The concept of ratio and ratios in their simplest form  (Page 3/3)

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:

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: $\frac{6}{\text{30}}$ = $\frac{\text{13}}{a}$ (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:

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

Memorandum

ACTIVITY 1

• :3:4:5
• $\frac{7}{2}$ : $\frac{9}{2}$ = 7:9
• :70:75 = 14:15
• :7 500:500 = 15:1
• :3 000:300 = 10:1

6. 3:7 = x: 2 520 = $\frac{3}{7}$ = $\frac{x}{\text{2520}}$

7 x = 3 × 2 520 x = $\frac{\text{32}\times \text{520}}{7}$

= 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: $\frac{\text{1330}}{\text{2102}}$ = 0,63 / 63,3%

Western Cape: 1000:1220 = $\frac{\text{1000}}{\text{1220}}$ = 0,82 / 81,97% = 82%

• Western Cape
• Own conclusion
• Own conclusion

b)

1.3 VP part of $\frac{3}{8}$ of R100 500,00 = R37 687,50

HMF part of $\frac{5}{8}$ of R100 500 = R62 812,50

Now you can try:

1.1 Zimbabwe: $\frac{\text{1200}}{1\text{.}\text{35}}$ = 888,90

South Africa: $\frac{0\text{.}\text{95}}{\text{135}}$ = 128,30

1.2 $\frac{\text{38}}{\text{73}}$ × $\frac{\text{100}}{1}$ = 52,1% / $\frac{\text{13}}{\text{43}}$ × $\frac{\text{100}}{1}$ = 30,2%

• 375:400 = $\frac{\text{375}}{\text{400}}$ = $\frac{\text{15}}{\text{16}}$ = 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

$\frac{5}{2}$ = $\frac{\text{1250}}{x}$

5 x = 2500

x = R500.00

ACTIVITY 4

• Drives 120 km in 1 hour
• $\frac{\text{120}}{2}$ = 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

$\frac{\text{24}}{7}$ = $\frac{\text{25}\text{.}\text{50}}{x}$

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

$\frac{3\text{.}5}{x}$ = $\frac{5\text{.}2}{\text{29}\text{.}2}$

5,2 x = 102,2

x = 19,7 m

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

Cycle x (less) $\frac{\text{15}}{\text{60}}$ = $\frac{3}{\text{12}}$ = $\frac{1}{4}$ h

5 x = 15 × $\frac{1}{4}$

x = 0,75 h = $\frac{3}{4}$ 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