Ratios and rates forms part of Whole numbers in the grade 8 and 9 syllabus.

1. WHOLE NUMBERS
RATIOS AND RATES
17 FEB 2024

2. LESSON OBJECTIVES
By the end of the lesson, learners should be
able to:
Compare two or more quantities of the same kind
(ratio)
Share in a given ratio where a whole is given
Compare two or more quantities of different
kind (rate)

3. PRE-KNOWLEDGE
• RATIO
• HIGHEST COMMON FACTOR

4. BASELINE ACTIVITY
1. Write the following ratios in their simplest
form.
a) 9 to 15
b) 12: 18: 30
2. Find the simplest form of the ratio 27
minutes to 1
1
2
hours.

5. TERMINOLOGY AND DEFINITIONS
• A ratio is a comparison between two quantities
that have the same unit.
A ratio of 3 : 5 (read as 3 to 5)
• A ratio divides a number into different parts.
• A ratio is also used to compare two or more
quantities of the same type

6. Example 1
Lebo has 8 apples and Sarah has 12 apple. What
is the ratio of Lebo’s apples to Sarah’s apples?
Solution:
We first find the HCF between 8 and 12 which is
4.
Then we divide both by the HCF:
8
4
:
12
4
= 2: 3

7. Example 2
Thabang walks 2km to school and Sello walks
800m. Express the ratio of Thabang’s distance to
Sello’s distance as a ratio, in its simplest
form.

8. Example 2
Solution:
First convert so that the units are the same:
Thabang walks 2km, this is equivalent to 2000m
Sello walks 800m
HCF = 400
Divide by HCF:
2000
400
:
800
400
= 5: 2

9. Example 4:
finding the missing number or
quantity
Simphiwe and Snazo run a relay race together.
The ratio of the distance they each run is 3 :
5. If Simphiwe runs a distance of 900m.
a) How many metres did Snazo run?
b) What is the total distance of the race?

10. Example 4:
finding the missing number or
quantity
Solutions
a) Simphiwe ran a distance of 900m which
represents 3 parts.
∴ 1 𝑝𝑎𝑟𝑡 =
900𝑚
3
= 300𝑚
From the ratio we also know that Snazo ran 5
parts (3 : 5)
Distance ran by Snazo = 300𝑚 × 5 = 1 500𝑚

11. Example 4: Dividing a number
in a certain ratio
Divide 72 into the ratio 3 : 4 : 5.

12. Example 4: Dividing a number
in a certain ratio
Solution
Step 1: Add all the ratios
3 + 4 + 5 = 12 (total no. of parts)
Step 2: Calculate one part
One part:
72
12
= 6
Step 3: Multiply one part into the given ratio
3 × 6: 4 × 6: 5 × 6
= 18: 24: 30

13. Example 4:
finding the missing number or
quantity
Solutions
b) To find total distance we first need to find
the total number of parts. This is done by
simply adding the two quantities in the ratio:
3 : 5 = 3 + 5 = 8 parts.
1 𝑝𝑎𝑟𝑡 = 300𝑚
∴ 8 𝑝𝑎𝑟𝑡𝑠 𝑤𝑖𝑙𝑙 𝑏𝑒 = 8 × 300𝑚 = 2 400𝑚
Therefore, the total distance of the race is 2
400 metres.

14. Example 5: dealing with
decimals
Express 0,2: 0,15 as a ratio between two whole
numbers in its simplest form

15. Example 5: dealing with
decimals
Solution:
Look at the number with the most decimal places,
which is 0,15. To make this a whole number, we
need to multiply by 100.
Multiply both parts by 100:
0,2 × 100: 0,15 × 100 = 20: 15
Now find HCF : 5
Divide by HCF:
20
5
:
15
5
= 4: 3

16. ACTIVITY