Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Calculate percentage increases and decreases (discounts, price changes).
• Calculate simple interest on savings and loans.
• Use ratios and proportions to solve practical problems.
• Calculate profit and loss in business contexts.
• Solve multi-step problems using these concepts.

Lesson summary

This week, we delve deeper into numbers and calculations, focusing on skills crucial for managing personal finances, interpreting data, and making informed decisions in everyday South African life. From understanding banking fees to budgeting for groceries, these skills are fundamental to your future success. We will specifically concentrate on percentages (including percentage increase and decrease, profit and loss), simple interest calculations, and working with ratios and proportions in practical contexts. Understanding these concepts will empower you to navigate financial decisions with confidence.

Lesson notes

Percentages: Increase, Decrease, Profit, and Loss A percentage is a way of expressing a number as a fraction of

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0. The word "percent" means "per hundred." Understanding percentages is vital for various applications, including calculating discounts, interest rates, and profit margins.

Percentage Increase: Occurs when a value increases.

The formula is: `Percentage Increase = [(New Value - Original Value) / Original Value] * 100` Percentage Decrease: Occurs when a value decreases.

The formula is: `Percentage Decrease = [(Original Value - New Value) / Original Value] * 100` Profit: The gain realized when the selling price of an item is greater than its cost price. `Profit = Selling Price - Cost Price` Loss: The deficit incurred when the selling price of an item is less than its cost price. `Loss = Cost Price - Selling Price` Percentage Profit: `Percentage Profit = (Profit / Cost Price) * 100` Percentage Loss: `Percentage Loss = (Loss / Cost Price) * 100` Example 1 (Percentage Increase): A loaf of bread cost R12.00 last year. It now costs R13.

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0. Calculate the percentage increase in the price.

Solution: Original Price: R12.00 New Price: R13.50 Percentage Increase = [(R13.50 - R12.00) / R12.00] 100 Percentage Increase = (R1.50 / R12.00) 100 Percentage Increase = 0.125 100 Percentage Increase = 12.5% Therefore, the price of bread has increased by 12.5%.

Example 2 (Percentage Decrease): A cellphone originally priced at R3000 is on sale for R

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0. What is the percentage discount?

Solution: Original Price: R3000 New Price: R2400 Percentage Decrease = [(R3000 - R2400) / R3000] 100 Percentage Decrease = (R600 / R3000) 100 Percentage Decrease = 0.2 100 Percentage Decrease = 20% Therefore, the cellphone has a 20% discount.

Example 3 (Profit and Loss): A street vendor buys mangoes for R2 each and sells them for R3.50 each. If he sells 50 mangoes, what is his profit or loss and percentage profit?

Solution: Cost Price per mango: R2 Selling Price per mango: R3.50 Profit per mango: R3.50 - R2 = R1.50 Total Profit: R1.50 50 = R75 Percentage Profit = (R75 / (R2 50)) * 100 Percentage Profit = (R75 / R100) 100 Percentage Profit = 75% The vendor made a profit of R75, which is a 75% profit. Simple Interest Simple interest is a method of calculating the interest charge on a loan or investment. It is calculated on the principal amount only. `Simple Interest (I) = P r t` Where: P = Principal amount (the initial amount borrowed or invested) r = Annual interest rate (expressed as a decimal) t = Time in years Total Amount (A) = P + I Example 4 (Simple Interest): You invest R5000 in a savings account that earns simple interest at a rate of 8% per annum. How much interest will you earn after 3 years? What will your total amount be?

Solution: P = R5000 r = 8% = 0.08 t = 3 years I = R5000 0.08 * 3 I = R1200 Total Amount = R5000 + R1200 = R6200 You will earn R1200 in interest, and your total amount will be R

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0. Ratios and Proportions A ratio is a comparison of two or more quantities.

It can be written as a:b or a/b. A proportion is a statement that two ratios are equal.

Example 5 (Ratios and Proportions): A recipe for vetkoek requires 3 cups of flour and 1 cup of water. If you want to make a larger batch using 9 cups of flour, how much water do you need?

Solution: The ratio of flour to water is 3:

1. Let x be the amount of water needed.

We can set up a proportion: 3/1 = 9/x Cross-multiply: 3x = 9 Divide by 3: x = 3 You need 3 cups of water. Guided Practice (With Solutions)

Question 1: A pair of jeans costs R

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0. During a sale, it is discounted by 15%. What is the new price of the jeans?

Solution: Original Price: R450 Discount: 15% Discount Amount: 15/100 R450 = R67.50 New Price: R450 - R67.50 = R382.50 The new price of the jeans is R382.

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0. We first calculate the discount amount by finding 15% of the original price and then subtract this amount from the original price to find the sale price.

Question 2: Sipho borrows R8000 from a bank at a simple interest rate of 12% per year. He needs to repay the loan in 5 years. Calculate the total amount Sipho needs to repay.

Solution: Principal (P): R8000 Interest Rate (r): 12% = 0.12 Time (t): 5 years Simple Interest (I) = P r t = R8000 0.12 * 5 = R4800 Total Amount (A) = P + I = R8000 + R4800 = R12800 Sipho needs to repay a total of R

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0. We calculated the simple interest first and then added it to the principal to get the total amount.

Question 3: A shop buys a t-shirt for R80 and sells it for R

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0. Calculate the percentage profit.

Solution: Cost Price: R80 Selling Price: R120 Profit = Selling Price - Cost Price = R120 - R80 = R40 Percentage Profit = (Profit / Cost Price) 100 = (R40 / R80) * 100 = 50% The percentage profit is 50%. The profit is calculated, then divided by the cost price, and the result is multiplied by

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0. Question 4: The ratio of boys to girls in a class is 2:

3. If there are 12 boys in the class, how many girls are there?