Solving simple ratio problems

Use ratios to solve sharing problems. Calculate unknown quantities in ratio problems. Apply ratio problem-solving strategies.

⏱️ 55 minutes
📊 Hard Level
🎯 Sharing problems, unknown quantities, strategies

🎯 Learning Journey

Identify Ratio and Total or Constraint
START: Read the problem carefully to find the given ratio and either the total amount to be shared or a constraint that helps solve the problem.
⬇️
Find Total Ratio Parts
ADD: Add all the numbers in the ratio together to find how many parts the total is divided into. For ratio 2:3, total parts = 2+3 = 5.
⬇️
Calculate Value of One Part
DIVIDE: Divide the total amount by the number of ratio parts to find the value of one part. This is your key to solving the problem.
⬇️
Multiply Each Ratio Part by Value
MULTIPLY: Multiply each number in the ratio by the value of one part to find how much each person or group gets.
⬇️
Check Answers Add Up Correctly
VERIFY: Add all your answers together to check they equal the original total. This confirms your solution is correct.

📖 Understanding the Topic

🎯 What You'll Learn

Ratio problems involve sharing quantities unequally according to a given ratio, or finding unknown amounts when part of a ratio relationship is known. These problems require systematic thinking and step-by-step problem-solving strategies to ensure accurate solutions.

🚀 Why This Matters

Sharing Prize Money

When prize money needs to be shared based on performance or contribution, ratios ensure fair distribution.

Distributing Resources Fairly

Organizations use ratios to distribute resources like funding, supplies, or responsibilities proportionally.

Business Partnerships

Business profits and losses are often shared according to investment ratios or agreed proportions.

💡 Worked Examples

Prize money £150 shared in ratio 2:3:5

How much does each person get?

Solution: Total parts = 2+3+5 = 10
Each part = £150 ÷ 10 = £15
Person 1: 2×£15 = £30
Person 2: 3×£15 = £45
Person 3: 5×£15 = £75
Check: £30+£45+£75 = £150 ✓

Two numbers in ratio 3:7, sum is 50

Find the numbers

Solution: Total parts = 3+7 = 10
Each part = 50 ÷ 10 = 5
First number = 3×5 = 15
Second number = 7×5 = 35
Check: 15+35 = 50 ✓
Answer: The numbers are 15 and 35

Ingredients mixed in ratio 2:5, need 21 units total

How much of each?

Solution: Total parts = 2+5 = 7
Each part = 21 ÷ 7 = 3 units
First ingredient = 2×3 = 6 units
Second ingredient = 5×3 = 15 units
Check: 6+15 = 21 ✓

✏️ Practice Questions

Question 1: Share £20 in ratio 2:3. How much does the first person get?
£10
£8
£6
£12
Question 2: Ratio 4:5, total is 36. Find the larger part.
16
18
22
20
Question 3: Ages in ratio 3:4, difference is 5 years. What is the younger age?
15 years
12 years
10 years
8 years

⚠️ Common Mistakes & How to Avoid Them

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

Common Misconceptions

What students often do wrong:

1. Sharing equally instead of proportionally: Dividing the total by the number of people rather than using the ratio

2. Adding ratio parts instead of using them as multipliers: Thinking 2:3 with total 10 means 2+3+5 instead of finding part value

How to Avoid These Mistakes

Correct approach: Always find total ratio parts first, then divide total by parts to get unit value, then multiply each ratio number by unit value.

Memory tip: "Add ratio parts, divide total, multiply each part" - follow this sequence every time

💡 Teacher's Tip

Always check your answer by adding all parts back together - they should equal the original total. This simple check catches most calculation errors.

📋 Chapter Summary

🎉 Congratulations!

You've mastered Solving simple ratio problems!

🎯 Skills You've Developed:

✓ Using ratios to solve sharing problems
✓ Calculating unknown quantities in ratio problems
✓ Applying systematic problem-solving strategies
✓ Verifying answers using checking methods

🚀 What's Next?

Next: Learn about scale factors in similar shapes and how to use them in enlargements and reductions

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