⚖️ Proportion

A proportion shows that two ratios are equal. It helps scale numbers up or down.

🎯 What You'll Learn

Understand what proportions are
Set up proportions from word problems
Use cross-multiplication to solve proportions
Apply proportions to real-world scenarios

✏️ Explanation

A proportion shows that two ratios are equal. It helps scale numbers up or down.

🔍 Why It Matters

Important in real life for scaling recipes, maps, and models. Essential for cooking, building, and understanding scale drawings.

🧭 Solving Proportions

Set up the proportion

Write two equal ratios

3:£1.50 = 6:x

Cross-multiply

Multiply diagonally across

3 × x = 6 × £1.50

Simplify

Calculate the products

3x = £9.00

Solve for x

Divide to find the answer

x = £9.00 ÷ 3 = £3.00

✏️ Worked Example

If 3 pencils cost £1.50, how much do 6 pencils cost?

Step 1: Set up the proportion

3 pencils : £1.50 = 6 pencils : x

Step 2: Cross-multiply

3 × x = 6 × £1.50

Step 3: Calculate

3x = £9.00

Step 4: Solve for x

x = £9.00 ÷ 3 = £3.00

Answer: 6 pencils cost £3.00

🧮 Proportion Calculator

: = :

Enter 'x' for the unknown value you want to find

Solution:

x = 3.00

6 pencils cost £3.00

Step 1: Set up the proportion

3 : 1.5 = 6 : x

Step 2: Cross-multiply

3 × x = 6 × 1.5

Step 3: Solve for x

3x = 9, so x = 3.00

🌍 Real-World Examples

🍰 Recipe Scaling

A recipe for 4 people needs 200g flour. How much for 6 people?

4 people : 200g = 6 people : x

x = 300g flour needed

🗺️ Map Scaling

On a map, 2cm represents 5km. What does 8cm represent?

2cm : 5km = 8cm : x

x = 20km real distance

🚗 Fuel Consumption

A car uses 8L for 100km. How much fuel for 250km?

8L : 100km = x : 250km

x = 20L fuel needed

💱 Currency Exchange

£2 = $3. How many dollars can you get for £8?

£2 : $3 = £8 : x

x = $12 dollars

🔢 Practice Exercises

1. If 4 books cost £8, how much do 2 books cost?

2. If 5 apples cost £2.50, how much do 10 apples cost?

3. If 1 can feeds 3 dogs, how many cans for 12 dogs?

cans

4. 3:6 = x:12. What is x?

x =

5. A recipe for 2 people uses 150g flour. How much flour for 6 people?

⚠️ Common Mistakes

Cross-multiplying incorrectly
Forgetting to scale both parts of the ratio
Setting up the proportion in the wrong order

✨ Quick Summary

Proportions are equal ratios. Use cross-multiplication to solve them.