Page 2: Comparing Percentages and Calculating Percentages of Groups

This section focuses on comparing percentages and calculating percentages of groups. It provides step-by-step instructions for solving percentage problems.

Example: Determining if 1/4 of a container's capacity is greater than 20% of its capacity.

The page also includes a detailed example of calculating what percentage of a class owns dogs, using a step-by-step approach.

Highlight: When calculating percentages of groups, always identify the part and the whole clearly before proceeding with calculations.

Page 3: Percentage Calculations in Real-World Scenarios

This page applies percentage calculations to real-world scenarios, such as car colors in a parking lot and audience demographics at a movie.

Example: Calculating the percentage of silver cars in a parking lot with 15 silver cars out of 30 total cars.

The page also includes problems on calculating percentages of shaded areas in geometric figures, reinforcing visual representation of percentages.

Highlight: In real-world scenarios, it's crucial to identify the total (100%) and the part you're calculating the percentage for.

Page 4: Calculating Percentages of Amounts and Price Changes

This section covers calculating specific percentages of monetary amounts and introduces the concept of price changes, including discounts and increases.

Example: Calculating 50%, 25%, 10%, and 1% of 500 zł.

The page also includes problems on calculating new prices after percentage discounts.

Highlight: When calculating discounts, subtract the discount amount from the original price to find the new price.

Page 5: More Complex Discount Problems and Class Size Calculations

This page delves into more complex discount problems and introduces calculations involving class sizes and percentage increases.

Example: Calculating the number of students in class VIb if it has 20% more students than class VIa, which has 25 students.

The page also compares different types of discounts to determine which is more advantageous for the consumer.

Highlight: When dealing with percentage increases, add the increase to 100% before calculating the new amount.

Page 6: Price Changes Over Time and Reverse Percentage Calculations

This section focuses on price changes over time and introduces reverse percentage calculations, where you need to find the whole when given a percentage.

Example: Calculating the original price of a bicycle that cost 800 zł in winter, increased by 10% in spring, and then decreased by 10% in autumn.

The page also includes problems on finding the whole when given a percentage of it.

Highlight: In reverse percentage calculations, set up an equation where the known percentage and amount equal 100% of the unknown whole.

Page 7: Additional Practice Problems

This page provides additional practice problems covering various aspects of percentage calculations, including more complex scenarios and multi-step problems.

Example: Calculating the original price of an item that costs 792 zł after a 10% discount.

The page reinforces concepts learned throughout the guide and encourages students to apply their knowledge to solve diverse percentage-related problems.

Highlight: Practice a variety of problem types to strengthen your understanding and application of percentage concepts.

Page 1: Converting Percentages to Decimals and Fractions

This page introduces fundamental concepts of converting percentages to decimals and fractions. It provides examples of how to perform these conversions accurately.

Example: Converting 90% to a decimal: 90% = 0.90

Example: Converting 30% to a fraction: 30% = 30/100 = 3/10

The page also includes a problem on calculating what percentage of a figure is shaded, demonstrating practical application of percentage concepts.

Highlight: When converting percentages to fractions, always simplify to the lowest terms.