3.2 Selection and computations

Mathematics

Grade 5

Ordinary and decimal fractions

Module 47

Selection and computations

Activity 1:

To calculate through selection and by using suitable computations [lo 1.8.3]

To describe observed relationships and rules in your own words [lo 2.2]

1. Look carefully at the following problems and explain to a friend what your approach would be in calculating the various answers.

1.1 $\frac{7}{8}-\frac{3}{4}$

1.2 $\frac{\text{11}}{\text{12}}-\frac{2}{3}$

1.3 $\frac{5}{6}-\frac{7}{\text{12}}$

1.4 $2\frac{1}{2}-1\frac{9}{\text{10}}$

1.5 $3\frac{1}{5}-1\frac{7}{\text{10}}$

1.6 $4\frac{1}{4}-2\frac{7}{8}$

Now calculate the answers.

2. Check your answers with your friend.

Activity 2:

To calculate through selection and by using suitable computations [lo 1.8.6]

To determine, through comparison and discussion, the equivalence and validity of different representations of the same problem [lo 2.6.2]

To describe observed relationships and rules in your own words [lo 2.2]

1. Sometimes one can use a pie graph to represent fractions. A survey was done of the extramural activities of a Grade 5 class and the results were represented by using a pie graph. See whether you can “read” it, and then complete the table.

2. It is important for us to be able to interpret the pie graph, otherwise we will not be able to make meaningful deductions from it and solve the problems. Work through the following problem with a friend and find out how many methods can be used to solve it.

If there are 50 learners in the class, how many learners play netball?

2.1 The question is $\frac{3}{\text{10}}$ of 50

$\frac{1}{\text{10}}$ of 50 = 5

$\frac{3}{\text{10}}$ of 50 will be 15

2.2 I must calculate $\frac{3}{\text{10}}$ of 50. I find out what $\frac{1}{\text{10}}$ is by dividing 50 by 10.

50 ÷ 10 = 5

If one tenth is 5, then 3 tenths will be 3 × 5. There are thus 15 pupils who play netball.

2.3 Girls = $\frac{3}{\text{10}}$ of 50

Thus: = (50 ÷ 10) × 3

= 5 × 3

= 15

2.4 $\frac{3}{\text{10}}$ of 50 = 3 × $\frac{1}{\text{10}}$ of 50

= 3 × 5

= 15

3. What would you say is the “rule” for these “of” sums?

4. Which of these methods do you prefer?

Why?

5. Look again at the methods at 2.1 and 2.2. What do you notice?

6. Can you say how many learners in Act. 2 participate in:

rugby?_______ ; swimming? _________

7 Now calculate:

7.1 $\frac{7}{\text{12}}$ of 36

7.2 $\frac{5}{8}$ of 32

7.3 $\frac{6}{7}$ of 350

7.4 $\frac{3}{4}$ of 224

Do you still remember?

1 000 m. = 1 litre

1 000 litre = 1 kℓ

1 000 g = 1 kg

1 000 kg = 1 t

1 000 mm = 1 m

1 000 m = 1 km

Activity 3:

To calculate through selection and by using suitable computations [lo 1.8.6]

1. Let us see whether you are able to successfully apply the knowledge that you have acquired up to now. Work on your own and calculate:

1.1 Five learners share 1 litre of cool drink equally. How many m $\ell$ does each learner get?

1.2 Zane lives 2 km from the school. He has already covered $\frac{3}{4}$ of the distance. How far has he walked? (Give your answer in m).

1.3 The mass of a bag of flour is 1 kg. Mom needs $\frac{3}{\text{10}}$ of this to bake a cake. How much flour will she use?

1.4 Joy buys 3 m of material but only uses $\frac{1}{6}$ of this to make a dress.

What fraction of material is left over?

How much material is left over?

Activity 4:

• To use tables and graphs to arrange and record data [LO 5.3]
• To draw and interpret a graph [LO 5.5.1]