🔧 Using Ratio to Solve Problems

Use ratios to divide quantities, calculate parts, or adjust values.

🎯 What You'll Learn

Solve ratio problems involving sharing quantities
Find parts when given a total and ratio
Calculate totals when given parts and ratios
Apply ratio problem-solving to real situations

✏️ Explanation

Use ratios to divide quantities, calculate parts, or adjust values.

🔍 Why It Matters

It's key for budgeting, planning, and sharing. Essential for dividing money fairly, adjusting recipes, and solving many real-world problems.

🧭 Ratio Problem Solver

Read the ratio

Identify the parts in the ratio

Ratio 1:3

Add the parts

Find total number of parts

1 + 3 = 4 parts

Divide the total

Find value of one part

£40 ÷ 4 = £10

Calculate shares

Multiply each part by the value

1×£10 = £10, 3×£10 = £30

✏️ Worked Example

Share £40 in the ratio 1:3

Step 1: Count the total parts

Total parts = 1 + 3 = 4

Step 2: Find the value of one part

£40 ÷ 4 = £10 per part

Step 3: Calculate each share

Share 1 = 1 × £10 = £10

Share 2 = 3 × £10 = £30

Answer: Shares are £10 and £30

Check: £10 + £30 = £40 ✓

🧮 Ratio Problem Calculator

Share in the ratio :

Solution:

Check: £10 + £30 = £40 ✓

Step 1: Add the parts

1 + 3 = 4 total parts

Step 2: Find value per part

£40 ÷ 4 = £10 per part

Step 3: Calculate shares

1 × £10 = £10, 3 × £10 = £30

🌍 Real-World Examples

💰 Sharing Prize Money

Three friends win £150 and decide to share it in the ratio 2:3:5. How much does each person get?

Total parts = 2 + 3 + 5 = 10
Per part = £150 ÷ 10 = £15
Shares: 2×£15 = £30, 3×£15 = £45, 5×£15 = £75

£30, £45, £75

🎨 Paint Mixing

To make 20L of purple paint, mix red and blue in the ratio 3:2. How much of each colour?

Total parts = 3 + 2 = 5
Per part = 20L ÷ 5 = 4L
Red: 3 × 4L = 12L, Blue: 2 × 4L = 8L

12L red, 8L blue

⏰ Time Allocation

A student has 4 hours to split between maths and science in the ratio 3:1. How long for each?

Total parts = 3 + 1 = 4
Per part = 4 hours ÷ 4 = 1 hour
Maths: 3 × 1 = 3 hours, Science: 1 × 1 = 1 hour

3 hours maths, 1 hour science

🍰 Recipe Scaling

A cake recipe uses flour and sugar in ratio 5:2. If you need 350g of mixture total, how much of each?

Total parts = 5 + 2 = 7
Per part = 350g ÷ 7 = 50g
Flour: 5 × 50g = 250g, Sugar: 2 × 50g = 100g

250g flour, 100g sugar

🔢 Practice Exercises

1. Share £60 in the ratio 2:3

First share: £ Second share: £

2. Divide 100 sweets in the ratio 5:5

First share: sweets, Second share: sweets

3. Divide 80 apples in the ratio 3:5

First share: apples, Second share: apples

4. Share £90 in the ratio 1:2

First share: £ Second share: £

5. 40 minutes split in the ratio 3:1

First part: minutes, Second part: minutes

⚠️ Common Mistakes

Not adding parts correctly
Misapplying the ratio to the total
Forgetting to check that shares add up to the original total

✨ Quick Summary

Convert ratio to parts, divide total, then multiply.