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Mathematics

Common fractions

Educator section

Memorandum

10. 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {} = 40 60 size 12{ { { size 8{"40"} } over { size 8{"60"} } } } {} ; 3 4 size 12{ { { size 8{3} } over { size 8{4} } } } {} = 45 60 size 12{ { { size 8{"45"} } over { size 8{"60"} } } } {} ; 4 5 size 12{ { { size 8{4} } over { size 8{5} } } } {} = 48 60 size 12{ { { size 8{"48"} } over { size 8{"60"} } } } {}

  • a) 0,5 b) 0,25

c) 0,125 d) 0,75

e) 0,55 f) 0,8

g) 0,625 h) 0,875

i) 0,66 j) 0,36

12.3 (1 ÷ 4) + 3 = 3,25

12.4 0,3333333

  • a) 0,6666666

b) 0,4545454

12.6 a) 0, 6 . size 12{ {6} cSup { size 8{ "." } } } {}

b) 0, 4 . 5 . size 12{ {4} cSup { size 8{ "." } } {5} cSup { size 8{ "." } } } {}

  • a) 0,667

b) 0,455

Leaner section

Content

Activity: fractions [lo 1.9.2, lo 1.10, lo 1.4]

10. BRAIN-TEASER!

In a competition, Abdul’s dolphin jumps 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {} of a metre out of the water. Fatima’s dolphin jumps 3 4 size 12{ { { size 8{3} } over { size 8{4} } } } {} of a metre out of the water, while Nazir’s dolphin jumps 4 5 size 12{ { { size 8{4} } over { size 8{5} } } } {} of a metre out of the water. Whose dolphin jumps the highest?

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11.1 Did you know?

To convert common fractions to decimal fractions we make

use of equivalent fractions.

e.g.
1 × 2
5 × 2
=
2
10
= 0,2

11. 2 Convert the following fractions to decimal fractions:

a) 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {} ___________________ b) 1 4 size 12{ { { size 8{1} } over { size 8{4} } } } {} ___________________
c) 1 8 size 12{ { { size 8{1} } over { size 8{8} } } } {} ___________________ d) 3 4 size 12{ { { size 8{3} } over { size 8{4} } } } {} ___________________
e) 11 20 size 12{ { { size 8{"11"} } over { size 8{"20"} } } } {} ___________________ f) 4 5 size 12{ { { size 8{4} } over { size 8{5} } } } {} ___________________
g) 5 8 size 12{ { { size 8{5} } over { size 8{8} } } } {} ___________________ h) 7 8 size 12{ { { size 8{7} } over { size 8{8} } } } {} ___________________
i) 33 50 size 12{ { { size 8{"33"} } over { size 8{"50"} } } } {} ___________________ j) 9 25 size 12{ { { size 8{9} } over { size 8{"25"} } } } {} ___________________

12. Do you still remember?

If we want to check the above with a calculator, e.g. , we key in: 7 ÷ 8 =

12.2 Check the exercise above (11.2) with your calculator.

12.3 How would you convert 3 and a quarter to a decimal fraction using your calculator?

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12.4 What will 1 3 size 12{ { { size 8{1} } over { size 8{3} } } } {} look like on a calculator?

Key in 1 ÷ 3 = and write the answer down: __________________________________

Did you know?

We call a fraction like 0,333333333333 a recurring decimal fraction,

and we write it like this: 0, °

12.5

a) What will two thirds ( 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {} ) look like on the calculator? _____________________________________________________________________

b) What will five elevenths ( 5 11 size 12{ { { size 8{5} } over { size 8{"11"} } } } {} ) look like on the calculator? _____________________________________________________________________

12.6

Write the above now in the short way:

a) __________________________________________________________________

b) __________________________________________________________________

12.7

Round off your answers to 3 decimal places:

a) __________________________________________________________________

b) __________________________________________________________________

13. TIME FOR SELF-ASSESSMENT

  • Colour in the applicable block for each of the following:
I know what rational numbers are 1 2 3
I know an example for a:
proper fraction 1 2 3
improper fraction 1 2 3
mixed number 1 2 3
I know how to form equivalent fractions 1 2 3
I can convert fractions to decimal fractions 1 2 3
I know how to key in fractions on a calculator 1 2 3
I know how to show a recurring decimal 1 2 3

Assessment

Learning Outcome 1: The learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.

Assessment Standard 1.9: We know this when the learner uses a range of techniques to perform calculations including:

1.9.2: using a calculator;

1.10: uses a range of strategies to check solutions and judges the reasonableness of solutions;

Assessment Standard 1.4: We know this when the learner recognises and uses equivalent forms of the rational numbers listed above.

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Source:  OpenStax, Mathematics grade 7. OpenStax CNX. Sep 16, 2009 Download for free at http://cnx.org/content/col11075/1.1
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