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3. When two different units are compared, in this instance km and hours (h), the answer is given as SPEED (km/h) or RATE.

RATE is always indicated as ……………. / (per) ………………….

4. Try to do the following:

4.1 The Kotzes’ telephone account for July came to R 180,88 for 234 units.

  1. Calculate the cost per unit.
  1. What would the account have been if the Kotzes had used 423 units?

4.2 My car used 45,6 litres of fuel over a distance of 730 km and my sister's car used 48,4 litres over a distance of 662,4 km. Which car uses fuel more economically?

4.3 Pick ‘n Pay sells Omo washing powder in boxes of two different sizes: 1,5 kg for R25,56 and a 2 kg box for R32,44. Which one is the better buy?

Activity 5

Differentiating between a direct proportion and an indirect proportion

[lo 1.5, 3.7, 4.1]

The recipe for success is also important in this exercise.

  • Set up a table.
  • The question is: More-more or less-less? The answer is obtained from your table.

(A): Direct proportion: More-more or less-less as the answer to the question.

[DIVIDE]

(B): Indirect Proportion: More-less or less -more as answer to the question.

[MULTIPLY]

(A): E.g.: 6 chocolate bars cost R55,45. How much will 13 bars cost?

Table:

CHOCOLATE BARS 6 13
COSTS 30 a

Your question: Will 13 chocolate bars cost more or less than R30,00?

Your answer : More.

Therefore: 6 ---- to R30 ->MORE

13 ---- to R a ->MORE

This therefore is direct proportion. “DIVISION”

Solution: 6 30 size 12{ { {6} over {"30"} } } {} = 13 a size 12{ { {"13"} over {a} } } {} (crosswise multiplication)

6 a = 13 x 30

6 a = 390

a = 65

Therefore: 13 chocolate bars cost R65.

(B): 6 men complete a task in 12h. How long will it take 8 men to do the same task?

Table:

MEN 6 8
TIME (H) 12 a

Your question: Will 8 men need more or less time to complete the task?

Your answer: Less.

Therefore: 6 ---- to 12 h ->MORE

8 ---- to a h ->LESS

This is an indirect proportion. “MULTIPLY”

Solution: 6 x 12 = 8 x a

72 = 8 a

9 = a

  • Now do the following. Indicate whether there is a direct or indirect proportion. The steps are given with no. 1, but you will have to do the rest yourself.

1. 2 dozen eggs cost R25,50. What do 7 eggs cost?

Table:

Your question:

Your answer:

Therefore: ---- to ->(more/less)

---- to ->(more/less)

This therefore is “ ”

Solution:

2. A 3,5 m-long stick casts a shadow that measures 5,20 m on the ground What is the height of a flagpole that casts a 29,20 m-long shadow?

3. François of 7th Avenue walks at a speed of 5 km/h and cycles at 15 km/h. If he cycles, he reaches the Coffee Den in 15 minutes. How long does he take when he walks?

4. The woodwork educator can cut 12 mm-long strips of wood of length 190 mm from a single length of wood. How many 250 mm-strips could he cut from the same length of wood?

5. A Boeing 747 of the SAA flies from the Cape Town International Airport to London in 17 hours, at an average speed of 1 200 km/h. What will the average speed be if the time is reduced to 13 hours?

Assessment

LO 3
Space and Form (geometry)The learner is able to describe and represent features of and relationships between two-dimensional forms and three-dimensional objects in a variety of orientations and positions.
We know this when the learner:
3.2 describes and classifies geometric figures and three-dimensional objects in terms of properties in contexts inclusive of those that can be used to promote awareness of social, cultural and environmental issues, including:3.2.1 sides, angles and diagonals and their relationships, focusing on triangles and quadrilaterals (e.g. types of triangles and quadrilaterals);
3.3 uses vocabulary to describe parallel lines that are cut by a transverse, perpendicular or intersection line, as well as triangles, with reference to angular relationships (e.g. vertically opposite, corresponding);3.4 uses a pair of compasses, a ruler and a protractor for accurately constructing geometric figures so that specific properties may be investigated and nets may be designed;3.5 designs and uses nets to make models of geometric three- dimensional objects that have been studied in the preceding grades and up till now;3.7 uses proportion to describe the effect of expansion and reduction on the properties of geometric figures;3.8 draws and interprets sketches of geometric three-dimensional objects from several perspectives, focusing on the retention of properties.
LO 4
MeasuringThe learner is able to use appropriate measuring units, instruments and formulas in a variety of contexts.
We know this when the learner:
4.1 solves more complicated problems involving time, inclusive of the ratio between time, distance and speed;4.2 solves problems involving the following:4.2.1 length;4.2.2 circumference and area of polygons and circles;4.2.3 volume and exterior area of rectangular prisms and cylinders;
4.3 solves problems using a variety of strategies, including:4.3.1 estimation;4.3.2 calculation to at least two decimal points;4.3.3 use and converting between appropriate S.I. units;
4.5 calculates the following with the use of appropriate formulas:4.5.1 circumference of polygons and circles;4.5.2 area of triangles, right angles and polygons by means of splitting up to triangles and right angles;4.5.3 volume of prisms with triangular and rectangular bases and cylinders;
4.7 estimates, compares, measures and draws triangles accurately to within one degree.

Memorandum

ACTIVITY 1

  • :3:4:5
  • 7 2 size 12{ { {7} over {2} } } {} : 9 2 size 12{ { {9} over {2} } } {} = 7:9
  • :70:75 = 14:15
  • :7 500:500 = 15:1
  • :3 000:300 = 10:1

6. 3:7 = x: 2 520 = 3 7 size 12{ { {3} over {7} } } {} = x 2520 size 12{ { {x} over {"2520"} } } {}

7 x = 3 × 2 520 x = 32 × 520 7 size 12{ { {"32" times "520"} over {7} } } {}

= 1 080

  • :1:35

315  35 = 9

  • :23 × 35 = 805
  • :32 – (700  35) = 12
  • :12 × R4 982,55 = R59 790,60

ACTIVITY 2

a)

1.1.1 2000 2003

Gauteng : 1 330 2 102

Western Cape : 1 000 1 220

  • Gauteng: 1330 2102 size 12{ { {"1330"} over {"2102"} } } {} = 0,63 / 63,3%

Western Cape: 1000:1220 = 1000 1220 size 12{ { {"1000"} over {"1220"} } } {} = 0,82 / 81,97% = 82%

  • Western Cape
  • Own conclusion
  • Own conclusion

b)

1.3 VP part of 3 8 size 12{ { {3} over {8} } } {} of R100 500,00 = R37 687,50

HMF part of 5 8 size 12{ { {5} over {8} } } {} of R100 500 = R62 812,50

Now you can try:

1.1 Zimbabwe: 1200 1 . 35 size 12{ { {"1200"} over {1 "." "35"} } } {} = 888,90

South Africa: 0 . 95 135 size 12{ { {0 "." "95"} over {"135"} } } {} = 128,30

1.2 38 73 size 12{ { {"38"} over {"73"} } } {} × 100 1 size 12{ { {"100"%} over {1} } } {} = 52,1% / 13 43 size 12{ { {"13"} over {"43"} } } {} × 100 1 size 12{ { {"100"%} over {1} } } {} = 30,2%

  • 375:400 = 375 400 size 12{ { {"375"} over {"400"} } } {} = 15 16 size 12{ { {"15"} over {"16"} } } {} = 15:16
  • a) 215  15 × 16 = 229
  1. 172  15 × 16 = 183
  2. 370  15 × 16 = 395

ACTIVITY 3

2.1 Ratio 5 (less than) 2

Amount 1 250 (less than) x

5:2 = 1 250: x

5 2 size 12{ { {5} over {2} } } {} = 1250 x size 12{ { {"1250"} over {x} } } {}

5 x = 2500

x = R500.00

ACTIVITY 4

  • Drives 120 km in 1 hour
  • 120 2 size 12{ { {"120"} over {2} } } {} = 60 km/h

4.1 a) 180,88  234 = R0,77/unit

  1. 423 × 0,77 = R325,71
  • 45,6 ℓ = 730 km = 16 km/ℓ

Sister: 48,4ℓ = 662,4 km = 13,69 km/ℓ

  • A: 25,56  1,5 = R17,04/ kg

B : 32,44  2 = R16,22/ kg = Best buy

ACTIVITY 5

1. Table:

dozens (number) 2(24) (less) 7

Price 25,50 (less) x

Therefore: 24 to 7 = less

25,50 to 7,44 = less

It is therefore an indirect

Solution:

24:7 = 25.50: x

24 7 size 12{ { {"24"} over {7} } } {} = 25 . 50 x size 12{ { {"25" "." "50"} over {x} } } {}

24 x = 178,50

x = R7,44

2. Length 3,5 m (more) x

Shadow 5.20 m (more) 29,20 m

3,5: x = 5,2:29,2

3 . 5 x size 12{ { {3 "." 5} over {x} } } {} = 5 . 2 29 . 2 size 12{ { {5 "." 2} over {"29" "." 2} } } {}

5,2 x = 102,2

x = 19,7 m

3. Walk 5 km/h (more) 15 km/h

Cycle x (less) 15 60 size 12{ { {"15"} over {"60"} } } {} = 3 12 size 12{ { {3} over {"12"} } } {} = 1 4 size 12{ { {1} over {4} } } {} h

5 x = 15 × 1 4 size 12{ { {1} over {4} } } {}

x = 0,75 h = 3 4 size 12{ { {3} over {4} } } {} h

4. Pieces 1 2 (less) x

mm 190 (more) 250

12 × 190 = 250 x

9.12 = x

9 pieces

5. Time 17 (less) 13

Speed 1200 (more) x

17 × 1200 = 13 x

1569 km/h = x

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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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