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Step 2: carry on dividing until a pattern becomes visible - the pattern will be indicated by the recurring numbers.

Now try the following:

5.1 7 9 size 12{ { { size 8{7} } over { size 8{9} } } } {}

5.2 5 5 6 size 12{ - 5 { { size 8{5} } over { size 8{6} } } } {}

5.3 3 13 99 size 12{3 { { size 8{"13"} } over { size 8{"99"} } } } {}

6. What is noticeable about fractions that are recurring decimal numbers (with regard to the denominator)?

7. Now, before we provide the steps for reducing a recurring decimal number to a common fraction, see if you are able to write the following as fractions by making use of the information from no. 6.

8. The following provides complete steps for reducing a recurring decimal number to a common fraction:

Suggestion : Multiply by 10 (if you have one recurring figure). Multiply by 100 (if there are 2 recurring figures), etc.

9. Now try to do no. 7.2 in the way that is discussed in no. 8.

Activity 3

Reducing percentages to fractions and vice versa

[lo 1.2.2, 1.2.6, 1.6.1, 1.9.1]

1. What is the meaning of % (percentage)? .....................................................................

2. If you have to reduce any fraction to a percentage, you have to reduce the denominator to 100.

  • If this is not possible, you have to x
    (This principle can be applied in any situation, e.g. when you want to reduce a test that is marked out of 15 to a mark out of 50, you need to multiply by 50 1 size 12{ { { size 8{"50"} } over { size 8{1} } } } {} )

Reduce the following mathematics test marks from a grade 8 class to percentages (to one decimal figure, where necessary):

2.1 17 20 size 12{ { { size 8{"17"} } over { size 8{"20"} } } } {} .......................................

2.2 19 40 size 12{ { { size 8{"19"} } over { size 8{"40"} } } } {} .......................................

2.3 38 50 size 12{ { { size 8{"38"} } over { size 8{"50"} } } } {} .......................................

2.4 45 60 size 12{ { { size 8{"45"} } over { size 8{"60"} } } } {} .......................................

3. Reduce each of the following percentages to a common fraction (or a mixed number):

3.1 55 % .......................................

3.2 15,5% .......................................

3.3 16 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} % .......................................

3.4 6 2 3 size 12{6 { { size 8{2} } over { size 8{3} } } } {} % .......................................

4. Each South African citizen should have access to some means of transport.

Bolokanang has a community of 25 500 people. Study the accompanying table indicating the number of people that use the given means of transport and answer the questions that follow.

Vehicle Number of users
Bicycle 4 1 8 size 12{4 { { size 8{1} } over { size 8{8} } } } {} %
Car 3 5 size 12{ { { size 8{3} } over { size 8{5} } } } {}
Motorbike 0,085

4.1 Indicate how many inhabitants make use of:

a) a bicycle

b) a car

c) a motorbike

4.2 Express the number of inhabitants that use a car as a fraction of those who travel by bicycle.

4.3 Which percentage of the inhabitants has no vehicle?

4.4 Which other means of transport do farm labourers use to get to the nearest town?

4.5 If the number of job opportunities in rural areas should increase, the fraction of citizens who use cars for transport will double. What fraction of the community will be using cars for transport under such conditions?

Activity 4

Adding and subtracting rational numbers (fractions)

[lo 1.2.2, 1.2.5, 1.2.6, 1.6.2, 1.7.1, 1.7.2, 1.9.1]

1. Reduce each of the following compound numbers to improper fractions.This is very important in addition, subtraction, multiplication and division of fractions.

1.1 5 4 7 size 12{ { { size 8{4} } over { size 8{7} } } } {} ................................ 1.2 7 7 9 size 12{ { { size 8{7} } over { size 8{9} } } } {} ................................

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Source:  OpenStax, Mathematics grade 8. OpenStax CNX. Sep 11, 2009 Download for free at http://cnx.org/content/col11034/1.1
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