Lesson Notes By Weeks and Term v5 - Grade 6

Lesson Video

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Performance objectives

• Define and express ratios in their simplest form.
• Distinguish between ratios and rates.
• Convert simple fractions to percentages and vice versa.
• Solve simple problems involving ratios, rates and percentages.
• Use ratio to compare relative sizes and quantities.

Lesson summary

This week, we embark on an exciting journey into the world of ratios, rates, and percentages! These are powerful mathematical tools that help us understand and compare quantities, costs, speeds, and much more. Think about sharing sweets with your friends, figuring out the best price at the shop, or calculating your cricket team's win rate. These are all examples where ratios, rates, and percentages come into play. This week's focus provides a foundational understanding essential for future mathematical concepts and everyday decision-making. Knowing these concepts will help you become a savvy shopper, a better athlete, and a more informed citizen.

Lesson notes

a) Ratios A ratio is a comparison of two or more quantities. It shows how much of one thing there is compared to another.

Ratios can be written in several ways: Using the word "to" (e.g., 3 to 4)

Using a colon (:) (e.g., 3:4) As a fraction (e.g., 3/4)

Important: The order of the numbers in a ratio matters! 3:4 is different from 4:

3. Simplifying Ratios: Just like fractions, ratios can be simplified. To simplify a ratio, divide all the numbers in the ratio by their highest common factor (HCF).

Example 1: In a class, there are 12 boys and 18 girls. What is the ratio of boys to girls?

Ratio of boys to girls: 12:18 HCF of 12 and 18 is

6. Divide both numbers by 6: 12/6 : 18/6 = 2:3 Therefore, the simplified ratio of boys to girls is 2:

3. This means for every 2 boys, there are 3 girls.

Example 2: A farmer has 25 sheep and 15 goats. What is the ratio of sheep to goats in its simplest form?

Ratio of sheep to goats: 25:15 HCF of 25 and 15 is

5. Divide both numbers by 5: 25/5 : 15/5 = 5:3 The simplified ratio is 5:3. b) Rates A rate is a comparison of two quantities with different units. Unlike ratios, rates always involve units.

Common examples of rates include: Speed (kilometres per hour - km/h) Price per kilogram (Rands per kg - R/kg)

Words per minute (WPM)

Example 1: A car travels 240 km in 3 hours. What is the average speed of the car? Rate = Distance / Time = 240 km / 3 hours = 80 km/h The average speed of the car is 80 kilometres per hour.

Example 2: Apples cost R25 for 5 kg. What is the price per kilogram? Rate = Total Cost / Quantity = R25 / 5 kg = R5/kg The price is R5 per kilogram. c) Percentages A percentage is a way of expressing a number as a fraction of

1

0

0. The word "percent" means "out of one hundred" or "per hundred". The symbol for percent is %.

Converting Fractions to Percentages: To convert a fraction to a percentage, multiply the fraction by 100%.

Example 1: Convert 1/2 to a percentage. (1/2) 100% = 50% Example 2: Convert 3/4 to a percentage. (3/4) 100% = 75% Converting Percentages to Fractions: To convert a percentage to a fraction, divide the percentage by 100 and simplify.

Example 1: Convert 25% to a fraction. 25% = 25/100 = 1/4 (simplified)

Example 2: Convert 60% to a fraction. 60% = 60/100 = 3/5 (simplified) Guided Practice (With Solutions)

Question 1: A recipe for vetkoek requires 2 cups of flour and 1 cup of water. What is the ratio of flour to water? Express it in its simplest form.

Solution: Ratio of flour to water: 2:1 This ratio is already in its simplest form since 2 and 1 have no common factors other than

1. Question 2: A taxi travels 150 km in 2 hours. What is the average speed of the taxi?

Solution: Speed = Distance / Time = 150 km / 2 hours = 75 km/h The average speed of the taxi is 75 km/h. We calculated the rate by dividing the distance travelled by the time taken. The units are important to include.

Question 3: What percentage is 1/5?

Solution: (1/5) 100% = 20% 1/5 is equal to 20%. We multiplied the fraction by 100% to convert it to a percentage.

Question 4: Express 80% as a fraction in its simplest form.

Solution: 80% = 80/100 = 4/5 (simplified) 80% is equal to 4/

5. We divided the percentage by 100 and then simplified the fraction by dividing both numerator and denominator by their highest common factor (20). Independent Practice (Questions Only) In a fruit basket, there are 8 oranges and 12 apples. What is the ratio of oranges to apples in its simplest form? A packet of chips costs R15 for 3 packets. What is the price per packet? Convert 1/4 to a percentage. Express 75% as a fraction in its simplest form. A shop sells 50 sweets, and 10 are lollipops. What is the ratio of lollipops to all sweets? Give your answer in its simplest form. A learner can read 60 pages in 2 hours. What is the rate of pages read per hour? What is 2/5 as a percentage? Express 30% as a simplified fraction. A garden has 16 roses and 8 sunflowers. What is the simplified ratio of sunflowers to roses? If a runner covers 400 meters in 50 seconds, what is the speed in meters per second?