The concept of ratio and ratios in their simplest form  (Page 2/3)

This is how it can be determined:

1.1 The ratio between the Aids Project (AP) and the Helpmekaar Fund (HMF) is 3 : 5.

What does this mean?

The AP will receive R3 for every R5 that the HMF gets.

• Therefore the first step would be to divide R8.

1.3 So we can do the following:

AP : HMF

3 : 5

The AP portion: $\frac{\text{.}\text{.}\text{.}\text{.}\text{.}\text{.}}{\text{.}\text{.}\text{.}\text{.}\text{.}\text{.}}$ to R = ………………………………………

The HMF portion of: $\frac{\text{.}\text{.}\text{.}\text{.}\text{.}\text{.}}{\text{.}\text{.}\text{.}\text{.}\text{.}\text{.}}$ to R …………. = ……………………………

(Use your calculator and round off to the nearest cent where necessary.)

Now try it yourself:

1. Compare each of the following ratios and indicate which one is bigger. Make use of percentages.

1.1 In Zimbabwe, the area of land available to black people as opposed to whites is 1 200 km² : 1,35 km². In South Africa the ratio of land available to black people to white people is 0,95 km² : 135 km².

What is the difference in land ownership between Zimbabwe and S.A. expressed as a percentage?

1.2 38 : 73 and 13 : 43

2. During 2003, the Mathematics HG paper indicated a grand total of 400 marks. A mistake crept in and the paper actually counted out of 375 marks.

2.1 Express the above information as a ratio in its simplest form.

2.2 Use the information in 2.1 to convert the marks of the following learners at the Primrose Private School from a mark out of 375 to a mark out of 400:

a) Sarie Neetling: 215

b) Thabo Nakane: 172

c) Maria Schmidt: 370

2.3 Calculate the average of the marks obtained for the Mathematics HG paper at this school:

Activity 3

Increasing or decreasing a given ratio

[lo 3.7, 4.1]

In the following activity, and in those that follow, the "recipe" that is given is of utmost importance.

• Recipe for success:

• Always set up a table.
• Always ask: Will the answer be more or less than what is given?

1. Increase R250 by the ratio of 2 : 3.

• Set up a table.
• Question: Where do I put down the R250? Yes, below the ratio of (2), because the amount must be increased to 3. Will the entry below ratio (3) be more or less than R250? Yes, more.
• Now present your information as ratios and calculate the required answer.

Table:

• Present your information as ratios: 2 : 3 = 250 : a
• 2 and R250 must be in the first positions. $\frac{2}{3}$ = $\frac{\text{250}}{a}$
• (Do crosswise multiplication ): 2 x a = 3 x 250
• 2 a = 750
• a = 375
• Check your calculation: Your answer should be more than R250.

2. Now do the following. Remember the recipe for success:

2.1 Ms Radetski is experiencing financial problems and she decides to ask her domestic helper who has been working 5 days per week to only come to work 2 days per week.

She decides to decrease her domestic worker's present salary of R1 250 per month to the ratio of 5 : 2.

Calculate the domestic worker's adjusted salary.

Table:

The price of a WV Polo is increased in the ratio of 3 : 5 for 2004. What will the price be in 2004 if the price in 2003 is R117 800?

Table:

Activity 4

Comparing two different amounts

[lo 3.7, 4.1]

1. A well-known example is: 120 km/h.

• What is the meaning of it?

2. You drive a distance of 120 km in 2 h. What is your average speed? (km/h means km per hour or km ÷ h.)