Sharing In A Ratio Quizzes

Introduction

Sharing in a ratio is a key skill in GCSE Maths that helps students divide quantities in a fair and proportional way. Ratios allow us to split amounts according to specified parts rather than equally. Understanding this concept is essential for solving real-life problems, including money division, recipe adjustments, and resource allocation.

Core Concepts

What Does "Sharing in a Ratio" Mean?

When we share an amount in a ratio, we divide it into parts proportional to the numbers in the ratio. For example, sharing £60 in the ratio 2:1 means one part is twice the size of the other.

Representing Ratios

Ratios can be written as:

• Colon form: 2:1
• Fraction form: 2/1 and 1/1 (optional step for calculation)
• Word form: “2 to 1”

Rules & Steps

To share an amount in a ratio:

1. Add together the parts of the ratio to find the total number of parts.
   Example: Ratio 3:2 → 3 + 2 = 5 parts
2. Divide the total amount by the total number of parts to find the value of one part.
   Example: Total £50 ÷ 5 parts = £10 per part
3. Multiply the value of one part by each part of the ratio.
   Example: 3 parts → 3 × £10 = £30, 2 parts → 2 × £10 = £20
4. Check your work: The sum of the shares should equal the original total.
   £30 + £20 = £50 ✅

Worked Examples

1. Example 1: Share £80 in the ratio 3:1.
   Total parts = 3 + 1 = 4
   Value per part = £80 ÷ 4 = £20
   Shares: 3 parts = 3 × £20 = £60, 1 part = 1 × £20 = £20
2. Example 2: Share 45 sweets in the ratio 2:3.
   Total parts = 2 + 3 = 5
   Value per part = 45 ÷ 5 = 9 sweets
   Shares: 2 parts = 18 sweets, 3 parts = 27 sweets
3. Example 3 (Higher Level): Share £120 in the ratio 2:3:5.
   Total parts = 2 + 3 + 5 = 10
   Value per part = £120 ÷ 10 = £12
   Shares: 2 parts = £24, 3 parts = £36, 5 parts = £60

Common Mistakes

• Adding amounts instead of ratio parts to find the total.
• Forgetting to check that the sum of shares equals the original total.
• Confusing the order of parts in multi-part ratios (2:3:5 is not the same as 3:2:5).
• Rounding too early—always divide first before multiplying.

Applications

Sharing in a ratio is used in various real-life situations:

• Dividing profits: Sharing money among business partners.
• Recipes: Adjusting ingredients for different numbers of servings.
• Time or resources: Allocating work hours or materials in proportion to needs.

Strategies & Tips

• Always add the ratio parts first to find the total parts.
• Find the value of one part before calculating individual shares.
• Check your work by summing all shares.
• Practice with three-term or more ratios to prepare for higher-level questions.

Summary

Sharing in a ratio allows quantities to be divided fairly according to specified proportions. Remember: sum the ratio parts, find the value of one part, multiply for each share, and check your work. With practice, sharing in a ratio becomes straightforward and useful in both exams and everyday life. Attempt the quizzes in this subcategory to reinforce your skills!