Lesson Notes By Weeks and Term v5 - Grade 6
Ratio, rate and percentage (intro) – Week 9 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Ratio, rate and percentage (intro) – Week 9 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Subject: Mathematics
Class: Grade 6
Term: 1st Term
Week: 9
Theme: General lesson support
This page supports the lesson note with a companion video and a short classroom-ready summary.
For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.
This week, we embark on an exciting journey into the world of ratios, rates, and percentages. These mathematical concepts are not just abstract ideas; they are powerful tools that help us understand and navigate the world around us. From calculating the best deals at the local spaza shop to understanding how quickly a taxi travels, ratios, rates, and percentages are woven into the fabric of our daily lives in South Africa. Understanding these concepts will empower you to make informed decisions, solve problems, and become critical thinkers. Think about sharing sweets with your friends. How many sweets does each person get? That's a ratio!
Ratio: A ratio is a way to compare two or more quantities of the same kind using division. It tells us how much of one thing there is compared to another.
We can write a ratio 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) The order of the numbers in a ratio matters!
The ratio 3:4 is different from the ratio 4:
3. Example: In a class, there are 12 girls and 15 boys. The ratio of girls to boys is 12 to 15, or 12:15, or 12/
1
5. We can simplify this ratio by dividing both numbers by their greatest common factor (3): 12/3 : 15/3 = 4:
5. So, the simplest form of the ratio of girls to boys is 4:
5. Rate: A rate is a ratio that compares two quantities with different units. Because the units are different, we must include them when expressing the rate. Common examples of rates include speed (distance/time), price per item (rand/item), and fuel consumption (liters/kilometer).
Example: A car travels 200 kilometers in 4 hours. The rate (speed) is 200 kilometers / 4 hours. We simplify this by dividing both quantities by 4: 50 kilometers / 1 hour. So, the rate is 50 kilometers per hour (50 km/h).
Percentage: A percentage is a special type of ratio or fraction where the denominator is always
1
0
0. The word "percent" means "out of one hundred". We use the symbol "%" to represent percentage. To convert a fraction or ratio to a percentage, we multiply it by 100%.
Example: Convert the fraction 1/4 to a percentage. (1/4) 100% = 25%.
Therefore, 1/4 is equal to 25%.
Example: If 30 out of 100 learners in a school play soccer, what percentage of the learners play soccer? The fraction representing the learners who play soccer is 30/100. (30/100) 100% = 30% Therefore, 30% of the learners play soccer. Important
Note: When working with ratios, rates, and percentages, make sure you understand the units involved and what they represent. Always simplify ratios and rates to their simplest form to make them easier to understand and compare. Guided Practice (With Solutions)
Question 1: In a fruit basket, there are 8 apples and 6 bananas. What is the ratio of apples to bananas? Simplify the ratio to its simplest form.
Solution:* The ratio of apples to bananas is 8:
6. To simplify, we find the greatest common factor of 8 and 6, which is
2. Divide both numbers by 2: 8/2 : 6/2 = 4:
3. The simplest form of the ratio of apples to bananas is 4:
3. Commentary:* This question reinforces the basic definition of a ratio and the importance of simplifying it.
Question 2: A taxi travels 150 kilometers in 3 hours. What is the average speed (rate) of the taxi in kilometers per hour?
Solution:* The rate is 150 kilometers / 3 hours.
Divide both quantities by 3: 150/3 kilometers / 3/3 hours = 50 kilometers / 1 hour. The average speed of the taxi is 50 km/h.
Commentary:* This problem illustrates the concept of rate and how to calculate it by dividing distance by time.
Question 3: A shop offers a 20% discount on a shirt that originally costs R
1
0
0. How much is the discount in Rands?
Solution:* 20% can be written as the fraction 20/
1
0
0. To find 20% of R100, multiply (20/100) R100 = R
2
0. The discount is R
2
0. Commentary:* This question demonstrates how to calculate a percentage of a given amount, a crucial skill for budgeting and shopping.
Question 4: A recipe for pap calls for 1 cup of maize meal for every 2 cups of water. What is the ratio of maize meal to water?
Solution:* The ratio of maize meal to water is 1:
2. This ratio is already in its simplest form.
Commentary:* This illustrates the use of ratio in a real life cooking situation.
Question 5: Express 3/5 as a percentage.
Solution:* To express 3/5 as a percentage, we multiply by 100%. (3/5) 100% = 60%.
Therefore, 3/5 is equal to 60%.
Commentary:* Reinforces the conversion of fractions to percentages. Independent Practice (Questions Only) In a bag of sweets, there are 10 red sweets and 15 blue sweets. What is the ratio of red sweets to blue sweets? Simplify the ratio to its simplest form. A runner completes a 10-kilometer race in 2 hours. What is the runner's average speed in kilometers per hour? A pair of shoes is on sale for 30% off the original price of R
2
5
0. How much is the discount in Rands? A farmer has 25 chickens and 10 cows. What is the ratio of chickens to cows? Simplify the ratio. Express 1/5 as a percentage. John earns R500 and saves R
1
0
0. What percentage of his earnings does he save? A cake recipe requires 2 eggs for every 3 cups of flour. If you want to make a larger cake and use 6 cups of flour, how many eggs will you need? A map has a scale of 1 cm representing 5 km. If two towns are 4 cm apart on the map, what is the actual distance between them?
Write the ratio 24:36 in its simplest form. Convert 75% to a fraction in its simplest form.