },
    {
      "correct_answer": "A",
      "difficulty": 2,
      "explanation": "The representation is [\ud83c\udf6a][\ud83c\udf6a][\ud83c\udf6a][\ud83c\udf6a][\ud83c\udf6a][\ud83e\uddc1][\ud83e\uddc1][\ud83e\uddc1], and the ratio is 5:3.",
      "id": 13,
      "options": [
        "A) 5:3",
        "B) 3:5",
        "C) 8:3",
        "D) 3:8"
      ],
      "question": "Draw a visual representation of a ratio of 5 cookies to 3 cupcakes, then write the ratio in numbers."
    },
    {
      "correct_answer": "C",
      "difficulty": 2,
      "explanation": "The representation is [\ud83c\udf4a][\ud83c\udf4a][\ud83c\udf4a][\ud83c\udf4a][\ud83c\udf4a][\ud83c\udf4a][\ud83c\udf4c][\ud83c\udf4c], and the ratio is 6:2.",
      "id": 14,
      "options": [
        "A) 2:6",
        "B) 3:1",
        "C) 6:2",
        "D) 1:3"
      ],
      "question": "Draw a visual representation of a ratio of 6 oranges to 2 bananas, then write the ratio in numbers."
    },
    {
      "correct_answer": "A",
      "difficulty": 2,
      "explanation": "The representation is [\ud83d\ude97][\ud83d\ude97][\ud83d\ude97][\ud83d\ude97][\ud83d\udeb2][\ud83d\udeb2][\ud83d\udeb2][\ud83d\udeb2][\ud83d\udeb2][\ud83d\udeb2], and the ratio is 2:3.",
      "id": 15,
      "options": [
        "A) 2:3",
        "B) 3:2",
        "C) 4:6",
        "D) 6:4"
      ],
      "question": "Draw a visual representation of a ratio of 4 cars to 6 bicycles, then write the ratio in numbers."
    },
    {
      "correct_answer": "B",
      "difficulty": 2,
      "explanation": "The representation is [\ud83d\udcda][\ud83d\udcda][\ud83d\udcda][\ud83d\udcd3], and the ratio is 3:1.",
      "id": 16,
      "options": [
        "A) 1:3",
        "B) 3:1",
        "C) 1:4",
        "D) 3:4"
      ],
      "question": "Draw a visual representation of a ratio of 3 books to 1 notebook, then write the ratio in numbers."
    },
    {
      "correct_answer": "B",
      "difficulty": 2,
      "explanation": "The representation is [\ud83d\udc36][\ud83d\udc36][\ud83d\udc31][\ud83d\udc31][\ud83d\udc31][\ud83d\udc31][\ud83d\udc31], and the ratio is 2:5.",
      "id": 17,
      "options": [
        "A) 5:2",
        "B) 2:5",
        "C) 3:7",
        "D) 7:3"
      ],
      "question": "Draw a visual representation of a ratio of 2 dogs to 5 cats, then write the ratio in numbers."
    },
    {
      "correct_answer": "A",
      "difficulty": 2,
      "explanation": "The representation is [\ud83c\udf3a][\ud83c\udf3a][\ud83c\udf3a][\ud83c\udf3a][\ud83c\udf43][\ud83c\udf43][\ud83c\udf43], and the ratio is 4:3.",
      "id": 18,
      "options": [
        "A) 4:3",
        "B) 3:4",
        "C) 5:3",
        "D) 3:5"
      ],
      "question": "Draw a visual representation of a ratio of 4 flowers to 3 leaves, then write the ratio in numbers."
    },
    {
      "correct_answer": "A",
      "difficulty": 2,
      "explanation": "The representation is [\ud83d\udc18][\ud83e\udd81][\ud83e\udd81], and the ratio is 1:2.",
      "id": 19,
      "options": [
        "A) 1:2",
        "B) 2:1",
        "C) 3:1",
        "D) 1:3"
      ],
      "question": "Draw a visual representation of a ratio of 1 elephant to 2 lions, then write the ratio in numbers."
    },
    {
      "correct_answer": "B",
      "difficulty": 2,
      "explanation": "The representation is [\u26aa][\u26aa][\u26aa][\u26aa][\u26aa][\u26aa][\u26aa][\u26bd][\u26bd][\u26bd], and the ratio is 7:3.",
      "id": 20,
      "options": [
        "A) 3:7",
        "B) 7:3",
        "C) 4:3",
        "D) 3:4"
      ],
      "question": "Draw a visual representation of a ratio of 7 marbles to 3 balls, then write the ratio in numbers."
    },
    {
      "correct_answer": "A",
      "difficulty": 3,
      "explanation": "The ratio is 12:8 which simplifies to 3:2. The number line shows the relationship.",
      "id": 21,
      "options": [
        "A) 3:2",
        "B) 2:3",
        "C) 4:3",
        "D) 1:1"
      ],
      "question": "You have 12 apples and 8 oranges. What is the ratio of apples to oranges? Draw a number line to verify your answer."
    },
    {
      "correct_answer": "A",
      "difficulty": 3,
      "explanation": "The ratio is 10:15 which simplifies to 2:3. The number line shows the relationship.",
      "id": 22,
      "options": [
        "A) 2:3",
        "B) 3:2",
        "C) 5:2",
        "D) 1:1"
      ],
      "question": "You have 10 red balls and 15 blue balls. What is the ratio of red balls to blue balls? Draw a number line to verify your answer."
    },
    {
      "correct_answer": "A",
      "difficulty": 3,
      "explanation": "The ratio is 6:9 which simplifies to 2:3. The number line shows the relationship.",
      "id": 23,
      "options": [
        "A) 3:2",
        "B) 2:3",
        "C) 1:1",
        "D) 4:3"
      ],
      "question": "You have 6 pencils and 9 erasers. What is the ratio of pencils to erasers? Draw a number line to verify your answer."
    },
    {
      "correct_answer": "B",
      "difficulty": 3,
      "explanation": "The ratio is 8:4 which simplifies to 2:1. The number line shows the relationship.",
      "id": 24,
      "options": [
        "A) 4:3",
        "B) 2:1",
        "C) 1:2",
        "D) 3:2"
      ],
      "question": "You have 8 chocolates and 4 candies. What is the ratio of chocolates to candies? Draw a number line to verify your answer."
    },
    {
      "correct_answer": "A",
      "difficulty": 3,
      "explanation": "The ratio is 15:10 which simplifies to 3:2. The number line shows the relationship.",
      "id": 25,
      "options": [
        "A) 3:2",
        "B) 2:3",
        "C) 5:3",
        "D) 1:1"
      ],
      "question": "You have 15 footballs and 10 basketballs. What is the ratio of footballs to basketballs? Draw a number line to verify your answer."
    },
    {
      "correct_answer": "A",
      "difficulty": 3,
      "explanation": "The ratio is 20:10 which simplifies to 2:1. The number line shows the relationship.",
      "id": 26,
      "options": [
        "A) 2:1",
        "B) 1:2",
        "C) 1:1",
        "D) 3:2"
      ],
      "question": "You have 20 oranges and 10 apples. What is the ratio of oranges to apples? Draw a number line to verify your answer."
    },
    {
      "correct_answer": "A",
      "difficulty": 3,
      "explanation": "The ratio is 7:14 which simplifies to 1:2. The number line shows the relationship.",
      "id": 27,
      "options": [
        "A) 1:2",
        "B) 2:1",
        "C) 3:4",
        "D) 4:3"
      ],
      "question": "You have 7 bikes and 14 scooters. What is the ratio of bikes to scooters? Draw a number line to verify your answer."
    },
    {
      "correct_answer": "A",
      "difficulty": 3,
      "explanation": "The ratio is 4:8 which simplifies to 1:2. The number line shows the relationship.",
      "id": 28,
      "options": [
        "A) 1:2",
        "B) 2:1",
        "C) 3:4",
        "D) 4:3"
      ],
      "question": "You have 4 books and 8 notebooks. What is the ratio of books to notebooks? Draw a number line to verify your answer."
    },
    {
      "correct_answer": "A",
      "difficulty": 3,
      "explanation": "The ratio is 10:5 which simplifies to 2:1. The number line shows the relationship.",
      "id": 29,
      "options": [
        "A) 2:1",
        "B) 1:2",
        "C) 1:1",
        "D) 3:2"
      ],
      "question": "You have 10 cats and 5 dogs. What is the ratio of cats to dogs? Draw a number line to verify your answer."
    },
    {
      "correct_answer": "A",
      "difficulty": 3,
      "explanation": "The ratio is 16:4 which simplifies to 4:1. The number line shows the relationship.",
      "id": 30,
      "options": [
        "A) 4:1",
        "B) 2:1",
        "C) 1:4",
        "D) 3:2"
      ],
      "question": "You have 16 chairs and 4 tables. What is the ratio of chairs to tables? Draw a number line to verify your answer."
    },
    {
      "correct_answer": "A",
      "difficulty": 4,
      "explanation": "The simplified ratio is 3:2. The number line shows the relationship of runs.",
      "id": 31,
      "options": [
        "A) 3:2",
        "B) 2:3",
        "C) 4:3",
        "D) 1:1"
      ],
      "question": "In a cricket match, the ratio of runs scored by Team A to Team B is 180:120. What is the simplified ratio? Draw a number line to verify your answer."
    },
    {
      "correct_answer": "A",
      "difficulty": 4,
      "explanation": "The simplified ratio is 4:3. The number line shows the relationship of prices.",
      "id": 32,
      "options": [
        "A) 4:3",
        "B) 3:4",
        "C) 2:1",
        "D) 1:2"
      ],
      "question": "In a market, the ratio of the price of apples to oranges is 40:30. What is the simplified ratio? Draw a number line to verify your answer."
    },
    {
      "correct_answer": "A",
      "difficulty": 4,
      "explanation": "The simplified ratio is 3:2. The number line shows the relationship of distances.",
      "id": 33,
      "options": [
        "A) 3:2",
        "B) 2:3",
        "C) 1:1",
        "D) 5:3"
      ],
      "question": "The ratio of distances travelled by two cars is 150 km to 100 km. What is the simplified ratio? Draw a number line to verify your answer."
    },
    {
      "correct_answer": "A",
      "difficulty": 4,
      "explanation": "The simplified ratio is 3:2. The number line shows the relationship of boys and girls.",
      "id": 34,
      "options": [
        "A) 3:2",
        "B) 2:3",
        "C) 4:3",
        "D) 1:1"
      ],
      "question": "In a class, the ratio of boys to girls is 12:8. What is the simplified ratio? Draw a number line to verify your answer."
    },
    {
      "correct_answer": "A",
      "difficulty": 4,
      "explanation": "The simplified ratio is 2:1. The number line shows the relationship of flower colors.",
      "id": 35,
      "options": [
        "A) 2:1",
        "B) 1:2",
        "C) 3:4",
        "D) 1:1"
      ],
      "question": "In a garden, the ratio of red flowers to yellow flowers is 10:5. What is the simplified ratio? Draw a number line to verify your answer."
    },
    {
      "correct_answer": "A",
      "difficulty": 4,
      "explanation": "The simplified ratio is 3:2. The number line shows the relationship of scores.",
      "id": 36,
      "options": [
        "A) 3:2",
        "B) 2:3",
        "C) 1:1",
        "D) 5:3"
      ],
      "question": "The ratio of scores of two students in a test is 90:60. What is the simplified ratio? Draw a number line to verify your answer."
    },
    {
      "correct_answer": "A",
      "difficulty": 4,
      "explanation": "The simplified ratio is 3:2. The number line shows the relationship of fruits.",
      "id": 37,
      "options": [
        "A) 3:2",
        "B) 2:3",
        "C) 1:1",
        "D) 5:3"
      ],
      "question": "In a fruit basket, the ratio of bananas to apples is 18:12. What is the simplified ratio? Draw a number line to verify your answer."
    },
    {
      "correct_answer": "A",
      "difficulty": 4,
      "explanation": "The simplified ratio is 7:3. The number line shows the relationship of party attendees.",
      "id": 38,
      "options": [
        "A) 7:3",
        "B) 3:7",
        "C) 2:3",
        "D) 1:1"
      ],
      "question": "In a party, the ratio of children to adults is 14:6. What is the simplified ratio? Draw a number line to verify your answer."
    },
    {
      "correct_answer": "A",
      "difficulty": 4,
      "explanation": "The ratio is already simplified as 1:20. The number line shows the relationship of teachers to students.",
      "id": 39,
      "options": [
        "A) 1:20",
        "B) 20:1",
        "C) 1:1",
        "D) 2:3"
      ],
      "question": "In a school, the ratio of teachers to students is 1:20. What is the simplified ratio? Draw a number line to verify your answer."
    },
    {
      "correct_answer": "A",
      "difficulty": 4,
      "explanation": "The ratio is already simplified as 5:2. The number line shows the relationship of vehicles.",
      "id": 40,
      "options": [
        "A) 5:2",
        "B) 2:5",
        "C) 3:2",
        "D) 1:1"
      ],
      "question": "In a city, the ratio of bicycles to cars is 5:2. What is the simplified ratio? Draw a number line to verify your answer."
    }
  ],
  "source_ixl_skills": [
    "Identify rational numbers",
    "Compare rational numbers",
    "Put rational numbers in order",
    "Add and subtract rational numbers",
    "Multiply and divide rational numbers"
  ],
  "topic": "Rational Numbers"
}