Ganita Prakash | Grade 8 | Figure it Out: PAGE-175 | CHAPTER-7 Proportional Reasoning-1

Master Proportional Reasoning: "Figure It Out" Solutions!

Hey Math Fans! 👋 Ever get stuck on ratio problems? You're not alone! Based on the Grade 8 chapter on Proportional Reasoning, we're breaking down the "Figure It Out" problems from page 17. Let's make ratios simple and fun!

💰 Problem 1: Dividing Money

Divide ₹4,500 into two parts in the ratio 2 : 3.

Let's Break It Down:

1. Find the total parts: The ratio is 2:3, so we add them together.
   2 + 3 = 5 total parts.
2. Find the value of one part: Divide the total amount by the number of parts.
   ₹4,500 ÷ 5 = ₹900 per part.
3. Calculate each share: Multiply the number of parts for each share by the value of one part.
   • First part (2 parts): 2 × ₹900 = ₹1,800
   • Second part (3 parts): 3 × ₹900 = ₹2,700

✅ The two parts are ₹1,800 and ₹2,700.

🧪 Problem 2: Science Lab Solution

In a science lab, acid and water are mixed in the ratio of 1 : 5. In a bottle that has 240 mL of the solution, how much acid and water does the solution contain?

Let's Break It Down:

1. Find the total parts: 1 (acid) + 5 (water) = 6 total parts.
2. Find the volume of one part: 240 mL ÷ 6 = 40 mL per part.
3. Calculate each amount:
   • Acid (1 part): 1 × 40 mL = 40 mL
   • Water (5 parts): 5 × 40 mL = 200 mL

✅ The solution contains 40 mL of acid and 200 mL of water.

🎨 Problem 3: Mixing Paint Colors

Blue and yellow paints are mixed in the ratio of 3 : 5 to produce 40 mL of green paint. How much of each is needed? Then, 20 mL of yellow is added. What is the new ratio?

Part A: The Initial Green Paint

1. Total parts: 3 (blue) + 5 (yellow) = 8 total parts.
2. Volume of one part: 40 mL ÷ 8 = 5 mL per part.
3. Initial amounts:
   • Blue paint (3 parts): 3 × 5 mL = 15 mL
   • Yellow paint (5 parts): 5 × 5 mL = 25 mL

Part B: The New Lighter Shade

1. Blue paint amount: This stays the same at 15 mL.
2. New yellow paint amount: 25 mL (initial) + 20 mL (added) = 45 mL.
3. Find the new ratio: The new ratio is Blue : Yellow = 15 : 45.
4. Simplify the ratio: Divide both numbers by their greatest common factor (which is 15).
   15 ÷ 15 = 1
   45 ÷ 15 = 3

✅ You need 15 mL of blue and 25 mL of yellow initially. The new ratio is 1 : 3.

🍚 Problem 4: The Perfect Idli Mix

To make soft idlis, mix rice and urad dal in a 2 : 1 ratio. If you need 6 cups of this mixture, how many cups of rice and urad dal will you need?

Let's Break It Down:

1. Total parts: 2 (rice) + 1 (urad dal) = 3 total parts.
2. Volume of one part: 6 cups ÷ 3 = 2 cups per part.
3. Calculate each ingredient:
   • Rice (2 parts): 2 × 2 cups = 4 cups
   • Urad dal (1 part): 1 × 2 cups = 2 cups

✅ You will need 4 cups of rice and 2 cups of urad dal.

🖌️ Problem 5: The Orange Paint Mystery

I have one bucket of orange paint made by mixing red and yellow paints in the ratio of 3 : 5. I added another bucket of yellow paint to this mixture. What is the new ratio of red to yellow?

Let's Break It Down:

Important Assumption: We'll assume the "another bucket" of yellow paint has the same total volume as the original "one bucket" of orange paint.

1. Represent the first bucket: The ratio is Red : Yellow = 3 : 5. Let's think of this as 3 units of red and 5 units of yellow.
2. Find the total units in the first bucket: 3 (red) + 5 (yellow) = 8 total units.
3. Represent the second bucket: This bucket is all yellow and has a volume equal to the first bucket, so it contains 8 units of yellow paint.
4. Calculate the new totals:
   • Total Red: 3 units (this didn't change).
   • Total Yellow: 5 units (from bucket 1) + 8 units (from bucket 2) = 13 units.
5. State the new ratio: The new ratio is Red : Yellow.

✅ The new ratio of red paint to yellow paint is 3 : 13.

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And there you have it! By breaking down each problem into simple steps, proportional reasoning becomes much easier to handle. Keep practicing, and you'll be a ratio master in no time! 🚀