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2.1. Write down the words "MATHEMATICAL LITERACY GRADE 12 LEARNER NOTES SSIP MATERIAL 2024 TERM 2." (2)

2.2. Write down in centimeters, the width of the king size bed to the width of the super king size bed as a simplified ratio. (2)

2.3. A bed company in South Africa wanted to see if the dimensions are [tex]100\%[/tex] correct and did the calculation below:

Conversion factors:
- 1 ft = 30.48 cm
- 1 inch = 2.54 cm

Calculations:
[tex]\[ (6 \times 30.48) + (3 \times 2.54) = 185.04 + 7.62 = 192.66 \, \text{cm} \][/tex]

192.66 cm is [tex]2.66 \, \text{cm}[/tex] larger than the specified size. Identify the mistake that they have made. (4)

Sagot :

GinnyAnswer
Certainly! Let's go through each part of the question one by one, providing detailed explanations and solutions.

### 2.1. Write down the MATHEMATICAL LITERACY GRADE 12 LEARNER NOTES SSIP MATERIAL 2024 TERM2 words.
This part is straightforward; it involves directly transcribing the given text. Therefore, the answer is:

MATHEMATICAL LITERACY GRADE 12 LEARNER NOTES SSIP MATERIAL 2024 TERM2

### 2.2. Write down in centimeters, the width of the king size to the width of the super king size beds as a simplified ratio.
Given:
- Width of a King Size bed = 180 cm
- Width of a Super King Size bed = 200 cm

To simplify the ratio, we need to find the greatest common divisor (GCD) of the two widths and divide both values by this GCD.

The GCD of 180 and 200 is 20. Thus, we can simplify the ratio as follows:
[tex]\[ \text{Ratio} = \left( \frac{180}{20}, \frac{200}{20} \right) = (9, 10) \][/tex]

Therefore, the simplified ratio of the width of a king size bed to the width of a super king size bed is [tex]\( 9:10 \)[/tex].

### 2.3. Identify the mistake that they have made.

The company provided the following conversion factors and calculations:

[tex]\[ \begin{array}{ll} \text{ft} \ &= 30.48 \ \text{cm} \\ 1 \ \text{inch} \ &= 2.54 \ \text{cm} \\ & \end{array} \][/tex]

Then they calculated the size:

[tex]\[ \text{=(6 × 30.84)+(3 × 2.54)} \\ \text{=185.04 + 7.62} \\ \text{=192.66 \ \text{cm}} \\ \][/tex]

Upon comparing it with the specified size, they found an error of [tex]\(2.66 \ \text{cm} \)[/tex].

Let’s identify the mistake step-by-step:

1. Conversion for feet to centimeters:
[tex]\[ 6 \times 30.48 = 182.88 \ \text{cm} \][/tex]

2. Conversion for inches to centimeters:
[tex]\[ 3 \times 2.54 = 7.62 \ \text{cm} \][/tex]

3. Total Calculated Size:
[tex]\[ 182.88 + 7.62 = 190.5 \ \text{cm} \][/tex]

The total calculated size is 190.5 cm. The company compared this with the specified size of 192.66 cm and should have found the error:

[tex]\[ \text{Error} = 190.5 - 192.66 = -2.16 \ \text{cm} \][/tex]

So, the actual mistake here is that they did not use the correct conversion factor for feet as provided (they used 30.84 cm instead of 30.48 cm per foot). Also, their arithmetic caused a minor discrepancy. The corrected error should be -2.16 cm, indicating their measurement is smaller than required, not larger.

Hence, the mistake identified involves incorrect use of the conversion factor and resultant arithmetic error, leading to a total incorrect comparison error of -2.16 cm.
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