Lesson Notes By Weeks and Term v5 - Grade 6

Lesson Video

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Performance objectives

• Define and write ratios in different ways.
• Simplify ratios to their simplest form.
• Define and calculate rates.
• Understand percentage as a ratio out of 100.
• Solve simple problems with ratios and rates.

Lesson summary

This week, we begin exploring the fascinating world of ratios, rates, and percentages. These concepts are fundamental building blocks in mathematics and are essential for understanding everyday situations. Ratios, rates, and percentages allow us to compare quantities, understand proportions, and make informed decisions. Think about sharing sweets with your friends (ratio), calculating the speed of a taxi (rate), or understanding discounts at a clothing store (percentage). These concepts are used all the time in shops, sports, cooking, and even understanding news reports!

Lesson notes

2.1 Ratio: Comparing Quantities A ratio is a way to compare two or more quantities of the same kind. It tells us how much of one thing there is compared to another.

Ratios can be written in three ways: Using a colon (:): a : b (read as "a to b") Using the word "to": a to b As a fraction: a/b Important: The order matters! 3:5 is different from 5:

3. Example 1: In a class, there are 15 boys and 10 girls. What is the ratio of boys to girls?

Boys to girls: 15 : 10 We can simplify this ratio by dividing both sides by their greatest common factor, which is

5. Simplified ratio: (15 ÷ 5) : (10 ÷ 5) = 3 : 2 This means for every 3 boys, there are 2 girls. We can also say that the ratio of girls to boys is 2:

3. Example 2: Sipho has 4 apples and Thandi has 8 apples. What is the ratio of Sipho's apples to Thandi's apples?

Sipho's apples to Thandi's apples: 4 : 8 Simplify the ratio by dividing both sides by 4: (4 ÷ 4) : (8 ÷ 4) = 1 : 2 This means Sipho has one apple for every two apples Thandi has.

Example 3: Ratios with more than two quantities: A fruit basket contains 5 bananas, 3 oranges, and 2 apples. What is the ratio of bananas to oranges to apples?

The ratio is 5 : 3 : 2 2.2 Rate: Comparing Quantities with Different Units A rate is a ratio that compares two quantities with different units. Common examples include speed (kilometers per hour), price per item (rand per apple), or words per minute.

Example 1: A car travels 240 kilometers in 3 hours. What is the speed (rate) of the car? Speed = Distance / Time Speed = 240 kilometers / 3 hours Speed = 80 kilometers per hour (80 km/h)

Example 2: A shop sells 5 apples for R

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0. What is the price per apple (rate)? Price per apple = Total price / Number of apples Price per apple = R20 / 5 apples Price per apple = R4 per apple 2.3 Percentage: A Ratio Out of 100 A percentage is a special type of ratio that expresses a number as a fraction of

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0. The word "percent" means "out of one hundred." The symbol for percentage 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 Decimals to Percentages: To convert a decimal to a percentage, multiply the decimal by 100%.

Example 1: Convert 0.25 to a percentage. 25 100% = 25% Example 2: Convert 0.8 to a percentage. 0.8 100% = 80% Understanding Percentages: If something costs R100 and there is a 20% discount, it means you get R20 off. 20% of R100 = (20/100) * R100 = R20 So the new price is R100 - R20 = R80 Guided Practice (With Solutions)

Question 1: A recipe calls for 2 cups of flour and 1 cup of sugar. What is the ratio of flour to sugar?

Solution: Flour to sugar: 2 : 1

Commentary: This is a straightforward application of the ratio definition. We simply identify the quantities and express them in the correct order.

Question 2: Simplify the ratio 12:

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8. Solution: Find the greatest common factor (GCF) of 12 and 18, which is

6. Divide both sides of the ratio by 6: (12 ÷ 6) : (18 ÷ 6) = 2 : 3 Simplified ratio: 2:3

Commentary: Simplifying ratios involves finding the GCF and dividing both sides by it. This makes the ratio easier to understand and use.

Question 3: A cyclist travels 60 km in 2 hours. What is the cyclist's average speed?

Solution: Speed = Distance / Time Speed = 60 km / 2 hours Speed = 30 km/h

Commentary: This is a direct application of the rate formula (speed = distance/time). Make sure to include the correct units (km/h).

Question 4: Convert 0.6 to a percentage.

Solution: 6 100% = 60%

Commentary: Converting a decimal to percentage is simply multiplying by 100 and including the percentage sign (%).

Question 5: Convert 1/5 to a percentage.

Solution: (1/5) 100% = 20%

Commentary: Converting a fraction to percentage is done by multiplying by 100 and adding the percentage sign. Independent Practice (Questions Only) In a group of children, 8 are wearing red shirts and 6 are wearing blue shirts. What is the ratio of children wearing red shirts to those wearing blue shirts? Simplify your answer.

Simplify the ratio 25:

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0. A tap fills a 20-liter bucket in 4 minutes. What is the flow rate of the tap in liters per minute? Convert 0.45 to a percentage. Convert 1/8 to a percentage. A store is selling sweets at a rate of R5 for 2 sweets. How much will 6 sweets cost? A farmer plants 3 rows of maize for every 2 rows of beans. If the farmer plants 12 rows of maize, how many rows of beans does the farmer plant? What percentage is 15 out of 50? What is the ratio of vowels to consonants in the word "MATHEMATICS"? (Remember that Y is sometimes a vowel, but not in this word). Sipho earns R500 per week and saves R

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0. What percentage of his earnings does he save?