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Make Tables of Equivalent Ratios

How Do You Make Tables of Equivalent Ratios?

{
 "voice_prompt": "",
 "manuscript": {
   "title": {
     "text": "How Do You Make Tables of Equivalent Ratios?",
     "audio": "How do you make tables of equivalent ratios?"
   },
   "description": {
     "text": "To make a table of equivalent ratios, follow these steps: 1. Draw a table with three columns: Multiplier, First Number, and Second Number. 2. In the first row, write 1 and the two numbers from the original ratio. 3. Add more rows by increasing the multiplier and multiplying both numbers by it.",
     "audio": "To make a table of equivalent ratios, follow these steps: 1. Draw a table with three columns: Multiplier, First Number, and Second Number. 2. In the first row, write 1 and the two numbers from the original ratio. 3. Add more rows by increasing the multiplier and multiplying both numbers by it."
   },
   "scenes": [
     {
       "text": "A table of equivalent ratios helps you see how two values grow or shrink together while keeping the same relationship. Let’s learn how to make one using a real-life classroom example — pencils and erasers!"
     },
     {
       "text": "Imagine a teacher gives out 3 pencils for every 2 erasers. That’s our starting ratio: 3 to 2.",
       "latex": "\\text{Pencils: 3, Erasers: 2} \\quad \\text{Ratio: } 3:2"
     },
     {
       "text": "Now let’s build the table with three columns labeled Multiplier, First Number, and Second Number. You can replace First Number and Second Number with Pencils and Erasers to match your example, In the first row, write 1 under Multiplier, 3 under Pencils, and 2 under Erasers — that’s our base ratio."
     },
     {
       "text": "To find equivalent ratios, multiply both numbers in the base ratio by the same number. Multiply by 2: 3 becomes 6 and 2 becomes 4. Multiply by 3: 3 becomes 9 and 2 becomes 6.",
       "latex": "\\text{3:2},\\quad \\text{6:4},\\quad \\text{9:6}"
     },
     {
       "text": "Here’s what the full table looks like:",
       "latex": "\\begin{array}{|c|c|c|}\\hline \\text{Multiplier} & \\text{Pencils} & \\text{Erasers} \\\\ \\hline 1 & 3 & 2 \\\\ 2 & 6 & 4 \\\\ 3 & 9 & 6 \\\\ 4 & 12 & 8 \\\\ 5 & 15 & 10 \\\\ \\hline \\end{array}"
     },
     {
       "text": "Each row shows the same ratio relationship, just scaled up. That’s what makes them equivalent ratios — the balance between pencils and erasers stays the same!"
     },
     {
       "text": "You can also scale down by dividing. For example, if you start with 12 pencils and 8 erasers, divide both numbers by 4. You get 3 to 2 again — the original ratio!",
       "latex": "\\frac{12}{4} = 3,\\quad \\frac{8}{4} = 2 \\quad \\Rightarrow 12:8 = 3:2"
     },
     {
       "text": "Tables of equivalent ratios are super useful when you need to scale things up or down — like packing school supplies, doubling a recipe, or solving math problems!"
     }
   ],
   "outro": {
     "text": "To make a table of equivalent ratios, follow these steps: 1. Draw a table with three columns: Multiplier, First Number, and Second Number. 2. In the first row, write 1 and the two numbers from the original ratio. 3. Add more rows by increasing the multiplier and multiplying both numbers by it.",
     "audio": "To make a table of equivalent ratios, follow these steps: 1. Draw a table with three columns: Multiplier, First Number, and Second Number. 2. In the first row, write 1 and the two numbers from the original ratio. 3. Add more rows by increasing the multiplier and multiplying both numbers by it."
   }
 }
}

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Displaying en_6_nq_equiv_ratio_tables.json.

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