Lesson Notes By Weeks and Term v5 - Grade 6

Lesson Video

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Performance objectives

• Define ratio, rate, and percentage.
• Express ratios in their simplest form.
• Solve simple problems involving ratio and rate.
• Calculate percentages of whole numbers.
• Express a part of a whole as a percentage.

Lesson summary

This week, we begin exploring three important concepts in mathematics: ratio, rate, and percentage. These ideas are essential for understanding proportions, making comparisons, and interpreting information that we encounter every day. You'll find these concepts used in the kitchen when you're baking, at the shops when you're looking for discounts, and even when comparing cricket scores! For instance, understanding percentages can help you calculate the discount during a Black Friday sale at Game or Shoprite, while ratios can help you scale up a family recipe for a larger gathering.

Lesson notes

Ratio: A ratio compares two or more quantities of the same kind. It shows how much of one thing there is compared to another.

We write ratios using a colon (:) or as a fraction. The order in which the numbers are written is very important.

Example: If there are 3 apples and 5 oranges in a fruit bowl, the ratio of apples to oranges is 3:5 (read as "3 to 5"). This can also be written as the fraction 3/

5. The ratio of oranges to apples is 5:

3. Notice the different order.

Simplifying Ratios: Just like fractions, ratios can be simplified. To simplify a ratio, you need to find the highest common factor (HCF) of the numbers in the ratio and divide each number by the HC

F. Example: The ratio 12:18 can be simplified. The HCF of 12 and 18 is

6. Dividing both sides by 6, we get 12/6 : 18/6 = 2:

3. This means 12:18 is equivalent to 2:

3. Rate: A rate compares two quantities of different kinds. It tells you how much of one quantity there is per unit of another quantity. Think of it as a special type of ratio where the units are different.

Example: If a car travels 200 kilometers in 4 hours, the rate is 200 km / 4 hours = 50 kilometers per hour (km/h). The units are kilometers and hours.

Unit Rate: A unit rate is a rate where the second quantity is

1. In the previous example, 50 km/h is a unit rate because it tells us the distance traveled per 1 hour.

Percentage: A percentage is a special fraction or ratio where the denominator is always

1

0

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

Example: 25% means 25 out of 100, which can be written as the fraction 25/

1

0

0. Calculating Percentages: To find a percentage of a quantity, you can convert the percentage to a fraction or decimal and then multiply.

Example: To find 20% of 80, you can do: As a fraction: (20/100) 80 = (1/5) * 80 = 16 As a decimal: 0.20 80 = 16 Expressing a Part as a Percentage: To express a part of a whole as a percentage, divide the part by the whole and then multiply by 100%.

Example: If 30 out of 50 learners passed a test, the percentage of learners who passed is (30/50) 100% = 0.6 * 100% = 60%.

Worked example

Ratio: A recipe for vetkoek requires 2 cups of flour and 1 cup of water. What is the ratio of flour to water?

Solution: The ratio of flour to water is 2:

1. Rate: A tap leaks 50 ml of water in 10 minutes. What is the rate of water leakage in ml per minute?

Solution: The rate is 50 ml / 10 minutes = 5 ml/minute.

Percentage: What is 35% of 200?

Solution: (35/100) 200 = 0.35 * 200 = 70

Expressing as a Percentage: 15 out of 25 children in a class walk to school. What percentage of the children walk to school?

Solution: (15/25) 100% = 0.6 * 100% = 60%

Guided Practice (With Solutions)

Question 1:

In a bag of sweets, there are 8 blue sweets and 12 red sweets.

a) What is the ratio of blue sweets to red sweets?