Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Calculate with percentages like discounts and VAT.
• Use ratios and proportions for sharing and map scales.
• Convert between different units of measurement.
• Calculate and interpret rates like speed and cost.
• Use rounding and estimation for quick calculations.

Lesson summary

This week, we delve deeper into working with numbers and performing calculations in a way that's relevant to everyday life in South Africa. We will be focusing on understanding and applying concepts like percentages, ratios, proportions, rates, and converting between different units of measurement within real-world contexts. This is crucial because these skills are essential for managing personal finances, understanding household budgeting, interpreting statistics related to employment and social issues, making informed consumer decisions, and even understanding concepts presented in the media.

Lesson notes

2.1 Percentages: A percentage is a way of expressing a number as a fraction of 100. "Percent" means "out of 100". The symbol "%" represents percent. Percentages are used to describe parts of a whole, changes in quantities, and financial transactions.

Calculating a Percentage of a Number: To find x percent of a number y, multiply y by x/

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0. Percentage Increase: ((New Value - Original Value) / Original Value) 100% Percentage Decrease: ((Original Value - New Value) / Original Value) 100% Discount: Discount Rate Original Price Price After Discount: Original Price - Discount VAT (Value Added Tax): In South Africa, VAT is currently 15%. To calculate the VAT amount on a price before VAT, multiply the price by 0.

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5. To calculate the price after VAT, multiply the price before VAT by 1.

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5. Example 1: Calculating a Discount A pair of sneakers originally costs R

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0. They are on sale with a 20% discount. What is the discount amount, and what is the sale price? Discount Amount = 20% of R800 = (20/100) R800 = R160 Sale Price = Original Price - Discount Amount = R800 - R160 = R640 Example 2: Calculating VAT A loaf of bread costs R12 (excluding VAT). What is the final price including VAT? VAT Amount = 15% of R12 = (15/100) R12 = R1.80 Final Price (including VAT) = R12 + R1.80 = R13.80 OR Final Price (including VAT) = R12 * 1.15 = R13.80 2.2 Ratios and Proportions: A ratio compares two or more quantities.

It can be written as a:b or a/b. A proportion states that two ratios are equal. If a/b = c/d, then a and d are the extremes, and b and c are the means. In a proportion, the product of the means equals the product of the extremes (cross-multiplication: ad = bc).

Example 3: Sharing in a Ratio Three friends, Thando, Aisha, and Bongani, decide to share the profits from their spaza shop in the ratio 2:3:

5. If the total profit is R5000, how much does each person receive? Total ratio parts = 2 + 3 + 5 = 10 Thando's share = (2/10) R5000 = R1000 Aisha's share = (3/10) R5000 = R1500 Bongani's share = (5/10) R5000 = R2500 Example 4: Map Scale A map has a scale of 1:50,

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0. This means that 1 cm on the map represents 50,000 cm (or 500 meters, or 0.5 kilometers) in real life. If the distance between two towns on the map is 8 cm, what is the actual distance between the towns in kilometers? Actual distance = 8 cm 50,000 cm/cm = 400,000 cm Convert cm to km: 400,000 cm / 100 cm/m / 1000 m/km = 4 km 2.3 Unit Conversions: Knowing how to convert between units is vital for practical calculations.

Some common conversions include: Length: 1 meter (m) = 100 centimeters (cm), 1 kilometer (km) = 1000 meters (m)

Mass: 1 kilogram (kg) = 1000 grams (g)

Volume: 1 liter (L) = 1000 milliliters (mL)

Currency: The exchange rate between the South African Rand (ZAR) and other currencies (e.g., USD, EUR, GBP) fluctuates. You'll need to look up the current exchange rate.

Example 5: Converting Units A recipe calls for 500 mL of milk. How many liters is this? 500 mL / 1000 mL/L = 0.5 L Example 6: Currency Conversion You want to buy a textbook online that costs $25 USD. If the exchange rate is 1 USD = 18 ZAR, how much will the textbook cost in Rands? Cost in ZAR = $25 18 ZAR/USD = R450 2.4 Rates: A rate compares two quantities with different units. Common examples include speed (distance/time), unit cost (price/quantity), and population density (people/area).

Example 7: Calculating Speed A taxi travels 120 km in 2 hours. What is its average speed? Speed = Distance / Time = 120 km / 2 hours = 60 km/h Example 8: Calculating Unit Cost A 5 kg bag of potatoes costs R

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0. What is the unit cost per kilogram? Unit Cost = Total Cost / Quantity = R40 / 5 kg = R8/kg 2.5 Estimation and Rounding: Rounding involves approximating a number to a nearby value for simplicity. Estimation involves making an approximate calculation, often using rounded numbers.

Example 9: Estimating the Total Cost You are buying groceries: bread (R15.50), milk (R22.75), and cheese (R38.20). Estimate the total cost by rounding each item to the nearest Rand and adding them together. Bread (R15.50) ≈ R16 Milk (R22.75) ≈ R23 Cheese (R38.20) ≈ R38 Estimated Total Cost = R16 + R23 + R38 = R77 Guided Practice (With Solutions)

Question 1: A cellphone originally costs R

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0. It is on sale with a 15% discount. Calculate the discount amount and the sale price.

Solution: Discount Amount = 15% of R3500 = (15/100) R3500 = R525 Sale Price = Original Price - Discount Amount = R3500 - R525 = R2975

Commentary: This question applies the percentage discount calculation directly. It's important to understand that the discount is subtracted from the original price.

Question 2: A recipe for vetkoek requires flour and water in the ratio 3:

2. If you want to make a larger batch of vetkoek using 6 cups of water, how many cups of flour will you need?

Solution: Let x be the amount of flour needed.