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Recognise and classify ordinary fractions

Module by: Siyavula Uploaders. E-mail the author

MATHEMATICS

Grade 5

ORDINARY AND DECIMAL FRACTIONS

Module 46

RECOGNISE AND CLASSIFY ORDINARY FRACTIONS

Activity 1:

To recognise and classify ordinary fractions in order to compare them [LO 1.3.2]

RELATIONSHIP SIGNS (< ; > ; =)

1. Compare the following fractions and then fill in<, > or =.

1.1 3535 size 12{ { { size 8{3} } over { size 8{5} } } } {} ____ 710710 size 12{ { { size 8{7} } over { size 8{"10"} } } } {}

1.2 1313 size 12{ { { size 8{1} } over { size 8{3} } } } {} ____ 1414 size 12{ { { size 8{1} } over { size 8{4} } } } {}

1.3 5858 size 12{ { { size 8{5} } over { size 8{8} } } } {} ____ 1212 size 12{ { { size 8{1} } over { size 8{2} } } } {}

1.4 1717 size 12{ { { size 8{1} } over { size 8{7} } } } {} ____ 1515 size 12{ { { size 8{1} } over { size 8{5} } } } {}

1.5 3434 size 12{ { { size 8{3} } over { size 8{4} } } } {} ____ 6868 size 12{ { { size 8{6} } over { size 8{8} } } } {}

1.6 3838 size 12{ { { size 8{3} } over { size 8{8} } } } {} ____ 1212 size 12{ { { size 8{1} } over { size 8{2} } } } {}

1.7 3434 size 12{ { { size 8{3} } over { size 8{4} } } } {} ____ 912912 size 12{ { { size 8{9} } over { size 8{"12"} } } } {}

1.8 3535 size 12{ { { size 8{3} } over { size 8{5} } } } {} ____ 710710 size 12{ { { size 8{7} } over { size 8{"10"} } } } {}

1.9 211211 size 12{ { { size 8{2} } over { size 8{"11"} } } } {} ____ 112112 size 12{ { { size 8{1} } over { size 8{"12"} } } } {}

1.10 12121212 size 12{ { { size 8{"12"} } over { size 8{"12"} } } } {} ____ 9999 size 12{ { { size 8{9} } over { size 8{9} } } } {}

2. Compare the following fractions and draw a circle around the one that is the greatest in each of the following:

2.1 1212 size 12{ { { size 8{1} } over { size 8{2} } } } {} ; 3434 size 12{ { { size 8{3} } over { size 8{4} } } } {}

2.2 2323 size 12{ { { size 8{2} } over { size 8{3} } } } {} ; 3636 size 12{ { { size 8{3} } over { size 8{6} } } } {}

2.3 3535 size 12{ { { size 8{3} } over { size 8{5} } } } {} ; 910910 size 12{ { { size 8{9} } over { size 8{"10"} } } } {}

2.4 1212 size 12{ { { size 8{1} } over { size 8{2} } } } {} ; 2626 size 12{ { { size 8{2} } over { size 8{6} } } } {}

2.5 3838 size 12{ { { size 8{3} } over { size 8{8} } } } {} ; 1212 size 12{ { { size 8{1} } over { size 8{2} } } } {}

2.6 4545 size 12{ { { size 8{4} } over { size 8{5} } } } {} ; 410410 size 12{ { { size 8{4} } over { size 8{"10"} } } } {}

Class discussion

HOW can we determine the answers for no. 1 and if we don’t have a diagram to help us?

3. In the following activity you will see how important your knowledge of equivalent fractions is. Once you have mastered it, you will find that it is child’s play to compare the fractions with each other.

Use the rule as determined during your class discussion and fill in <, > or =.

3.1 3535 size 12{ { { size 8{3} } over { size 8{5} } } } {}____ 715715 size 12{ { { size 8{7} } over { size 8{"15"} } } } {}

3.2 711711 size 12{ { { size 8{7} } over { size 8{"11"} } } } {}____ 13221322 size 12{ { { size 8{"13"} } over { size 8{"22"} } } } {}

3.3 5959 size 12{ { { size 8{5} } over { size 8{9} } } } {} ____ 15271527 size 12{ { { size 8{"15"} } over { size 8{"27"} } } } {}

3.4 5656 size 12{ { { size 8{5} } over { size 8{6} } } } {} ____ 20242024 size 12{ { { size 8{"20"} } over { size 8{"24"} } } } {}

4. Now use your knowledge and fill in <, > or =.

4.1 4545 size 12{ { { size 8{4} } over { size 8{5} } } } {}____ 5656 size 12{ { { size 8{5} } over { size 8{6} } } } {}

4.2 2323 size 12{ { { size 8{2} } over { size 8{3} } } } {} ____ 4545 size 12{ { { size 8{4} } over { size 8{5} } } } {}

4.3 5656 size 12{ { { size 8{5} } over { size 8{6} } } } {} ____ 7979 size 12{ { { size 8{7} } over { size 8{9} } } } {}

4.4 7878 size 12{ { { size 8{7} } over { size 8{8} } } } {} ____ 6767 size 12{ { { size 8{6} } over { size 8{7} } } } {}

To calculate by selecting and using operations [LO 1.8.3]

1. Split up into groups of three. See if you know how to solve the problems.

1.1 Gizelle and her twin brother, Donovan, receive pocket money every month. Gizelle saves two sixths of her pocket money. Donovan saves four ninths of his. Who saves most if they get the same amount of pocket money?

1.2 Mom likes making pancakes. She gives Jake and his friends three quarters to eat. Then Mom makes the same number of pancakes. She sends four fifths of the pancakes to school for Dimitri and his friends to enjoy. Who got the most pancakes from Mom?

1.3 Vusi and Sipho wrote the same test. Vusi answered four sevenths of the questions correctly. Sipho had five eighths right. Who did better in the test?

1.4 Two identical taxis transport passengers between Johannesburg and Pretoria. The one taxi is two thirds full, while the other one is three quarters full. Which taxi transports the most passengers?

Another BRAIN-TEASER!

Arrange the following fractions from biggest to smallest:

2323 size 12{ { { size 8{2} } over { size 8{3} } } } {} ; 1212 size 12{ { { size 8{1} } over { size 8{2} } } } {} ; 5656 size 12{ { { size 8{5} } over { size 8{6} } } } {} ; 7979 size 12{ { { size 8{7} } over { size 8{9} } } } {}

SIMPLIFYING

Did you know?

In order to write a fraction in its simplest form we divide the numerator and denominator by the same number. The value of the fraction does not change because we are actually dividing the fraction by 1.

Table 1
E.g. 18 24 18 24 size 12{ { {"18"} over {"24"} } } {}
6
 6
= 3 4 3 4 size 12{ { {3} over {4} } } {} and 10 15 10 15 size 12{ { {"10"} over {"15"} } } {}  
5
5
= 2 3 2 3 size 12{ { {2} over {3} } } {}

Activity 3:

To simplify common fractions [LO 1.3.2]

1. Now that you know how to simplify a fraction, see whether you can complete the following table:

Table 2
  Fraction ÷ by Simplified
E.g. 18 27 18 27 size 12{ { { size 8{"18"} } over { size 8{"27"} } } } {} 9 9 9 9 size 12{ { { size 8{9} } over { size 8{9} } } } {} 2 3 2 3 size 12{ { { size 8{2} } over { size 8{3} } } } {}
1.1 40 45 40 45 size 12{ { { size 8{"40"} } over { size 8{"45"} } } } {} .................. ..................
1.2 15 25 15 25 size 12{ { { size 8{"15"} } over { size 8{"25"} } } } {} .................. ..................
1.3 12 16 12 16 size 12{ { { size 8{"12"} } over { size 8{"16"} } } } {} .................. ..................
1.4 24 30 24 30 size 12{ { { size 8{"24"} } over { size 8{"30"} } } } {} .................. ..................
1.5 48 54 48 54 size 12{ { { size 8{"48"} } over { size 8{"54"} } } } {} .................. ..................

Activity 4:

To use a series of techniques to do calculations [LO 1.10.3]

1. In the previous modules you often rounded off whole numbers. Now we are going to round off mixed numbers to the nearest whole number. Connect the number in column A to the correct answer in column B.

Table 3
  ANumber   BRounded off to the nearest whole number
E.g. 2 8 10 2 8 10 size 12{2 { { size 8{8} } over { size 8{"10"} } } } {} 3
1.1 3 1 6 3 1 6 size 12{3 { { size 8{1} } over { size 8{6} } } } {}   5
1.2 3 5 8 3 5 8 size 12{3 { { size 8{5} } over { size 8{8} } } } {}   2
1.3 4 7 9 4 7 9 size 12{4 { { size 8{7} } over { size 8{9} } } } {}   7
1.4 2 2 5 2 2 5 size 12{2 { { size 8{2} } over { size 8{5} } } } {}   3
1.5 6 1 8 6 1 8 size 12{6 { { size 8{1} } over { size 8{8} } } } {}   4
1.6 7 1 4 7 1 4 size 12{7 { { size 8{1} } over { size 8{4} } } } {}   6

Activity 5:

To calculate through selection and use of suitable computations [LO 1.8.3]

1.1 Now answer the following questions:

a) 15+3515+35 size 12{ { { size 8{1} } over { size 8{5} } } + { { size 8{3} } over { size 8{5} } } } {} = .........................

b) 115+25115+25 size 12{1 { { size 8{1} } over { size 8{5} } } + { { size 8{2} } over { size 8{5} } } } {} = .........................

c) 25+4525+45 size 12{ { { size 8{2} } over { size 8{5} } } + { { size 8{4} } over { size 8{5} } } } {} = .........................

d) 115+15115+15 size 12{1 { { size 8{1} } over { size 8{5} } } + { { size 8{1} } over { size 8{5} } } } {} = .........................

e) Calculate:

23+7923+79 size 12{ { { size 8{2} } over { size 8{3} } } + { { size 8{7} } over { size 8{9} } } } {}; 45+91045+910 size 12{ { { size 8{4} } over { size 8{5} } } + { { size 8{9} } over { size 8{"10"} } } } {}

56+2356+23 size 12{ { { size 8{5} } over { size 8{6} } } + { { size 8{2} } over { size 8{3} } } } {}; 78+3478+34 size 12{ { { size 8{7} } over { size 8{8} } } + { { size 8{3} } over { size 8{4} } } } {}

58+1258+12 size 12{ { { size 8{5} } over { size 8{8} } } + { { size 8{1} } over { size 8{2} } } } {}; 14+5814+58 size 12{ { { size 8{1} } over { size 8{4} } } + { { size 8{5} } over { size 8{8} } } } {}

Activity 6:

To calculate through selection and the use of suitable computations [LO 1.8.3]

To recognise and use equivalent forms of fractions [LO 1.5.1]

To write number sentences in order to describe a problem situation [LO 2.4]

1. Split up into groups of three. Work through the following problems and see if you can find solutions:

a) A farmer transports his fruit to the market by lorry. On arrival he discovers the following: one quarter of the bananas, one eighth of the apples and three eighths of the pears have become spoiled. Which fraction of the fruit could not be off-loaded to be sold at the market?

b) The learners of the Khayelitsha Primary School decided to add some colour to the informal settlement nearby. They painted two fifths of the shacks yellow. Later three tenths of the remaining shacks were painted blue.

i) What fraction of all the shacks was painted?

ii) What fraction still had to be painted?

iii) Which colour would you paint them and why?

c. Mrs Johnny decided to start a soup kitchen in her area.

i) If she gives 5 and seven ninths of the pea soup, and 3 and two thirds of the bean soup to less privileged people on a certain day, what fraction of the soup is eaten altogether on that specific day?

ii) What is your favourite kind of soup?

d. It takes 2 and a half hours to fly from Cape Town to Johannesburg. A flight from Johannesburg to London takes 9 and three quarters of an hour. How long will it take you altogether to fly to London if you depart from Cape Town? Give your answer as a mixed number.

e. Mrs Zuqa makes delicious fruit juices to give to the learners at school during break. She mixes 4 and three quarters of orange juice with 1 and a half litre of pineapple juice. What is the difference between these two quantities?

f. Mrs Sonn helps her friend to bake cakes for the learners. She buys 5 kg of sugar and uses 3 and a third of this quantity. How many kilograms of sugar are left?

2. Your teacher will now ask you to explain one of the above-mentioned problems to the rest of the class.

3. Compare your solutions to those of other groups in the class.

4. Discuss the differences and / or similarities between the different methods that were used.

Assessment

Table 4
Learning outcomes(LOs)
 
LO 1
Numbers, Operations and RelationshipsThe learner is able to recognise, describe and represent numbers and their relationships, and counts, estimates, calculates and checks with competence and confidence in solving problems.
Assessment standards(ASs)
 
We know this when the learner:
1.1 counts forwards and backwards fractions;
1.2 describes and illustrates various ways of writing numbers in different cultures (including local) throughout history;
1.3 recognises and represents the following numbers in order to describe and compare them:
  • common fractions to at least twelfths;
1.5 recognises and uses equivalent forms of the numbers listed above, including:
1.5.1 common fractions with denominators that are multiples of each other;
1.6 solves problems in context including contexts that may be used to build awareness of other Learning Areas, as well as human rights, social, economic and environmental issues such as:
  • financial (including buying and selling, profit and loss, and simple budgets);

Memorandum

ACTIVITY 1

1.

1.1 < 1.2 >

1.3 > 1.4 <

1.5 = 1.6 <

1.7 = 1.8 <

1.9 > 1.10 =

2. 2.1 3434 size 12{ { { size 8{3} } over { size 8{4} } } } {} 2.2 2323 size 12{ { { size 8{2} } over { size 8{3} } } } {}

2.3 910910 size 12{ { { size 8{9} } over { size 8{"10"} } } } {} 2.4 1212 size 12{ { { size 8{1} } over { size 8{2} } } } {}

2.5 1212 size 12{ { { size 8{1} } over { size 8{2} } } } {} 2.6 4545 size 12{ { { size 8{4} } over { size 8{5} } } } {}

CLASS DISCUSSION

First make both nominators the same by finding the smallest common denominator

OR

First simplify the fraction, if you can

3. 3.1 >

3.2 >

3.3 =

3.4 =

4. 4.1 <

4.2 <

4.3 >

4.4 >

Another BRAIN-TEASER!

5656 size 12{ { { size 8{5} } over { size 8{6} } } } {}; 7979 size 12{ { { size 8{7} } over { size 8{9} } } } {}; 2323 size 12{ { { size 8{2} } over { size 8{3} } } } {}; 1212 size 12{ { { size 8{1} } over { size 8{2} } } } {}

ACTIVITY 3

1.

Table 5
1.1 5 5 5 5 size 12{ { { size 8{5} } over { size 8{5} } } } {} 8 9 8 9 size 12{ { { size 8{8} } over { size 8{9} } } } {}
1.2 5 5 5 5 size 12{ { { size 8{5} } over { size 8{5} } } } {} 3 5 3 5 size 12{ { { size 8{3} } over { size 8{5} } } } {}
1.3 4 4 4 4 size 12{ { { size 8{4} } over { size 8{4} } } } {} 3 4 3 4 size 12{ { { size 8{3} } over { size 8{4} } } } {}
1.4 6 6 6 6 size 12{ { { size 8{6} } over { size 8{6} } } } {} 4 5 4 5 size 12{ { { size 8{4} } over { size 8{5} } } } {}
1.5 6 6 6 6 size 12{ { { size 8{6} } over { size 8{6} } } } {} 8 9 8 9 size 12{ { { size 8{8} } over { size 8{9} } } } {}

ACTIVITY 4

1.

  • 3 1616 size 12{ { { size 8{1} } over { size 8{6} } } } {} size 12{ rightarrow } {} 3 1.2 3 5858 size 12{ { { size 8{5} } over { size 8{8} } } } {} size 12{ rightarrow } {} 4

1.3 4 7979 size 12{ { { size 8{7} } over { size 8{9} } } } {} size 12{ rightarrow } {} 5 1.4 2 2525 size 12{ { { size 8{2} } over { size 8{5} } } } {} size 12{ rightarrow } {} 2

1.5 6 1818 size 12{ { { size 8{1} } over { size 8{8} } } } {} size 12{ rightarrow } {} 6 1.6 7 1414 size 12{ { { size 8{1} } over { size 8{4} } } } {} size 12{ rightarrow } {} 7

BRAIN-TEASER!

9

ACTIVITY 5

1.1

a) 4545 size 12{ { { size 8{4} } over { size 8{5} } } } {};

b) 1 3535 size 12{ { { size 8{3} } over { size 8{5} } } } {};

c) 1 1515 size 12{ { { size 8{1} } over { size 8{5} } } } {};

d) 1 2525 size 12{ { { size 8{2} } over { size 8{5} } } } {}

e) (i) 1 4949 size 12{ { { size 8{4} } over { size 8{9} } } } {}

(ii) 1 710710 size 12{ { { size 8{7} } over { size 8{"10"} } } } {}

(iii) 1 1212 size 12{ { { size 8{1} } over { size 8{2} } } } {}

(iv) 1 5858 size 12{ { { size 8{5} } over { size 8{8} } } } {}

(v) 118118 size 12{1 { { size 8{1} } over { size 8{8} } } } {}

(vi) 7878 size 12{ { { size 8{7} } over { size 8{8} } } } {}

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