Understanding Percentages

Practical applications involving money, growth, and data comparison in real-world contexts

CAPS Grade 10 Mathematical Literacy

This document provides a comprehensive overview of how percentages are applied in Grade 10 Mathematical Literacy, focusing on practical problems involving money, growth, and data comparison. It covers basic percentage calculations, percentage increase and decrease, and the context of Value-Added Tax (VAT) in South Africa.

Key Percentage Concepts

Mastering percentages is essential for solving practical problems in finance, shopping, and data analysis.

Core Skills

Percentage of Amount Part as Percentage Original Amount Percentage Increase Percentage Decrease VAT (15%) Discounts Interest

Percentage Challenge Game

Test your percentage skills in real-world scenarios!

Score
0
Questions
1/6
Streak
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Shopping at a clothing store
A jacket costs R450. You get a 15% discount. How much do you pay?

1. Basic Percentage Calculations

Finding a Percentage of an Amount

Method 1

To find a percentage of a given amount, convert the percentage into a fraction over 100 or a decimal, and then multiply it by the amount.

15% of R200 = 0.15 × R200 = R30

Step 1
Convert 15% to a decimal: 15% = 0.15
Step 2
Multiply by the amount: 0.15 × R200 = R30

Expressing a Part as a Percentage

Method 2

To express a part as a percentage of the whole, divide the part by the whole and then multiply by 100.

35 out of 60 = (35 ÷ 60) × 100 = 58.33%

Step 1
Divide the part by the whole: 35 ÷ 60 = 0.5833
Step 2
Multiply by 100: 0.5833 × 100 = 58.33%

Finding the Original Amount

Method 3

This calculation is used when you know the final value after a percentage has been added or subtracted.

After 20% increase → R120. Original = R120 ÷ 1.20 = R100

Step 1
Let original be X: X + 0.20X = R120
Step 2
Simplify: 1.20X = R120
Step 3
Divide: X = R120 ÷ 1.20 = R100

2. Percentage Increase and Decrease

Price Increase

R200 + 10% = R220

Discount

R200 - 20% = R160

Percentage Change

R100 → R120 = 20%

To Find the New Value (Increase)

Add the percentage to 100% and multiply by the original amount.

Example: 10% increase on R200
New Value = R200 × 1.10 = R220
(100% + 10% = 110% = 1.10)

To Find the New Value (Decrease)

Subtract the percentage from 100% and multiply by the original amount.

Example: 20% discount on R200
New Value = R200 × 0.80 = R160
(100% - 20% = 80% = 0.80)

To Find the Percentage Change

Use the formula: (New Value - Old Value) ÷ Old Value × 100

Example: Price increases from R100 to R120
Percentage Change = ((R120 - R100) ÷ R100) × 100
= (20 ÷ 100) × 100 = 20% increase

3. Key Context: Value-Added Tax (VAT)

South African VAT Calculator (15%)

VAT Inclusive (Add VAT)

Price including VAT:
R115.00
VAT amount: R15.00

× 1.15 to add VAT

VAT Exclusive (Remove VAT)

Price excluding VAT:
R100.00
VAT amount: R15.00

÷ 1.15 to remove VAT

Zero-rated Items

Certain items, such as basic foodstuffs, are exempt from VAT (0%) to assist lower-income households. Understanding which items are zero-rated can help consumers make informed purchasing decisions.

Brown Bread
0% VAT
Milk
0% VAT
Eggs
0% VAT
Maize Meal
0% VAT
Fruits & Veg
0% VAT
Water
0% VAT

Real-World Examples

Salary Increase

A worker earns R8,500 per month. She receives a 6.5% salary increase.

Calculate:

Increase amount: R8,500 × 0.065 = R552.50
New salary: R8,500 × 1.065 = R9,052.50

Test Score

A learner scores 42 out of 60 on a Mathematical Literacy test.

Calculate:

Percentage: (42 ÷ 60) × 100 = 70%
To get 80% needed: 60 × 0.8 = 48 marks

Discount Shopping

A store offers 25% off all items. A jacket costs R650 before the discount.

Calculate:

Discount amount: R650 × 0.25 = R162.50
Sale price: R650 × 0.75 = R487.50

Finding Original Price

After a 15% discount, you pay R255 for a pair of shoes.

Calculate:

Original price: R255 ÷ 0.85 = R300
Check: 15% of R300 = R45, R300 - R45 = R255 ✓

Practice Problems

VAT Calculation

A laptop costs R4,500 excluding VAT. What is the total price including 15% VAT?

Solution

  • VAT amount: R4,500 × 0.15 = R675
  • Total: R4,500 + R675 = R5,175
  • Or: R4,500 × 1.15 = R5,175

Percentage Change

Electricity price increased from R1.20 to R1.38 per kWh. Find the percentage increase.

Solution

  • Increase = R1.38 - R1.20 = R0.18
  • % increase = (0.18 ÷ 1.20) × 100 = 15%

Commission

A salesperson earns 8% commission on sales. If she sells R25,000 worth of goods, how much commission does she earn?

Solution

  • Commission = R25,000 × 0.08 = R2,000

CAPS Curriculum Requirements

Knowledge & Understanding

  • Calculate percentages of given amounts
  • Express one quantity as a percentage of another
  • Find original amounts after percentage changes
  • Understand VAT calculations (inclusive and exclusive)

Skills & Applications

  • Calculate percentage increase and decrease
  • Apply percentages to financial contexts (VAT, discounts)
  • Solve real-world problems involving percentages
  • Interpret percentage data in tables and graphs

Competencies

  • Make informed financial decisions using percentages
  • Compare values using percentage differences
  • Calculate with percentages in budgeting contexts
  • Understand zero-rated items and VAT implications

Learning Resources

Percentage Games

Interactive games to practice percentage calculations

VAT Worksheets

Practice worksheets with real till slips and VAT calculations

Discount Problems

Real-world problems involving sales and discounts

Data Interpretation

Percentage-based data interpretation from graphs