Chapter 4.6: Unequal sharing using ratio

🎯 Learning Journey

Identify Ratio for Sharing

START: Read the problem to find the ratio that determines how the quantity should be shared unequally between people or groups.

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Add Ratio Parts to Find Total Parts

ADD: Add all the numbers in the ratio together. This tells you how many equal parts the total quantity is divided into.

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Calculate Value of One Part

CALCULATE: Divide the total amount to be shared by the number of ratio parts. This gives you the value of each individual part.

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Multiply Each Ratio Number by Part Value

MULTIPLY: Multiply each person's ratio number by the part value to find how much each person receives from the total.

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Verify All Shares Add to Original Total

VERIFY: Add up all the individual shares to check they equal the original total amount. This confirms your calculations are correct.

📖 Understanding the Topic

🎯 What You'll Learn

Unequal sharing using ratios means distributing a total amount according to specific proportions rather than giving everyone equal amounts. This type of sharing is based on factors like contribution, investment, effort, or agreed proportions. Understanding unequal sharing helps solve real-world problems involving fair but proportional distribution.

🚀 Why This Matters

Profit Sharing Based on Investment

Business partners share profits proportionally based on how much money or effort each person contributed to the business.

Inheritance Division

Family inheritances are often divided according to specific ratios mentioned in wills or legal documents.

Resource Allocation

Organizations distribute budgets, supplies, or responsibilities based on departmental needs or performance ratios.

💡 Worked Examples

Business partnership: profits shared in ratio of hours worked

Partner A works 30 hours, Partner B works 45 hours. Share £600 profit

Solution: Ratio = 30:45 = 2:3 (simplified)
Total parts = 2+3 = 5
Each part = £600 ÷ 5 = £120
Partner A: 2×£120 = £240
Partner B: 3×£120 = £360
Check: £240+£360 = £600 ✓

Pocket money shared between siblings aged 8, 12, 16

In ratio of their ages. Total £36. How much each?

Solution: Ratio = 8:12:16 = 2:3:4 (÷4)
Total parts = 2+3+4 = 9
Each part = £36 ÷ 9 = £4
Child 1 (8yr): 2×£4 = £8
Child 2 (12yr): 3×£4 = £12
Child 3 (16yr): 4×£4 = £16

Garden plot divided in ratio 3:4:5

For vegetables, flowers, lawn. Total area 240 square meters

Solution: Total parts = 3+4+5 = 12
Each part = 240 ÷ 12 = 20 m²
Vegetables: 3×20 = 60 m²
Flowers: 4×20 = 80 m²
Lawn: 5×20 = 100 m²
Check: 60+80+100 = 240 m² ✓

✏️ Practice Questions

Question 1: Share £60 between two people in ratio 1:4. How much does the first person get?

Question 2: Three children share sweets in ratio 2:3:5. Total 40 sweets. How many does the middle child get?

Question 3: Divide 45 marbles in ratio 2:7. How many marbles does the person with the larger share get?

⚠️ Common Mistakes & How to Avoid Them

Learn from typical errors students make and discover how to avoid them!

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Common Misconceptions

What students often do wrong:

1. Sharing equally when ratio is given: Dividing the total equally instead of using the given ratio proportions

2. Not understanding that ratio determines proportion of total: Thinking ratio numbers are the actual amounts rather than proportions

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How to Avoid These Mistakes

Correct approach: Always use the ratio to determine proportions. Add ratio parts first, then divide total by parts to find unit value.

Memory tip: "Ratio shows proportion, not amount" - the ratio tells you how to split, not what each person gets directly

💡 Teacher's Tip

Use physical objects like coins or counters to model unequal sharing. This helps students visualize why ratios create different amounts for different people.

📋 Chapter Summary

🎉 Congratulations!

You've mastered Unequal sharing using ratio!

🎯 Skills You've Developed:

✓ Sharing quantities unequally according to given ratios

✓ Solving problems involving unequal distribution

✓ Applying unequal sharing in real contexts

✓ Understanding proportional division principles

🚀 What's Next?

Next: Learn about best value and unit pricing to compare costs and find the most economical options