The concept of ratio and ratios in their simplest form

Mathematics

Grade 8

Ratio and proportion

Measurement

Constructions

Module 15

The concept ratio and ratios in their simplest form

Activity 1

Explaining the concept of ratio and expressing ratios in their simplest form

[lo 1.4, 1.5]

1. The [ : ] sign means that you can express two or more quantities (of the same kind) as a ratio, e.g., if you receive R10 and I receive R15, we could express the two amounts as a ratio: 10 : 15.

Note: Units are not named when we deal with ratios.

2. Ratios can also be written as fractions and be simplified,

$\frac{2}{3}$ $\frac{\text{10}}{\text{15}}$ e.g.:

10 : 15 = = 2 : 3 (The ratio is now expressed in its simplest form.)

3. How are the following ratios expressed in its simplest form? 1 $\frac{1}{4}$ : 1 $\frac{1}{8}$ ?

Suggestion: Write mixed numbers as fractions and treat the problem as division of fractions.

4. Now write each of the following ratios in its simplest form:

4.1: 18 : 24 : 30

4.2: 3 $\frac{1}{2}$ : 4 $\frac{1}{2}$

4.3: 70 min : 1 $\frac{1}{4}$ h

4.4: 7,5 kg : 500 g

4.5: 30 m : 300 cm

5. Given: ratio 3 : 5.

5.1 What is the smaller amount if the bigger amount is R50?

Suggestion:

• Always draw a table.
• In the first column, write: ratio and money.
• Fill in the given data.
• Calculate a.

6. Job opportunities in Langa:

Draw a table and calculate the following:

• How many men are there in Langa if the ratio in numbers between men and women is 3 : 7 , and the number of women is 2 520?

7. At present, education policy in South Africa requires the following in schools: one educator for every 35 learners.

7.1 How many educators may be appointed at the Morningstar Primary School if 315 learners have been enrolled?

7.2 What must the number of learners be if the school has 23 educators?

8. The Education Department attempts to ensure a proportional ratio between educators and learners in all schools:

8.1 How many teachers are in excess and are therefore paid by the school's management council if a particular school has 700 learners and 32 educators?

8.2 What does it cost the parents to pay the salaries of the extra teachers if a teacher earns R4 982,55 per month?

ACTIVITY 2

Using ratios for easy comparison of particular data and for the division of any unit

[lo 1.4, 1.5, 3.7, 4.1]

a) Comparing data by making use of ratios

1. Building costs of low cost housing developments in the Western Cape increased from R1 000 to R1 220 /m² between 2000 and 2003 as opposed to an increase from R1 330 to R2 102/m², in Gauteng.

1.1 How would you indicate that the increase is fair?

1.1.1 Express all the data as ratios.

1.1.2 Express each ratio as a decimal number or a percentage. (Make use of your calculator.)

Gauteng:

Western Cape:

1.1.3 Which ratio is larger?

1.1.4 Is the increase fair?

1.1.5 To what would you ascribe the difference?

b) Division by making use of ratios

1. Mr Verkuil of the Langverwacht Primary School won R 150 500 in the Lotto last Saturday. He set aside R50 000 for personal use and decided to divide the rest of the money between the school's Aids project and the Helpmekaar Fund for needy farm workers.

He decided to divide the money to the ration of 3 : 5. How much money will each fund obtain?